diff --git a/CMakeLists.txt b/CMakeLists.txt
index 4b9c3dd6f0b6df7d24de6c1d651f7b82ed7f4940..74ae1598f81c6b6fc6708c1ba0474e34acf8a199 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -100,9 +100,9 @@ if (WIN32) # TODO(nick) Should do based upon compiler (VS)
set(CMAKE_CXX_FLAGS_RELEASE "/O2")
else()
add_definitions(-DUNIX)
- set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++17")
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++17 -msse3")
set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -D_DEBUG -pg -Wall")
- set(CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE} -O3 -msse3 -mfpmath=sse")
+ set(CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE} -O3 -mfpmath=sse")
endif()
SET(CMAKE_USE_RELATIVE_PATHS ON)
diff --git a/cv-node/CMakeLists.txt b/cv-node/CMakeLists.txt
index 392520d3466257c9546a752ccc368cb5d9aca2aa..ef5221d0fd5c7e33ec08943cdc83e619ea9b1679 100644
--- a/cv-node/CMakeLists.txt
+++ b/cv-node/CMakeLists.txt
@@ -2,6 +2,8 @@
include_directories(${PROJECT_SOURCE_DIR}/cv-node/include)
#include_directories(${PROJECT_BINARY_DIR})
+add_subdirectory(lib)
+
# Check for optional opencv components
set(CMAKE_REQUIRED_INCLUDES ${OpenCV_INCLUDE_DIRS})
check_include_file_cxx("opencv2/viz.hpp" HAVE_VIZ)
diff --git a/cv-node/include/elas.h b/cv-node/include/elas.h
new file mode 100644
index 0000000000000000000000000000000000000000..a88439e6a1d0d42c37d14fda8ef13b4f6fe3ec30
--- /dev/null
+++ b/cv-node/include/elas.h
@@ -0,0 +1,236 @@
+/*
+Copyright 2011. All rights reserved.
+Institute of Measurement and Control Systems
+Karlsruhe Institute of Technology, Germany
+
+This file is part of libelas.
+Authors: Andreas Geiger
+
+libelas is free software; you can redistribute it and/or modify it under the
+terms of the GNU General Public License as published by the Free Software
+Foundation; either version 3 of the License, or any later version.
+
+libelas is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+libelas; if not, write to the Free Software Foundation, Inc., 51 Franklin
+Street, Fifth Floor, Boston, MA 02110-1301, USA
+*/
+
+// Main header file. Include this to use libelas in your code.
+
+#ifndef __ELAS_H__
+#define __ELAS_H__
+
+#include <iostream>
+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+#include <vector>
+#include <emmintrin.h>
+
+// define fixed-width datatypes for Visual Studio projects
+#ifndef _MSC_VER
+ #include <stdint.h>
+#else
+ typedef __int8 int8_t;
+ typedef __int16 int16_t;
+ typedef __int32 int32_t;
+ typedef __int64 int64_t;
+ typedef unsigned __int8 uint8_t;
+ typedef unsigned __int16 uint16_t;
+ typedef unsigned __int32 uint32_t;
+ typedef unsigned __int64 uint64_t;
+#endif
+
+#ifdef PROFILE
+#include "timer.h"
+#endif
+
+class Elas {
+
+public:
+
+ enum setting {ROBOTICS,MIDDLEBURY};
+
+ // parameter settings
+ struct parameters {
+ int32_t disp_min; // min disparity
+ int32_t disp_max; // max disparity
+ float support_threshold; // max. uniqueness ratio (best vs. second best support match)
+ int32_t support_texture; // min texture for support points
+ int32_t candidate_stepsize; // step size of regular grid on which support points are matched
+ int32_t incon_window_size; // window size of inconsistent support point check
+ int32_t incon_threshold; // disparity similarity threshold for support point to be considered consistent
+ int32_t incon_min_support; // minimum number of consistent support points
+ bool add_corners; // add support points at image corners with nearest neighbor disparities
+ int32_t grid_size; // size of neighborhood for additional support point extrapolation
+ float beta; // image likelihood parameter
+ float gamma; // prior constant
+ float sigma; // prior sigma
+ float sradius; // prior sigma radius
+ int32_t match_texture; // min texture for dense matching
+ int32_t lr_threshold; // disparity threshold for left/right consistency check
+ float speckle_sim_threshold; // similarity threshold for speckle segmentation
+ int32_t speckle_size; // maximal size of a speckle (small speckles get removed)
+ int32_t ipol_gap_width; // interpolate small gaps (left<->right, top<->bottom)
+ bool filter_median; // optional median filter (approximated)
+ bool filter_adaptive_mean; // optional adaptive mean filter (approximated)
+ bool postprocess_only_left; // saves time by not postprocessing the right image
+ bool subsampling; // saves time by only computing disparities for each 2nd pixel
+ // note: for this option D1 and D2 must be passed with size
+ // width/2 x height/2 (rounded towards zero)
+
+ // constructor
+ parameters (setting s=ROBOTICS) {
+
+ // default settings in a robotics environment
+ // (do not produce results in half-occluded areas
+ // and are a bit more robust towards lighting etc.)
+ if (s==ROBOTICS) {
+ disp_min = 0;
+ disp_max = 255;
+ support_threshold = 0.85;
+ support_texture = 10;
+ candidate_stepsize = 5;
+ incon_window_size = 5;
+ incon_threshold = 5;
+ incon_min_support = 5;
+ add_corners = 0;
+ grid_size = 20;
+ beta = 0.02;
+ gamma = 3;
+ sigma = 1;
+ sradius = 2;
+ match_texture = 1;
+ lr_threshold = 2;
+ speckle_sim_threshold = 1;
+ speckle_size = 200;
+ ipol_gap_width = 3;
+ filter_median = 0;
+ filter_adaptive_mean = 1;
+ postprocess_only_left = 1;
+ subsampling = 0;
+
+ // default settings for middlebury benchmark
+ // (interpolate all missing disparities)
+ } else {
+ disp_min = 0;
+ disp_max = 255;
+ support_threshold = 0.95;
+ support_texture = 10;
+ candidate_stepsize = 5;
+ incon_window_size = 5;
+ incon_threshold = 5;
+ incon_min_support = 5;
+ add_corners = 1;
+ grid_size = 20;
+ beta = 0.02;
+ gamma = 5;
+ sigma = 1;
+ sradius = 3;
+ match_texture = 0;
+ lr_threshold = 2;
+ speckle_sim_threshold = 1;
+ speckle_size = 200;
+ ipol_gap_width = 5000;
+ filter_median = 1;
+ filter_adaptive_mean = 0;
+ postprocess_only_left = 0;
+ subsampling = 0;
+ }
+ }
+ };
+
+ // constructor, input: parameters
+ Elas (parameters param) : param(param) {}
+
+ // deconstructor
+ ~Elas () {}
+
+ // matching function
+ // inputs: pointers to left (I1) and right (I2) intensity image (uint8, input)
+ // pointers to left (D1) and right (D2) disparity image (float, output)
+ // dims[0] = width of I1 and I2
+ // dims[1] = height of I1 and I2
+ // dims[2] = bytes per line (often equal to width, but allowed to differ)
+ // note: D1 and D2 must be allocated before (bytes per line = width)
+ // if subsampling is not active their size is width x height,
+ // otherwise width/2 x height/2 (rounded towards zero)
+ void process (uint8_t* I1,uint8_t* I2,float* D1,float* D2,const int32_t* dims);
+
+private:
+
+ struct support_pt {
+ int32_t u;
+ int32_t v;
+ int32_t d;
+ support_pt(int32_t u,int32_t v,int32_t d):u(u),v(v),d(d){}
+ };
+
+ struct triangle {
+ int32_t c1,c2,c3;
+ float t1a,t1b,t1c;
+ float t2a,t2b,t2c;
+ triangle(int32_t c1,int32_t c2,int32_t c3):c1(c1),c2(c2),c3(c3){}
+ };
+
+ inline uint32_t getAddressOffsetImage (const int32_t& u,const int32_t& v,const int32_t& width) {
+ return v*width+u;
+ }
+
+ inline uint32_t getAddressOffsetGrid (const int32_t& x,const int32_t& y,const int32_t& d,const int32_t& width,const int32_t& disp_num) {
+ return (y*width+x)*disp_num+d;
+ }
+
+ // support point functions
+ void removeInconsistentSupportPoints (int16_t* D_can,int32_t D_can_width,int32_t D_can_height);
+ void removeRedundantSupportPoints (int16_t* D_can,int32_t D_can_width,int32_t D_can_height,
+ int32_t redun_max_dist, int32_t redun_threshold, bool vertical);
+ void addCornerSupportPoints (std::vector<support_pt> &p_support);
+ inline int16_t computeMatchingDisparity (const int32_t &u,const int32_t &v,uint8_t* I1_desc,uint8_t* I2_desc,const bool &right_image);
+ std::vector<support_pt> computeSupportMatches (uint8_t* I1_desc,uint8_t* I2_desc);
+
+ // triangulation & grid
+ std::vector<triangle> computeDelaunayTriangulation (std::vector<support_pt> p_support,int32_t right_image);
+ void computeDisparityPlanes (std::vector<support_pt> p_support,std::vector<triangle> &tri,int32_t right_image);
+ void createGrid (std::vector<support_pt> p_support,int32_t* disparity_grid,int32_t* grid_dims,bool right_image);
+
+ // matching
+ inline void updatePosteriorMinimum (__m128i* I2_block_addr,const int32_t &d,const int32_t &w,
+ const __m128i &xmm1,__m128i &xmm2,int32_t &val,int32_t &min_val,int32_t &min_d);
+ inline void updatePosteriorMinimum (__m128i* I2_block_addr,const int32_t &d,
+ const __m128i &xmm1,__m128i &xmm2,int32_t &val,int32_t &min_val,int32_t &min_d);
+ inline void findMatch (int32_t &u,int32_t &v,float &plane_a,float &plane_b,float &plane_c,
+ int32_t* disparity_grid,int32_t *grid_dims,uint8_t* I1_desc,uint8_t* I2_desc,
+ int32_t *P,int32_t &plane_radius,bool &valid,bool &right_image,float* D);
+ void computeDisparity (std::vector<support_pt> p_support,std::vector<triangle> tri,int32_t* disparity_grid,int32_t* grid_dims,
+ uint8_t* I1_desc,uint8_t* I2_desc,bool right_image,float* D);
+
+ // L/R consistency check
+ void leftRightConsistencyCheck (float* D1,float* D2);
+
+ // postprocessing
+ void removeSmallSegments (float* D);
+ void gapInterpolation (float* D);
+
+ // optional postprocessing
+ void adaptiveMean (float* D);
+ void median (float* D);
+
+ // parameter set
+ parameters param;
+
+ // memory aligned input images + dimensions
+ uint8_t *I1,*I2;
+ int32_t width,height,bpl;
+
+ // profiling timer
+#ifdef PROFILE
+ Timer timer;
+#endif
+};
+
+#endif
diff --git a/cv-node/lib/CMakeLists.txt b/cv-node/lib/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6525db95dddf47fafa28434674119602f8f933ff
--- /dev/null
+++ b/cv-node/lib/CMakeLists.txt
@@ -0,0 +1,13 @@
+
+### Lib ELAS ###################################################################
+
+# directories
+set (LIBELAS_SRC_DIR elas)
+# sources
+FILE(GLOB LIBELAS_SRC_FILES "elas/*.cpp")
+
+add_library(libelas ${LIBELAS_SRC_FILES})
+target_include_directories(libelas
+ PRIVATE elas)
+
+
diff --git a/cv-node/lib/elas/descriptor.cpp b/cv-node/lib/elas/descriptor.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..6420afd43f10f217205232ec0653a0a903686e1a
--- /dev/null
+++ b/cv-node/lib/elas/descriptor.cpp
@@ -0,0 +1,114 @@
+/*
+Copyright 2011. All rights reserved.
+Institute of Measurement and Control Systems
+Karlsruhe Institute of Technology, Germany
+
+This file is part of libelas.
+Authors: Andreas Geiger
+
+libelas is free software; you can redistribute it and/or modify it under the
+terms of the GNU General Public License as published by the Free Software
+Foundation; either version 3 of the License, or any later version.
+
+libelas is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+libelas; if not, write to the Free Software Foundation, Inc., 51 Franklin
+Street, Fifth Floor, Boston, MA 02110-1301, USA
+*/
+
+#include "descriptor.h"
+#include "filter.h"
+#include <emmintrin.h>
+
+using namespace std;
+
+Descriptor::Descriptor(uint8_t* I,int32_t width,int32_t height,int32_t bpl,bool half_resolution) {
+ I_desc = (uint8_t*)_mm_malloc(16*width*height*sizeof(uint8_t),16);
+ uint8_t* I_du = (uint8_t*)_mm_malloc(bpl*height*sizeof(uint8_t),16);
+ uint8_t* I_dv = (uint8_t*)_mm_malloc(bpl*height*sizeof(uint8_t),16);
+ filter::sobel3x3(I,I_du,I_dv,bpl,height);
+ createDescriptor(I_du,I_dv,width,height,bpl,half_resolution);
+ _mm_free(I_du);
+ _mm_free(I_dv);
+}
+
+Descriptor::~Descriptor() {
+ _mm_free(I_desc);
+}
+
+void Descriptor::createDescriptor (uint8_t* I_du,uint8_t* I_dv,int32_t width,int32_t height,int32_t bpl,bool half_resolution) {
+
+ uint8_t *I_desc_curr;
+ uint32_t addr_v0,addr_v1,addr_v2,addr_v3,addr_v4;
+
+ // do not compute every second line
+ if (half_resolution) {
+
+ // create filter strip
+ for (int32_t v=4; v<height-3; v+=2) {
+
+ addr_v2 = v*bpl;
+ addr_v0 = addr_v2-2*bpl;
+ addr_v1 = addr_v2-1*bpl;
+ addr_v3 = addr_v2+1*bpl;
+ addr_v4 = addr_v2+2*bpl;
+
+ for (int32_t u=3; u<width-3; u++) {
+ I_desc_curr = I_desc+(v*width+u)*16;
+ *(I_desc_curr++) = *(I_du+addr_v0+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v1+u-2);
+ *(I_desc_curr++) = *(I_du+addr_v1+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v1+u+2);
+ *(I_desc_curr++) = *(I_du+addr_v2+u-1);
+ *(I_desc_curr++) = *(I_du+addr_v2+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v2+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v2+u+1);
+ *(I_desc_curr++) = *(I_du+addr_v3+u-2);
+ *(I_desc_curr++) = *(I_du+addr_v3+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v3+u+2);
+ *(I_desc_curr++) = *(I_du+addr_v4+u+0);
+ *(I_desc_curr++) = *(I_dv+addr_v1+u+0);
+ *(I_desc_curr++) = *(I_dv+addr_v2+u-1);
+ *(I_desc_curr++) = *(I_dv+addr_v2+u+1);
+ *(I_desc_curr++) = *(I_dv+addr_v3+u+0);
+ }
+ }
+
+ // compute full descriptor images
+ } else {
+
+ // create filter strip
+ for (int32_t v=3; v<height-3; v++) {
+
+ addr_v2 = v*bpl;
+ addr_v0 = addr_v2-2*bpl;
+ addr_v1 = addr_v2-1*bpl;
+ addr_v3 = addr_v2+1*bpl;
+ addr_v4 = addr_v2+2*bpl;
+
+ for (int32_t u=3; u<width-3; u++) {
+ I_desc_curr = I_desc+(v*width+u)*16;
+ *(I_desc_curr++) = *(I_du+addr_v0+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v1+u-2);
+ *(I_desc_curr++) = *(I_du+addr_v1+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v1+u+2);
+ *(I_desc_curr++) = *(I_du+addr_v2+u-1);
+ *(I_desc_curr++) = *(I_du+addr_v2+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v2+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v2+u+1);
+ *(I_desc_curr++) = *(I_du+addr_v3+u-2);
+ *(I_desc_curr++) = *(I_du+addr_v3+u+0);
+ *(I_desc_curr++) = *(I_du+addr_v3+u+2);
+ *(I_desc_curr++) = *(I_du+addr_v4+u+0);
+ *(I_desc_curr++) = *(I_dv+addr_v1+u+0);
+ *(I_desc_curr++) = *(I_dv+addr_v2+u-1);
+ *(I_desc_curr++) = *(I_dv+addr_v2+u+1);
+ *(I_desc_curr++) = *(I_dv+addr_v3+u+0);
+ }
+ }
+ }
+
+}
diff --git a/cv-node/lib/elas/descriptor.h b/cv-node/lib/elas/descriptor.h
new file mode 100644
index 0000000000000000000000000000000000000000..7abb0e718de3bd5988a1075ee127ca1d689a7e63
--- /dev/null
+++ b/cv-node/lib/elas/descriptor.h
@@ -0,0 +1,69 @@
+/*
+Copyright 2011. All rights reserved.
+Institute of Measurement and Control Systems
+Karlsruhe Institute of Technology, Germany
+
+This file is part of libelas.
+Authors: Andreas Geiger
+
+libelas is free software; you can redistribute it and/or modify it under the
+terms of the GNU General Public License as published by the Free Software
+Foundation; either version 3 of the License, or any later version.
+
+libelas is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+libelas; if not, write to the Free Software Foundation, Inc., 51 Franklin
+Street, Fifth Floor, Boston, MA 02110-1301, USA
+*/
+
+// NOTE: This descripter is a sparse approximation to the 50-dimensional
+// descriptor described in the paper. It produces similar results, but
+// is faster to compute.
+
+#ifndef __DESCRIPTOR_H__
+#define __DESCRIPTOR_H__
+
+#include <iostream>
+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+#include <math.h>
+
+// Define fixed-width datatypes for Visual Studio projects
+#ifndef _MSC_VER
+ #include <stdint.h>
+#else
+ typedef __int8 int8_t;
+ typedef __int16 int16_t;
+ typedef __int32 int32_t;
+ typedef __int64 int64_t;
+ typedef unsigned __int8 uint8_t;
+ typedef unsigned __int16 uint16_t;
+ typedef unsigned __int32 uint32_t;
+ typedef unsigned __int64 uint64_t;
+#endif
+
+class Descriptor {
+
+public:
+
+ // constructor creates filters
+ Descriptor(uint8_t* I,int32_t width,int32_t height,int32_t bpl,bool half_resolution);
+
+ // deconstructor releases memory
+ ~Descriptor();
+
+ // descriptors accessible from outside
+ uint8_t* I_desc;
+
+private:
+
+ // build descriptor I_desc from I_du and I_dv
+ void createDescriptor(uint8_t* I_du,uint8_t* I_dv,int32_t width,int32_t height,int32_t bpl,bool half_resolution);
+
+};
+
+#endif
diff --git a/cv-node/lib/elas/elas.cpp b/cv-node/lib/elas/elas.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..bddf239f142929337c7ab69680585af0a3951c1a
--- /dev/null
+++ b/cv-node/lib/elas/elas.cpp
@@ -0,0 +1,1560 @@
+/*
+Copyright 2011. All rights reserved.
+Institute of Measurement and Control Systems
+Karlsruhe Institute of Technology, Germany
+
+This file is part of libelas.
+Authors: Andreas Geiger
+
+libelas is free software; you can redistribute it and/or modify it under the
+terms of the GNU General Public License as published by the Free Software
+Foundation; either version 3 of the License, or any later version.
+
+libelas is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+libelas; if not, write to the Free Software Foundation, Inc., 51 Franklin
+Street, Fifth Floor, Boston, MA 02110-1301, USA
+*/
+
+#include "elas.h"
+
+#include <algorithm>
+#include <math.h>
+#include "descriptor.h"
+#include "triangle.h"
+#include "matrix.h"
+
+using namespace std;
+
+void Elas::process (uint8_t* I1_,uint8_t* I2_,float* D1,float* D2,const int32_t* dims){
+
+ // get width, height and bytes per line
+ width = dims[0];
+ height = dims[1];
+ bpl = width + 15-(width-1)%16;
+
+ // copy images to byte aligned memory
+ I1 = (uint8_t*)_mm_malloc(bpl*height*sizeof(uint8_t),16);
+ I2 = (uint8_t*)_mm_malloc(bpl*height*sizeof(uint8_t),16);
+ memset (I1,0,bpl*height*sizeof(uint8_t));
+ memset (I2,0,bpl*height*sizeof(uint8_t));
+ if (bpl==dims[2]) {
+ memcpy(I1,I1_,bpl*height*sizeof(uint8_t));
+ memcpy(I2,I2_,bpl*height*sizeof(uint8_t));
+ } else {
+ for (int32_t v=0; v<height; v++) {
+ memcpy(I1+v*bpl,I1_+v*dims[2],width*sizeof(uint8_t));
+ memcpy(I2+v*bpl,I2_+v*dims[2],width*sizeof(uint8_t));
+ }
+ }
+
+#ifdef PROFILE
+ timer.start("Descriptor");
+#endif
+ Descriptor desc1(I1,width,height,bpl,param.subsampling);
+ Descriptor desc2(I2,width,height,bpl,param.subsampling);
+
+#ifdef PROFILE
+ timer.start("Support Matches");
+#endif
+ vector<support_pt> p_support = computeSupportMatches(desc1.I_desc,desc2.I_desc);
+
+ // if not enough support points for triangulation
+ if (p_support.size()<3) {
+ cout << "ERROR: Need at least 3 support points!" << endl;
+ _mm_free(I1);
+ _mm_free(I2);
+ return;
+ }
+
+#ifdef PROFILE
+ timer.start("Delaunay Triangulation");
+#endif
+ vector<triangle> tri_1 = computeDelaunayTriangulation(p_support,0);
+ vector<triangle> tri_2 = computeDelaunayTriangulation(p_support,1);
+
+#ifdef PROFILE
+ timer.start("Disparity Planes");
+#endif
+ computeDisparityPlanes(p_support,tri_1,0);
+ computeDisparityPlanes(p_support,tri_2,1);
+
+#ifdef PROFILE
+ timer.start("Grid");
+#endif
+
+ // allocate memory for disparity grid
+ int32_t grid_width = (int32_t)ceil((float)width/(float)param.grid_size);
+ int32_t grid_height = (int32_t)ceil((float)height/(float)param.grid_size);
+ int32_t grid_dims[3] = {param.disp_max+2,grid_width,grid_height};
+ int32_t* disparity_grid_1 = (int32_t*)calloc((param.disp_max+2)*grid_height*grid_width,sizeof(int32_t));
+ int32_t* disparity_grid_2 = (int32_t*)calloc((param.disp_max+2)*grid_height*grid_width,sizeof(int32_t));
+
+ createGrid(p_support,disparity_grid_1,grid_dims,0);
+ createGrid(p_support,disparity_grid_2,grid_dims,1);
+
+#ifdef PROFILE
+ timer.start("Matching");
+#endif
+ computeDisparity(p_support,tri_1,disparity_grid_1,grid_dims,desc1.I_desc,desc2.I_desc,0,D1);
+ computeDisparity(p_support,tri_2,disparity_grid_2,grid_dims,desc1.I_desc,desc2.I_desc,1,D2);
+
+#ifdef PROFILE
+ timer.start("L/R Consistency Check");
+#endif
+ leftRightConsistencyCheck(D1,D2);
+
+#ifdef PROFILE
+ timer.start("Remove Small Segments");
+#endif
+ removeSmallSegments(D1);
+ if (!param.postprocess_only_left)
+ removeSmallSegments(D2);
+
+#ifdef PROFILE
+ timer.start("Gap Interpolation");
+#endif
+ gapInterpolation(D1);
+ if (!param.postprocess_only_left)
+ gapInterpolation(D2);
+
+ if (param.filter_adaptive_mean) {
+#ifdef PROFILE
+ timer.start("Adaptive Mean");
+#endif
+ adaptiveMean(D1);
+ if (!param.postprocess_only_left)
+ adaptiveMean(D2);
+ }
+
+ if (param.filter_median) {
+#ifdef PROFILE
+ timer.start("Median");
+#endif
+ median(D1);
+ if (!param.postprocess_only_left)
+ median(D2);
+ }
+
+#ifdef PROFILE
+ timer.plot();
+#endif
+
+ // release memory
+ free(disparity_grid_1);
+ free(disparity_grid_2);
+ _mm_free(I1);
+ _mm_free(I2);
+}
+
+void Elas::removeInconsistentSupportPoints (int16_t* D_can,int32_t D_can_width,int32_t D_can_height) {
+
+ // for all valid support points do
+ for (int32_t u_can=0; u_can<D_can_width; u_can++) {
+ for (int32_t v_can=0; v_can<D_can_height; v_can++) {
+ int16_t d_can = *(D_can+getAddressOffsetImage(u_can,v_can,D_can_width));
+ if (d_can>=0) {
+
+ // compute number of other points supporting the current point
+ int32_t support = 0;
+ for (int32_t u_can_2=u_can-param.incon_window_size; u_can_2<=u_can+param.incon_window_size; u_can_2++) {
+ for (int32_t v_can_2=v_can-param.incon_window_size; v_can_2<=v_can+param.incon_window_size; v_can_2++) {
+ if (u_can_2>=0 && v_can_2>=0 && u_can_2<D_can_width && v_can_2<D_can_height) {
+ int16_t d_can_2 = *(D_can+getAddressOffsetImage(u_can_2,v_can_2,D_can_width));
+ if (d_can_2>=0 && abs(d_can-d_can_2)<=param.incon_threshold)
+ support++;
+ }
+ }
+ }
+
+ // invalidate support point if number of supporting points is too low
+ if (support<param.incon_min_support)
+ *(D_can+getAddressOffsetImage(u_can,v_can,D_can_width)) = -1;
+ }
+ }
+ }
+}
+
+void Elas::removeRedundantSupportPoints(int16_t* D_can,int32_t D_can_width,int32_t D_can_height,
+ int32_t redun_max_dist, int32_t redun_threshold, bool vertical) {
+
+ // parameters
+ int32_t redun_dir_u[2] = {0,0};
+ int32_t redun_dir_v[2] = {0,0};
+ if (vertical) {
+ redun_dir_v[0] = -1;
+ redun_dir_v[1] = +1;
+ } else {
+ redun_dir_u[0] = -1;
+ redun_dir_u[1] = +1;
+ }
+
+ // for all valid support points do
+ for (int32_t u_can=0; u_can<D_can_width; u_can++) {
+ for (int32_t v_can=0; v_can<D_can_height; v_can++) {
+ int16_t d_can = *(D_can+getAddressOffsetImage(u_can,v_can,D_can_width));
+ if (d_can>=0) {
+
+ // check all directions for redundancy
+ bool redundant = true;
+ for (int32_t i=0; i<2; i++) {
+
+ // search for support
+ int32_t u_can_2 = u_can;
+ int32_t v_can_2 = v_can;
+ int16_t d_can_2;
+ bool support = false;
+ for (int32_t j=0; j<redun_max_dist; j++) {
+ u_can_2 += redun_dir_u[i];
+ v_can_2 += redun_dir_v[i];
+ if (u_can_2<0 || v_can_2<0 || u_can_2>=D_can_width || v_can_2>=D_can_height)
+ break;
+ d_can_2 = *(D_can+getAddressOffsetImage(u_can_2,v_can_2,D_can_width));
+ if (d_can_2>=0 && abs(d_can-d_can_2)<=redun_threshold) {
+ support = true;
+ break;
+ }
+ }
+
+ // if we have no support => point is not redundant
+ if (!support) {
+ redundant = false;
+ break;
+ }
+ }
+
+ // invalidate support point if it is redundant
+ if (redundant)
+ *(D_can+getAddressOffsetImage(u_can,v_can,D_can_width)) = -1;
+ }
+ }
+ }
+}
+
+void Elas::addCornerSupportPoints(vector<support_pt> &p_support) {
+
+ // list of border points
+ vector<support_pt> p_border;
+ p_border.push_back(support_pt(0,0,0));
+ p_border.push_back(support_pt(0,height-1,0));
+ p_border.push_back(support_pt(width-1,0,0));
+ p_border.push_back(support_pt(width-1,height-1,0));
+
+ // find closest d
+ for (int32_t i=0; i<p_border.size(); i++) {
+ int32_t best_dist = 10000000;
+ for (int32_t j=0; j<p_support.size(); j++) {
+ int32_t du = p_border[i].u-p_support[j].u;
+ int32_t dv = p_border[i].v-p_support[j].v;
+ int32_t curr_dist = du*du+dv*dv;
+ if (curr_dist<best_dist) {
+ best_dist = curr_dist;
+ p_border[i].d = p_support[j].d;
+ }
+ }
+ }
+
+ // for right image
+ p_border.push_back(support_pt(p_border[2].u+p_border[2].d,p_border[2].v,p_border[2].d));
+ p_border.push_back(support_pt(p_border[3].u+p_border[3].d,p_border[3].v,p_border[3].d));
+
+ // add border points to support points
+ for (int32_t i=0; i<p_border.size(); i++)
+ p_support.push_back(p_border[i]);
+}
+
+inline int16_t Elas::computeMatchingDisparity (const int32_t &u,const int32_t &v,uint8_t* I1_desc,uint8_t* I2_desc,const bool &right_image) {
+
+ const int32_t u_step = 2;
+ const int32_t v_step = 2;
+ const int32_t window_size = 3;
+
+ int32_t desc_offset_1 = -16*u_step-16*width*v_step;
+ int32_t desc_offset_2 = +16*u_step-16*width*v_step;
+ int32_t desc_offset_3 = -16*u_step+16*width*v_step;
+ int32_t desc_offset_4 = +16*u_step+16*width*v_step;
+
+ __m128i xmm1,xmm2,xmm3,xmm4,xmm5,xmm6;
+
+ // check if we are inside the image region
+ if (u>=window_size+u_step && u<=width-window_size-1-u_step && v>=window_size+v_step && v<=height-window_size-1-v_step) {
+
+ // compute desc and start addresses
+ int32_t line_offset = 16*width*v;
+ uint8_t *I1_line_addr,*I2_line_addr;
+ if (!right_image) {
+ I1_line_addr = I1_desc+line_offset;
+ I2_line_addr = I2_desc+line_offset;
+ } else {
+ I1_line_addr = I2_desc+line_offset;
+ I2_line_addr = I1_desc+line_offset;
+ }
+
+ // compute I1 block start addresses
+ uint8_t* I1_block_addr = I1_line_addr+16*u;
+ uint8_t* I2_block_addr;
+
+ // we require at least some texture
+ int32_t sum = 0;
+ for (int32_t i=0; i<16; i++)
+ sum += abs((int32_t)(*(I1_block_addr+i))-128);
+ if (sum<param.support_texture)
+ return -1;
+
+ // load first blocks to xmm registers
+ xmm1 = _mm_load_si128((__m128i*)(I1_block_addr+desc_offset_1));
+ xmm2 = _mm_load_si128((__m128i*)(I1_block_addr+desc_offset_2));
+ xmm3 = _mm_load_si128((__m128i*)(I1_block_addr+desc_offset_3));
+ xmm4 = _mm_load_si128((__m128i*)(I1_block_addr+desc_offset_4));
+
+ // declare match energy for each disparity
+ int32_t u_warp;
+
+ // best match
+ int16_t min_1_E = 32767;
+ int16_t min_1_d = -1;
+ int16_t min_2_E = 32767;
+ int16_t min_2_d = -1;
+
+ // get valid disparity range
+ int32_t disp_min_valid = max(param.disp_min,0);
+ int32_t disp_max_valid = param.disp_max;
+ if (!right_image) disp_max_valid = min(param.disp_max,u-window_size-u_step);
+ else disp_max_valid = min(param.disp_max,width-u-window_size-u_step);
+
+ // assume, that we can compute at least 10 disparities for this pixel
+ if (disp_max_valid-disp_min_valid<10)
+ return -1;
+
+ // for all disparities do
+ for (int16_t d=disp_min_valid; d<=disp_max_valid; d++) {
+
+ // warp u coordinate
+ if (!right_image) u_warp = u-d;
+ else u_warp = u+d;
+
+ // compute I2 block start addresses
+ I2_block_addr = I2_line_addr+16*u_warp;
+
+ // compute match energy at this disparity
+ xmm6 = _mm_load_si128((__m128i*)(I2_block_addr+desc_offset_1));
+ xmm6 = _mm_sad_epu8(xmm1,xmm6);
+ xmm5 = _mm_load_si128((__m128i*)(I2_block_addr+desc_offset_2));
+ xmm6 = _mm_add_epi16(_mm_sad_epu8(xmm2,xmm5),xmm6);
+ xmm5 = _mm_load_si128((__m128i*)(I2_block_addr+desc_offset_3));
+ xmm6 = _mm_add_epi16(_mm_sad_epu8(xmm3,xmm5),xmm6);
+ xmm5 = _mm_load_si128((__m128i*)(I2_block_addr+desc_offset_4));
+ xmm6 = _mm_add_epi16(_mm_sad_epu8(xmm4,xmm5),xmm6);
+ sum = _mm_extract_epi16(xmm6,0)+_mm_extract_epi16(xmm6,4);
+
+ // best + second best match
+ if (sum<min_1_E) {
+ min_2_E = min_1_E;
+ min_2_d = min_1_d;
+ min_1_E = sum;
+ min_1_d = d;
+ } else if (sum<min_2_E) {
+ min_2_E = sum;
+ min_2_d = d;
+ }
+ }
+
+ // check if best and second best match are available and if matching ratio is sufficient
+ if (min_1_d>=0 && min_2_d>=0 && (float)min_1_E<param.support_threshold*(float)min_2_E)
+ return min_1_d;
+ else
+ return -1;
+
+ } else
+ return -1;
+}
+
+vector<Elas::support_pt> Elas::computeSupportMatches (uint8_t* I1_desc,uint8_t* I2_desc) {
+
+ // be sure that at half resolution we only need data
+ // from every second line!
+ int32_t D_candidate_stepsize = param.candidate_stepsize;
+ if (param.subsampling)
+ D_candidate_stepsize += D_candidate_stepsize%2;
+
+ // create matrix for saving disparity candidates
+ int32_t D_can_width = 0;
+ int32_t D_can_height = 0;
+ for (int32_t u=0; u<width; u+=D_candidate_stepsize) D_can_width++;
+ for (int32_t v=0; v<height; v+=D_candidate_stepsize) D_can_height++;
+ int16_t* D_can = (int16_t*)calloc(D_can_width*D_can_height,sizeof(int16_t));
+
+ // loop variables
+ int32_t u,v;
+ int16_t d,d2;
+
+ // for all point candidates in image 1 do
+ for (int32_t u_can=1; u_can<D_can_width; u_can++) {
+ u = u_can*D_candidate_stepsize;
+ for (int32_t v_can=1; v_can<D_can_height; v_can++) {
+ v = v_can*D_candidate_stepsize;
+
+ // initialize disparity candidate to invalid
+ *(D_can+getAddressOffsetImage(u_can,v_can,D_can_width)) = -1;
+
+ // find forwards
+ d = computeMatchingDisparity(u,v,I1_desc,I2_desc,false);
+ if (d>=0) {
+
+ // find backwards
+ d2 = computeMatchingDisparity(u-d,v,I1_desc,I2_desc,true);
+ if (d2>=0 && abs(d-d2)<=param.lr_threshold)
+ *(D_can+getAddressOffsetImage(u_can,v_can,D_can_width)) = d;
+ }
+ }
+ }
+
+ // remove inconsistent support points
+ removeInconsistentSupportPoints(D_can,D_can_width,D_can_height);
+
+ // remove support points on straight lines, since they are redundant
+ // this reduces the number of triangles a little bit and hence speeds up
+ // the triangulation process
+ removeRedundantSupportPoints(D_can,D_can_width,D_can_height,5,1,true);
+ removeRedundantSupportPoints(D_can,D_can_width,D_can_height,5,1,false);
+
+ // move support points from image representation into a vector representation
+ vector<support_pt> p_support;
+ for (int32_t u_can=1; u_can<D_can_width; u_can++)
+ for (int32_t v_can=1; v_can<D_can_height; v_can++)
+ if (*(D_can+getAddressOffsetImage(u_can,v_can,D_can_width))>=0)
+ p_support.push_back(support_pt(u_can*D_candidate_stepsize,
+ v_can*D_candidate_stepsize,
+ *(D_can+getAddressOffsetImage(u_can,v_can,D_can_width))));
+
+ // if flag is set, add support points in image corners
+ // with the same disparity as the nearest neighbor support point
+ if (param.add_corners)
+ addCornerSupportPoints(p_support);
+
+ // free memory
+ free(D_can);
+
+ // return support point vector
+ return p_support;
+}
+
+vector<Elas::triangle> Elas::computeDelaunayTriangulation (vector<support_pt> p_support,int32_t right_image) {
+
+ // input/output structure for triangulation
+ struct triangulateio in, out;
+ int32_t k;
+
+ // inputs
+ in.numberofpoints = p_support.size();
+ in.pointlist = (float*)malloc(in.numberofpoints*2*sizeof(float));
+ k=0;
+ if (!right_image) {
+ for (int32_t i=0; i<p_support.size(); i++) {
+ in.pointlist[k++] = p_support[i].u;
+ in.pointlist[k++] = p_support[i].v;
+ }
+ } else {
+ for (int32_t i=0; i<p_support.size(); i++) {
+ in.pointlist[k++] = p_support[i].u-p_support[i].d;
+ in.pointlist[k++] = p_support[i].v;
+ }
+ }
+ in.numberofpointattributes = 0;
+ in.pointattributelist = NULL;
+ in.pointmarkerlist = NULL;
+ in.numberofsegments = 0;
+ in.numberofholes = 0;
+ in.numberofregions = 0;
+ in.regionlist = NULL;
+
+ // outputs
+ out.pointlist = NULL;
+ out.pointattributelist = NULL;
+ out.pointmarkerlist = NULL;
+ out.trianglelist = NULL;
+ out.triangleattributelist = NULL;
+ out.neighborlist = NULL;
+ out.segmentlist = NULL;
+ out.segmentmarkerlist = NULL;
+ out.edgelist = NULL;
+ out.edgemarkerlist = NULL;
+
+ // do triangulation (z=zero-based, n=neighbors, Q=quiet, B=no boundary markers)
+ char parameters[] = "zQB";
+ triangulate(parameters, &in, &out, NULL);
+
+ // put resulting triangles into vector tri
+ vector<triangle> tri;
+ k=0;
+ for (int32_t i=0; i<out.numberoftriangles; i++) {
+ tri.push_back(triangle(out.trianglelist[k],out.trianglelist[k+1],out.trianglelist[k+2]));
+ k+=3;
+ }
+
+ // free memory used for triangulation
+ free(in.pointlist);
+ free(out.pointlist);
+ free(out.trianglelist);
+
+ // return triangles
+ return tri;
+}
+
+void Elas::computeDisparityPlanes (vector<support_pt> p_support,vector<triangle> &tri,int32_t right_image) {
+
+ // init matrices
+ Matrix A(3,3);
+ Matrix b(3,1);
+
+ // for all triangles do
+ for (int32_t i=0; i<tri.size(); i++) {
+
+ // get triangle corner indices
+ int32_t c1 = tri[i].c1;
+ int32_t c2 = tri[i].c2;
+ int32_t c3 = tri[i].c3;
+
+ // compute matrix A for linear system of left triangle
+ A.val[0][0] = p_support[c1].u;
+ A.val[1][0] = p_support[c2].u;
+ A.val[2][0] = p_support[c3].u;
+ A.val[0][1] = p_support[c1].v; A.val[0][2] = 1;
+ A.val[1][1] = p_support[c2].v; A.val[1][2] = 1;
+ A.val[2][1] = p_support[c3].v; A.val[2][2] = 1;
+
+ // compute vector b for linear system (containing the disparities)
+ b.val[0][0] = p_support[c1].d;
+ b.val[1][0] = p_support[c2].d;
+ b.val[2][0] = p_support[c3].d;
+
+ // on success of gauss jordan elimination
+ if (b.solve(A)) {
+
+ // grab results from b
+ tri[i].t1a = b.val[0][0];
+ tri[i].t1b = b.val[1][0];
+ tri[i].t1c = b.val[2][0];
+
+ // otherwise: invalid
+ } else {
+ tri[i].t1a = 0;
+ tri[i].t1b = 0;
+ tri[i].t1c = 0;
+ }
+
+ // compute matrix A for linear system of right triangle
+ A.val[0][0] = p_support[c1].u-p_support[c1].d;
+ A.val[1][0] = p_support[c2].u-p_support[c2].d;
+ A.val[2][0] = p_support[c3].u-p_support[c3].d;
+ A.val[0][1] = p_support[c1].v; A.val[0][2] = 1;
+ A.val[1][1] = p_support[c2].v; A.val[1][2] = 1;
+ A.val[2][1] = p_support[c3].v; A.val[2][2] = 1;
+
+ // compute vector b for linear system (containing the disparities)
+ b.val[0][0] = p_support[c1].d;
+ b.val[1][0] = p_support[c2].d;
+ b.val[2][0] = p_support[c3].d;
+
+ // on success of gauss jordan elimination
+ if (b.solve(A)) {
+
+ // grab results from b
+ tri[i].t2a = b.val[0][0];
+ tri[i].t2b = b.val[1][0];
+ tri[i].t2c = b.val[2][0];
+
+ // otherwise: invalid
+ } else {
+ tri[i].t2a = 0;
+ tri[i].t2b = 0;
+ tri[i].t2c = 0;
+ }
+ }
+}
+
+void Elas::createGrid(vector<support_pt> p_support,int32_t* disparity_grid,int32_t* grid_dims,bool right_image) {
+
+ // get grid dimensions
+ int32_t grid_width = grid_dims[1];
+ int32_t grid_height = grid_dims[2];
+
+ // allocate temporary memory
+ int32_t* temp1 = (int32_t*)calloc((param.disp_max+1)*grid_height*grid_width,sizeof(int32_t));
+ int32_t* temp2 = (int32_t*)calloc((param.disp_max+1)*grid_height*grid_width,sizeof(int32_t));
+
+ // for all support points do
+ for (int32_t i=0; i<p_support.size(); i++) {
+
+ // compute disparity range to fill for this support point
+ int32_t x_curr = p_support[i].u;
+ int32_t y_curr = p_support[i].v;
+ int32_t d_curr = p_support[i].d;
+ int32_t d_min = max(d_curr-1,0);
+ int32_t d_max = min(d_curr+1,param.disp_max);
+
+ // fill disparity grid helper
+ for (int32_t d=d_min; d<=d_max; d++) {
+ int32_t x;
+ if (!right_image)
+ x = floor((float)(x_curr/param.grid_size));
+ else
+ x = floor((float)(x_curr-d_curr)/(float)param.grid_size);
+ int32_t y = floor((float)y_curr/(float)param.grid_size);
+
+ // point may potentially lay outside (corner points)
+ if (x>=0 && x<grid_width &&y>=0 && y<grid_height) {
+ int32_t addr = getAddressOffsetGrid(x,y,d,grid_width,param.disp_max+1);
+ *(temp1+addr) = 1;
+ }
+ }
+ }
+
+ // diffusion pointers
+ const int32_t* tl = temp1 + (0*grid_width+0)*(param.disp_max+1);
+ const int32_t* tc = temp1 + (0*grid_width+1)*(param.disp_max+1);
+ const int32_t* tr = temp1 + (0*grid_width+2)*(param.disp_max+1);
+ const int32_t* cl = temp1 + (1*grid_width+0)*(param.disp_max+1);
+ const int32_t* cc = temp1 + (1*grid_width+1)*(param.disp_max+1);
+ const int32_t* cr = temp1 + (1*grid_width+2)*(param.disp_max+1);
+ const int32_t* bl = temp1 + (2*grid_width+0)*(param.disp_max+1);
+ const int32_t* bc = temp1 + (2*grid_width+1)*(param.disp_max+1);
+ const int32_t* br = temp1 + (2*grid_width+2)*(param.disp_max+1);
+
+ int32_t* result = temp2 + (1*grid_width+1)*(param.disp_max+1);
+ int32_t* end_input = temp1 + grid_width*grid_height*(param.disp_max+1);
+
+ // diffuse temporary grid
+ for( ; br != end_input; tl++, tc++, tr++, cl++, cc++, cr++, bl++, bc++, br++, result++ )
+ *result = *tl | *tc | *tr | *cl | *cc | *cr | *bl | *bc | *br;
+
+ // for all grid positions create disparity grid
+ for (int32_t x=0; x<grid_width; x++) {
+ for (int32_t y=0; y<grid_height; y++) {
+
+ // start with second value (first is reserved for count)
+ int32_t curr_ind = 1;
+
+ // for all disparities do
+ for (int32_t d=0; d<=param.disp_max; d++) {
+
+ // if yes => add this disparity to current cell
+ if (*(temp2+getAddressOffsetGrid(x,y,d,grid_width,param.disp_max+1))>0) {
+ *(disparity_grid+getAddressOffsetGrid(x,y,curr_ind,grid_width,param.disp_max+2))=d;
+ curr_ind++;
+ }
+ }
+
+ // finally set number of indices
+ *(disparity_grid+getAddressOffsetGrid(x,y,0,grid_width,param.disp_max+2))=curr_ind-1;
+ }
+ }
+
+ // release temporary memory
+ free(temp1);
+ free(temp2);
+}
+
+inline void Elas::updatePosteriorMinimum(__m128i* I2_block_addr,const int32_t &d,const int32_t &w,
+ const __m128i &xmm1,__m128i &xmm2,int32_t &val,int32_t &min_val,int32_t &min_d) {
+ xmm2 = _mm_load_si128(I2_block_addr);
+ xmm2 = _mm_sad_epu8(xmm1,xmm2);
+ val = _mm_extract_epi16(xmm2,0)+_mm_extract_epi16(xmm2,4)+w;
+ if (val<min_val) {
+ min_val = val;
+ min_d = d;
+ }
+}
+
+inline void Elas::updatePosteriorMinimum(__m128i* I2_block_addr,const int32_t &d,
+ const __m128i &xmm1,__m128i &xmm2,int32_t &val,int32_t &min_val,int32_t &min_d) {
+ xmm2 = _mm_load_si128(I2_block_addr);
+ xmm2 = _mm_sad_epu8(xmm1,xmm2);
+ val = _mm_extract_epi16(xmm2,0)+_mm_extract_epi16(xmm2,4);
+ if (val<min_val) {
+ min_val = val;
+ min_d = d;
+ }
+}
+
+inline void Elas::findMatch(int32_t &u,int32_t &v,float &plane_a,float &plane_b,float &plane_c,
+ int32_t* disparity_grid,int32_t *grid_dims,uint8_t* I1_desc,uint8_t* I2_desc,
+ int32_t *P,int32_t &plane_radius,bool &valid,bool &right_image,float* D){
+
+ // get image width and height
+ const int32_t disp_num = grid_dims[0]-1;
+ const int32_t window_size = 2;
+
+ // address of disparity we want to compute
+ uint32_t d_addr;
+ if (param.subsampling) d_addr = getAddressOffsetImage(u/2,v/2,width/2);
+ else d_addr = getAddressOffsetImage(u,v,width);
+
+ // check if u is ok
+ if (u<window_size || u>=width-window_size)
+ return;
+
+ // compute line start address
+ int32_t line_offset = 16*width*max(min(v,height-3),2);
+ uint8_t *I1_line_addr,*I2_line_addr;
+ if (!right_image) {
+ I1_line_addr = I1_desc+line_offset;
+ I2_line_addr = I2_desc+line_offset;
+ } else {
+ I1_line_addr = I2_desc+line_offset;
+ I2_line_addr = I1_desc+line_offset;
+ }
+
+ // compute I1 block start address
+ uint8_t* I1_block_addr = I1_line_addr+16*u;
+
+ // does this patch have enough texture?
+ int32_t sum = 0;
+ for (int32_t i=0; i<16; i++)
+ sum += abs((int32_t)(*(I1_block_addr+i))-128);
+ if (sum<param.match_texture)
+ return;
+
+ // compute disparity, min disparity and max disparity of plane prior
+ int32_t d_plane = (int32_t)(plane_a*(float)u+plane_b*(float)v+plane_c);
+ int32_t d_plane_min = max(d_plane-plane_radius,0);
+ int32_t d_plane_max = min(d_plane+plane_radius,disp_num-1);
+
+ // get grid pointer
+ int32_t grid_x = (int32_t)floor((float)u/(float)param.grid_size);
+ int32_t grid_y = (int32_t)floor((float)v/(float)param.grid_size);
+ uint32_t grid_addr = getAddressOffsetGrid(grid_x,grid_y,0,grid_dims[1],grid_dims[0]);
+ int32_t num_grid = *(disparity_grid+grid_addr);
+ int32_t* d_grid = disparity_grid+grid_addr+1;
+
+ // loop variables
+ int32_t d_curr, u_warp, val;
+ int32_t min_val = 10000;
+ int32_t min_d = -1;
+ __m128i xmm1 = _mm_load_si128((__m128i*)I1_block_addr);
+ __m128i xmm2;
+
+ // left image
+ if (!right_image) {
+ for (int32_t i=0; i<num_grid; i++) {
+ d_curr = d_grid[i];
+ if (d_curr<d_plane_min || d_curr>d_plane_max) {
+ u_warp = u-d_curr;
+ if (u_warp<window_size || u_warp>=width-window_size)
+ continue;
+ updatePosteriorMinimum((__m128i*)(I2_line_addr+16*u_warp),d_curr,xmm1,xmm2,val,min_val,min_d);
+ }
+ }
+ for (d_curr=d_plane_min; d_curr<=d_plane_max; d_curr++) {
+ u_warp = u-d_curr;
+ if (u_warp<window_size || u_warp>=width-window_size)
+ continue;
+ updatePosteriorMinimum((__m128i*)(I2_line_addr+16*u_warp),d_curr,valid?*(P+abs(d_curr-d_plane)):0,xmm1,xmm2,val,min_val,min_d);
+ }
+
+ // right image
+ } else {
+ for (int32_t i=0; i<num_grid; i++) {
+ d_curr = d_grid[i];
+ if (d_curr<d_plane_min || d_curr>d_plane_max) {
+ u_warp = u+d_curr;
+ if (u_warp<window_size || u_warp>=width-window_size)
+ continue;
+ updatePosteriorMinimum((__m128i*)(I2_line_addr+16*u_warp),d_curr,xmm1,xmm2,val,min_val,min_d);
+ }
+ }
+ for (d_curr=d_plane_min; d_curr<=d_plane_max; d_curr++) {
+ u_warp = u+d_curr;
+ if (u_warp<window_size || u_warp>=width-window_size)
+ continue;
+ updatePosteriorMinimum((__m128i*)(I2_line_addr+16*u_warp),d_curr,valid?*(P+abs(d_curr-d_plane)):0,xmm1,xmm2,val,min_val,min_d);
+ }
+ }
+
+ // set disparity value
+ if (min_d>=0) *(D+d_addr) = min_d; // MAP value (min neg-Log probability)
+ else *(D+d_addr) = -1; // invalid disparity
+}
+
+// TODO: %2 => more elegantly
+void Elas::computeDisparity(vector<support_pt> p_support,vector<triangle> tri,int32_t* disparity_grid,int32_t *grid_dims,
+ uint8_t* I1_desc,uint8_t* I2_desc,bool right_image,float* D) {
+
+ // number of disparities
+ const int32_t disp_num = grid_dims[0]-1;
+
+ // descriptor window_size
+ int32_t window_size = 2;
+
+ // init disparity image to -10
+ if (param.subsampling) {
+ for (int32_t i=0; i<(width/2)*(height/2); i++)
+ *(D+i) = -10;
+ } else {
+ for (int32_t i=0; i<width*height; i++)
+ *(D+i) = -10;
+ }
+
+ // pre-compute prior
+ float two_sigma_squared = 2*param.sigma*param.sigma;
+ int32_t* P = new int32_t[disp_num];
+ for (int32_t delta_d=0; delta_d<disp_num; delta_d++)
+ P[delta_d] = (int32_t)((-log(param.gamma+exp(-delta_d*delta_d/two_sigma_squared))+log(param.gamma))/param.beta);
+ int32_t plane_radius = (int32_t)max((float)ceil(param.sigma*param.sradius),(float)2.0);
+
+ // loop variables
+ int32_t c1, c2, c3;
+ float plane_a,plane_b,plane_c,plane_d;
+
+ // for all triangles do
+ for (uint32_t i=0; i<tri.size(); i++) {
+
+ // get plane parameters
+ uint32_t p_i = i*3;
+ if (!right_image) {
+ plane_a = tri[i].t1a;
+ plane_b = tri[i].t1b;
+ plane_c = tri[i].t1c;
+ plane_d = tri[i].t2a;
+ } else {
+ plane_a = tri[i].t2a;
+ plane_b = tri[i].t2b;
+ plane_c = tri[i].t2c;
+ plane_d = tri[i].t1a;
+ }
+
+ // triangle corners
+ c1 = tri[i].c1;
+ c2 = tri[i].c2;
+ c3 = tri[i].c3;
+
+ // sort triangle corners wrt. u (ascending)
+ float tri_u[3];
+ if (!right_image) {
+ tri_u[0] = p_support[c1].u;
+ tri_u[1] = p_support[c2].u;
+ tri_u[2] = p_support[c3].u;
+ } else {
+ tri_u[0] = p_support[c1].u-p_support[c1].d;
+ tri_u[1] = p_support[c2].u-p_support[c2].d;
+ tri_u[2] = p_support[c3].u-p_support[c3].d;
+ }
+ float tri_v[3] = {p_support[c1].v,p_support[c2].v,p_support[c3].v};
+
+ for (uint32_t j=0; j<3; j++) {
+ for (uint32_t k=0; k<j; k++) {
+ if (tri_u[k]>tri_u[j]) {
+ float tri_u_temp = tri_u[j]; tri_u[j] = tri_u[k]; tri_u[k] = tri_u_temp;
+ float tri_v_temp = tri_v[j]; tri_v[j] = tri_v[k]; tri_v[k] = tri_v_temp;
+ }
+ }
+ }
+
+ // rename corners
+ float A_u = tri_u[0]; float A_v = tri_v[0];
+ float B_u = tri_u[1]; float B_v = tri_v[1];
+ float C_u = tri_u[2]; float C_v = tri_v[2];
+
+ // compute straight lines connecting triangle corners
+ float AB_a = 0; float AC_a = 0; float BC_a = 0;
+ if ((int32_t)(A_u)!=(int32_t)(B_u)) AB_a = (A_v-B_v)/(A_u-B_u);
+ if ((int32_t)(A_u)!=(int32_t)(C_u)) AC_a = (A_v-C_v)/(A_u-C_u);
+ if ((int32_t)(B_u)!=(int32_t)(C_u)) BC_a = (B_v-C_v)/(B_u-C_u);
+ float AB_b = A_v-AB_a*A_u;
+ float AC_b = A_v-AC_a*A_u;
+ float BC_b = B_v-BC_a*B_u;
+
+ // a plane is only valid if itself and its projection
+ // into the other image is not too much slanted
+ bool valid = fabs(plane_a)<0.7 && fabs(plane_d)<0.7;
+
+ // first part (triangle corner A->B)
+ if ((int32_t)(A_u)!=(int32_t)(B_u)) {
+ for (int32_t u=max((int32_t)A_u,0); u<min((int32_t)B_u,width); u++){
+ if (!param.subsampling || u%2==0) {
+ int32_t v_1 = (uint32_t)(AC_a*(float)u+AC_b);
+ int32_t v_2 = (uint32_t)(AB_a*(float)u+AB_b);
+ for (int32_t v=min(v_1,v_2); v<max(v_1,v_2); v++)
+ if (!param.subsampling || v%2==0) {
+ findMatch(u,v,plane_a,plane_b,plane_c,disparity_grid,grid_dims,
+ I1_desc,I2_desc,P,plane_radius,valid,right_image,D);
+ }
+ }
+ }
+ }
+
+ // second part (triangle corner B->C)
+ if ((int32_t)(B_u)!=(int32_t)(C_u)) {
+ for (int32_t u=max((int32_t)B_u,0); u<min((int32_t)C_u,width); u++){
+ if (!param.subsampling || u%2==0) {
+ int32_t v_1 = (uint32_t)(AC_a*(float)u+AC_b);
+ int32_t v_2 = (uint32_t)(BC_a*(float)u+BC_b);
+ for (int32_t v=min(v_1,v_2); v<max(v_1,v_2); v++)
+ if (!param.subsampling || v%2==0) {
+ findMatch(u,v,plane_a,plane_b,plane_c,disparity_grid,grid_dims,
+ I1_desc,I2_desc,P,plane_radius,valid,right_image,D);
+ }
+ }
+ }
+ }
+
+ }
+
+ delete[] P;
+}
+
+void Elas::leftRightConsistencyCheck(float* D1,float* D2) {
+
+ // get disparity image dimensions
+ int32_t D_width = width;
+ int32_t D_height = height;
+ if (param.subsampling) {
+ D_width = width/2;
+ D_height = height/2;
+ }
+
+ // make a copy of both images
+ float* D1_copy = (float*)malloc(D_width*D_height*sizeof(float));
+ float* D2_copy = (float*)malloc(D_width*D_height*sizeof(float));
+ memcpy(D1_copy,D1,D_width*D_height*sizeof(float));
+ memcpy(D2_copy,D2,D_width*D_height*sizeof(float));
+
+ // loop variables
+ uint32_t addr,addr_warp;
+ float u_warp_1,u_warp_2,d1,d2;
+
+ // for all image points do
+ for (int32_t u=0; u<D_width; u++) {
+ for (int32_t v=0; v<D_height; v++) {
+
+ // compute address (u,v) and disparity value
+ addr = getAddressOffsetImage(u,v,D_width);
+ d1 = *(D1_copy+addr);
+ d2 = *(D2_copy+addr);
+ if (param.subsampling) {
+ u_warp_1 = (float)u-d1/2;
+ u_warp_2 = (float)u+d2/2;
+ } else {
+ u_warp_1 = (float)u-d1;
+ u_warp_2 = (float)u+d2;
+ }
+
+
+ // check if left disparity is valid
+ if (d1>=0 && u_warp_1>=0 && u_warp_1<D_width) {
+
+ // compute warped image address
+ addr_warp = getAddressOffsetImage((int32_t)u_warp_1,v,D_width);
+
+ // if check failed
+ if (fabs(*(D2_copy+addr_warp)-d1)>param.lr_threshold)
+ *(D1+addr) = -10;
+
+ // set invalid
+ } else
+ *(D1+addr) = -10;
+
+ // check if right disparity is valid
+ if (d2>=0 && u_warp_2>=0 && u_warp_2<D_width) {
+
+ // compute warped image address
+ addr_warp = getAddressOffsetImage((int32_t)u_warp_2,v,D_width);
+
+ // if check failed
+ if (fabs(*(D1_copy+addr_warp)-d2)>param.lr_threshold)
+ *(D2+addr) = -10;
+
+ // set invalid
+ } else
+ *(D2+addr) = -10;
+ }
+ }
+
+ // release memory
+ free(D1_copy);
+ free(D2_copy);
+}
+
+void Elas::removeSmallSegments (float* D) {
+
+ // get disparity image dimensions
+ int32_t D_width = width;
+ int32_t D_height = height;
+ int32_t D_speckle_size = param.speckle_size;
+ if (param.subsampling) {
+ D_width = width/2;
+ D_height = height/2;
+ D_speckle_size = sqrt((float)param.speckle_size)*2;
+ }
+
+ // allocate memory on heap for dynamic programming arrays
+ int32_t *D_done = (int32_t*)calloc(D_width*D_height,sizeof(int32_t));
+ int32_t *seg_list_u = (int32_t*)calloc(D_width*D_height,sizeof(int32_t));
+ int32_t *seg_list_v = (int32_t*)calloc(D_width*D_height,sizeof(int32_t));
+ int32_t seg_list_count;
+ int32_t seg_list_curr;
+ int32_t u_neighbor[4];
+ int32_t v_neighbor[4];
+ int32_t u_seg_curr;
+ int32_t v_seg_curr;
+
+ // declare loop variables
+ int32_t addr_start, addr_curr, addr_neighbor;
+
+ // for all pixels do
+ for (int32_t u=0; u<D_width; u++) {
+ for (int32_t v=0; v<D_height; v++) {
+
+ // get address of first pixel in this segment
+ addr_start = getAddressOffsetImage(u,v,D_width);
+
+ // if this pixel has not already been processed
+ if (*(D_done+addr_start)==0) {
+
+ // init segment list (add first element
+ // and set it to be the next element to check)
+ *(seg_list_u+0) = u;
+ *(seg_list_v+0) = v;
+ seg_list_count = 1;
+ seg_list_curr = 0;
+
+ // add neighboring segments as long as there
+ // are none-processed pixels in the seg_list;
+ // none-processed means: seg_list_curr<seg_list_count
+ while (seg_list_curr<seg_list_count) {
+
+ // get current position from seg_list
+ u_seg_curr = *(seg_list_u+seg_list_curr);
+ v_seg_curr = *(seg_list_v+seg_list_curr);
+
+ // get address of current pixel in this segment
+ addr_curr = getAddressOffsetImage(u_seg_curr,v_seg_curr,D_width);
+
+ // fill list with neighbor positions
+ u_neighbor[0] = u_seg_curr-1; v_neighbor[0] = v_seg_curr;
+ u_neighbor[1] = u_seg_curr+1; v_neighbor[1] = v_seg_curr;
+ u_neighbor[2] = u_seg_curr; v_neighbor[2] = v_seg_curr-1;
+ u_neighbor[3] = u_seg_curr; v_neighbor[3] = v_seg_curr+1;
+
+ // for all neighbors do
+ for (int32_t i=0; i<4; i++) {
+
+ // check if neighbor is inside image
+ if (u_neighbor[i]>=0 && v_neighbor[i]>=0 && u_neighbor[i]<D_width && v_neighbor[i]<D_height) {
+
+ // get neighbor pixel address
+ addr_neighbor = getAddressOffsetImage(u_neighbor[i],v_neighbor[i],D_width);
+
+ // check if neighbor has not been added yet and if it is valid
+ if (*(D_done+addr_neighbor)==0 && *(D+addr_neighbor)>=0) {
+
+ // is the neighbor similar to the current pixel
+ // (=belonging to the current segment)
+ if (fabs(*(D+addr_curr)-*(D+addr_neighbor))<=param.speckle_sim_threshold) {
+
+ // add neighbor coordinates to segment list
+ *(seg_list_u+seg_list_count) = u_neighbor[i];
+ *(seg_list_v+seg_list_count) = v_neighbor[i];
+ seg_list_count++;
+
+ // set neighbor pixel in I_done to "done"
+ // (otherwise a pixel may be added 2 times to the list, as
+ // neighbor of one pixel and as neighbor of another pixel)
+ *(D_done+addr_neighbor) = 1;
+ }
+ }
+
+ }
+ }
+
+ // set current pixel in seg_list to "done"
+ seg_list_curr++;
+
+ // set current pixel in I_done to "done"
+ *(D_done+addr_curr) = 1;
+
+ } // end: while (seg_list_curr<seg_list_count)
+
+ // if segment NOT large enough => invalidate pixels
+ if (seg_list_count<D_speckle_size) {
+
+ // for all pixels in current segment invalidate pixels
+ for (int32_t i=0; i<seg_list_count; i++) {
+ addr_curr = getAddressOffsetImage(*(seg_list_u+i),*(seg_list_v+i),D_width);
+ *(D+addr_curr) = -10;
+ }
+ }
+ } // end: if (*(I_done+addr_start)==0)
+
+ }
+ }
+
+ // free memory
+ free(D_done);
+ free(seg_list_u);
+ free(seg_list_v);
+}
+
+void Elas::gapInterpolation(float* D) {
+
+ // get disparity image dimensions
+ int32_t D_width = width;
+ int32_t D_height = height;
+ int32_t D_ipol_gap_width = param.ipol_gap_width;
+ if (param.subsampling) {
+ D_width = width/2;
+ D_height = height/2;
+ D_ipol_gap_width = param.ipol_gap_width/2+1;
+ }
+
+ // discontinuity threshold
+ float discon_threshold = 3.0;
+
+ // declare loop variables
+ int32_t count,addr,v_first,v_last,u_first,u_last;
+ float d1,d2,d_ipol;
+
+ // 1. Row-wise:
+ // for each row do
+ for (int32_t v=0; v<D_height; v++) {
+
+ // init counter
+ count = 0;
+
+ // for each element of the row do
+ for (int32_t u=0; u<D_width; u++) {
+
+ // get address of this location
+ addr = getAddressOffsetImage(u,v,D_width);
+
+ // if disparity valid
+ if (*(D+addr)>=0) {
+
+ // check if speckle is small enough
+ if (count>=1 && count<=D_ipol_gap_width) {
+
+ // first and last value for interpolation
+ u_first = u-count;
+ u_last = u-1;
+
+ // if value in range
+ if (u_first>0 && u_last<D_width-1) {
+
+ // compute mean disparity
+ d1 = *(D+getAddressOffsetImage(u_first-1,v,D_width));
+ d2 = *(D+getAddressOffsetImage(u_last+1,v,D_width));
+ if (fabs(d1-d2)<discon_threshold) d_ipol = (d1+d2)/2;
+ else d_ipol = min(d1,d2);
+
+ // set all values to d_ipol
+ for (int32_t u_curr=u_first; u_curr<=u_last; u_curr++)
+ *(D+getAddressOffsetImage(u_curr,v,D_width)) = d_ipol;
+ }
+
+ }
+
+ // reset counter
+ count = 0;
+
+ // otherwise increment counter
+ } else {
+ count++;
+ }
+ }
+
+ // if full size disp map requested
+ if (param.add_corners) {
+
+ // extrapolate to the left
+ for (int32_t u=0; u<D_width; u++) {
+
+ // get address of this location
+ addr = getAddressOffsetImage(u,v,D_width);
+
+ // if disparity valid
+ if (*(D+addr)>=0) {
+ for (int32_t u2=max(u-D_ipol_gap_width,0); u2<u; u2++)
+ *(D+getAddressOffsetImage(u2,v,D_width)) = *(D+addr);
+ break;
+ }
+ }
+
+ // extrapolate to the right
+ for (int32_t u=D_width-1; u>=0; u--) {
+
+ // get address of this location
+ addr = getAddressOffsetImage(u,v,D_width);
+
+ // if disparity valid
+ if (*(D+addr)>=0) {
+ for (int32_t u2=u; u2<=min(u+D_ipol_gap_width,D_width-1); u2++)
+ *(D+getAddressOffsetImage(u2,v,D_width)) = *(D+addr);
+ break;
+ }
+ }
+ }
+ }
+
+ // 2. Column-wise:
+ // for each column do
+ for (int32_t u=0; u<D_width; u++) {
+
+ // init counter
+ count = 0;
+
+ // for each element of the column do
+ for (int32_t v=0; v<D_height; v++) {
+
+ // get address of this location
+ addr = getAddressOffsetImage(u,v,D_width);
+
+ // if disparity valid
+ if (*(D+addr)>=0) {
+
+ // check if gap is small enough
+ if (count>=1 && count<=D_ipol_gap_width) {
+
+ // first and last value for interpolation
+ v_first = v-count;
+ v_last = v-1;
+
+ // if value in range
+ if (v_first>0 && v_last<D_height-1) {
+
+ // compute mean disparity
+ d1 = *(D+getAddressOffsetImage(u,v_first-1,D_width));
+ d2 = *(D+getAddressOffsetImage(u,v_last+1,D_width));
+ if (fabs(d1-d2)<discon_threshold) d_ipol = (d1+d2)/2;
+ else d_ipol = min(d1,d2);
+
+ // set all values to d_ipol
+ for (int32_t v_curr=v_first; v_curr<=v_last; v_curr++)
+ *(D+getAddressOffsetImage(u,v_curr,D_width)) = d_ipol;
+ }
+
+ }
+
+ // reset counter
+ count = 0;
+
+ // otherwise increment counter
+ } else {
+ count++;
+ }
+ }
+
+ // added extrapolation to top and bottom since bottom rows sometimes stay unlabeled...
+ // DS 5/12/2014
+
+ // if full size disp map requested
+ if (param.add_corners) {
+
+ // extrapolate towards top
+ for (int32_t v=0; v<D_height; v++) {
+
+ // get address of this location
+ addr = getAddressOffsetImage(u,v,D_width);
+
+ // if disparity valid
+ if (*(D+addr)>=0) {
+ for (int32_t v2=max(v-D_ipol_gap_width,0); v2<v; v2++)
+ *(D+getAddressOffsetImage(u,v2,D_width)) = *(D+addr);
+ break;
+ }
+ }
+
+ // extrapolate towards the bottom
+ for (int32_t v=D_height-1; v>=0; v--) {
+
+ // get address of this location
+ addr = getAddressOffsetImage(u,v,D_width);
+
+ // if disparity valid
+ if (*(D+addr)>=0) {
+ for (int32_t v2=v; v2<=min(v+D_ipol_gap_width,D_height-1); v2++)
+ *(D+getAddressOffsetImage(u,v2,D_width)) = *(D+addr);
+ break;
+ }
+ }
+ }
+ }
+}
+
+// implements approximation to bilateral filtering
+void Elas::adaptiveMean (float* D) {
+
+ // get disparity image dimensions
+ int32_t D_width = width;
+ int32_t D_height = height;
+ if (param.subsampling) {
+ D_width = width/2;
+ D_height = height/2;
+ }
+
+ // allocate temporary memory
+ float* D_copy = (float*)malloc(D_width*D_height*sizeof(float));
+ float* D_tmp = (float*)malloc(D_width*D_height*sizeof(float));
+ memcpy(D_copy,D,D_width*D_height*sizeof(float));
+
+ // zero input disparity maps to -10 (this makes the bilateral
+ // weights of all valid disparities to 0 in this region)
+ for (int32_t i=0; i<D_width*D_height; i++) {
+ if (*(D+i)<0) {
+ *(D_copy+i) = -10;
+ *(D_tmp+i) = -10;
+ }
+ }
+
+ __m128 xconst0 = _mm_set1_ps(0);
+ __m128 xconst4 = _mm_set1_ps(4);
+ __m128 xval,xweight1,xweight2,xfactor1,xfactor2;
+
+ float *val = (float *)_mm_malloc(8*sizeof(float),16);
+ float *weight = (float*)_mm_malloc(4*sizeof(float),16);
+ float *factor = (float*)_mm_malloc(4*sizeof(float),16);
+
+ // set absolute mask
+ __m128 xabsmask = _mm_set1_ps(0x7FFFFFFF);
+
+ // when doing subsampling: 4 pixel bilateral filter width
+ if (param.subsampling) {
+
+ // horizontal filter
+ for (int32_t v=3; v<D_height-3; v++) {
+
+ // init
+ for (int32_t u=0; u<3; u++)
+ val[u] = *(D_copy+v*D_width+u);
+
+ // loop
+ for (int32_t u=3; u<D_width; u++) {
+
+ // set
+ float val_curr = *(D_copy+v*D_width+(u-1));
+ val[u%4] = *(D_copy+v*D_width+u);
+
+ xval = _mm_load_ps(val);
+ xweight1 = _mm_sub_ps(xval,_mm_set1_ps(val_curr));
+ xweight1 = _mm_and_ps(xweight1,xabsmask);
+ xweight1 = _mm_sub_ps(xconst4,xweight1);
+ xweight1 = _mm_max_ps(xconst0,xweight1);
+ xfactor1 = _mm_mul_ps(xval,xweight1);
+
+ _mm_store_ps(weight,xweight1);
+ _mm_store_ps(factor,xfactor1);
+
+ float weight_sum = weight[0]+weight[1]+weight[2]+weight[3];
+ float factor_sum = factor[0]+factor[1]+factor[2]+factor[3];
+
+ if (weight_sum>0) {
+ float d = factor_sum/weight_sum;
+ if (d>=0) *(D_tmp+v*D_width+(u-1)) = d;
+ }
+ }
+ }
+
+ // vertical filter
+ for (int32_t u=3; u<D_width-3; u++) {
+
+ // init
+ for (int32_t v=0; v<3; v++)
+ val[v] = *(D_tmp+v*D_width+u);
+
+ // loop
+ for (int32_t v=3; v<D_height; v++) {
+
+ // set
+ float val_curr = *(D_tmp+(v-1)*D_width+u);
+ val[v%4] = *(D_tmp+v*D_width+u);
+
+ xval = _mm_load_ps(val);
+ xweight1 = _mm_sub_ps(xval,_mm_set1_ps(val_curr));
+ xweight1 = _mm_and_ps(xweight1,xabsmask);
+ xweight1 = _mm_sub_ps(xconst4,xweight1);
+ xweight1 = _mm_max_ps(xconst0,xweight1);
+ xfactor1 = _mm_mul_ps(xval,xweight1);
+
+ _mm_store_ps(weight,xweight1);
+ _mm_store_ps(factor,xfactor1);
+
+ float weight_sum = weight[0]+weight[1]+weight[2]+weight[3];
+ float factor_sum = factor[0]+factor[1]+factor[2]+factor[3];
+
+ if (weight_sum>0) {
+ float d = factor_sum/weight_sum;
+ if (d>=0) *(D+(v-1)*D_width+u) = d;
+ }
+ }
+ }
+
+ // full resolution: 8 pixel bilateral filter width
+ } else {
+
+
+ // horizontal filter
+ for (int32_t v=3; v<D_height-3; v++) {
+
+ // init
+ for (int32_t u=0; u<7; u++)
+ val[u] = *(D_copy+v*D_width+u);
+
+ // loop
+ for (int32_t u=7; u<D_width; u++) {
+
+ // set
+ float val_curr = *(D_copy+v*D_width+(u-3));
+ val[u%8] = *(D_copy+v*D_width+u);
+
+ xval = _mm_load_ps(val);
+ xweight1 = _mm_sub_ps(xval,_mm_set1_ps(val_curr));
+ xweight1 = _mm_and_ps(xweight1,xabsmask);
+ xweight1 = _mm_sub_ps(xconst4,xweight1);
+ xweight1 = _mm_max_ps(xconst0,xweight1);
+ xfactor1 = _mm_mul_ps(xval,xweight1);
+
+ xval = _mm_load_ps(val+4);
+ xweight2 = _mm_sub_ps(xval,_mm_set1_ps(val_curr));
+ xweight2 = _mm_and_ps(xweight2,xabsmask);
+ xweight2 = _mm_sub_ps(xconst4,xweight2);
+ xweight2 = _mm_max_ps(xconst0,xweight2);
+ xfactor2 = _mm_mul_ps(xval,xweight2);
+
+ xweight1 = _mm_add_ps(xweight1,xweight2);
+ xfactor1 = _mm_add_ps(xfactor1,xfactor2);
+
+ _mm_store_ps(weight,xweight1);
+ _mm_store_ps(factor,xfactor1);
+
+ float weight_sum = weight[0]+weight[1]+weight[2]+weight[3];
+ float factor_sum = factor[0]+factor[1]+factor[2]+factor[3];
+
+ if (weight_sum>0) {
+ float d = factor_sum/weight_sum;
+ if (d>=0) *(D_tmp+v*D_width+(u-3)) = d;
+ }
+ }
+ }
+
+ // vertical filter
+ for (int32_t u=3; u<D_width-3; u++) {
+
+ // init
+ for (int32_t v=0; v<7; v++)
+ val[v] = *(D_tmp+v*D_width+u);
+
+ // loop
+ for (int32_t v=7; v<D_height; v++) {
+
+ // set
+ float val_curr = *(D_tmp+(v-3)*D_width+u);
+ val[v%8] = *(D_tmp+v*D_width+u);
+
+ xval = _mm_load_ps(val);
+ xweight1 = _mm_sub_ps(xval,_mm_set1_ps(val_curr));
+ xweight1 = _mm_and_ps(xweight1,xabsmask);
+ xweight1 = _mm_sub_ps(xconst4,xweight1);
+ xweight1 = _mm_max_ps(xconst0,xweight1);
+ xfactor1 = _mm_mul_ps(xval,xweight1);
+
+ xval = _mm_load_ps(val+4);
+ xweight2 = _mm_sub_ps(xval,_mm_set1_ps(val_curr));
+ xweight2 = _mm_and_ps(xweight2,xabsmask);
+ xweight2 = _mm_sub_ps(xconst4,xweight2);
+ xweight2 = _mm_max_ps(xconst0,xweight2);
+ xfactor2 = _mm_mul_ps(xval,xweight2);
+
+ xweight1 = _mm_add_ps(xweight1,xweight2);
+ xfactor1 = _mm_add_ps(xfactor1,xfactor2);
+
+ _mm_store_ps(weight,xweight1);
+ _mm_store_ps(factor,xfactor1);
+
+ float weight_sum = weight[0]+weight[1]+weight[2]+weight[3];
+ float factor_sum = factor[0]+factor[1]+factor[2]+factor[3];
+
+ if (weight_sum>0) {
+ float d = factor_sum/weight_sum;
+ if (d>=0) *(D+(v-3)*D_width+u) = d;
+ }
+ }
+ }
+ }
+
+ // free memory
+ _mm_free(val);
+ _mm_free(weight);
+ _mm_free(factor);
+ free(D_copy);
+ free(D_tmp);
+}
+
+void Elas::median (float* D) {
+
+ // get disparity image dimensions
+ int32_t D_width = width;
+ int32_t D_height = height;
+ if (param.subsampling) {
+ D_width = width/2;
+ D_height = height/2;
+ }
+
+ // temporary memory
+ float *D_temp = (float*)calloc(D_width*D_height,sizeof(float));
+
+ int32_t window_size = 3;
+
+ float *vals = new float[window_size*2+1];
+ int32_t i,j;
+ float temp;
+
+ // first step: horizontal median filter
+ for (int32_t u=window_size; u<D_width-window_size; u++) {
+ for (int32_t v=window_size; v<D_height-window_size; v++) {
+ if (*(D+getAddressOffsetImage(u,v,D_width))>=0) {
+ j = 0;
+ for (int32_t u2=u-window_size; u2<=u+window_size; u2++) {
+ temp = *(D+getAddressOffsetImage(u2,v,D_width));
+ i = j-1;
+ while (i>=0 && *(vals+i)>temp) {
+ *(vals+i+1) = *(vals+i);
+ i--;
+ }
+ *(vals+i+1) = temp;
+ j++;
+ }
+ *(D_temp+getAddressOffsetImage(u,v,D_width)) = *(vals+window_size);
+ } else {
+ *(D_temp+getAddressOffsetImage(u,v,D_width)) = *(D+getAddressOffsetImage(u,v,D_width));
+ }
+
+ }
+ }
+
+ // second step: vertical median filter
+ for (int32_t u=window_size; u<D_width-window_size; u++) {
+ for (int32_t v=window_size; v<D_height-window_size; v++) {
+ if (*(D+getAddressOffsetImage(u,v,D_width))>=0) {
+ j = 0;
+ for (int32_t v2=v-window_size; v2<=v+window_size; v2++) {
+ temp = *(D_temp+getAddressOffsetImage(u,v2,D_width));
+ i = j-1;
+ while (i>=0 && *(vals+i)>temp) {
+ *(vals+i+1) = *(vals+i);
+ i--;
+ }
+ *(vals+i+1) = temp;
+ j++;
+ }
+ *(D+getAddressOffsetImage(u,v,D_width)) = *(vals+window_size);
+ } else {
+ *(D+getAddressOffsetImage(u,v,D_width)) = *(D+getAddressOffsetImage(u,v,D_width));
+ }
+ }
+ }
+
+ free(D_temp);
+ free(vals);
+}
diff --git a/cv-node/lib/elas/filter.cpp b/cv-node/lib/elas/filter.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..d4f7954181e642bf337088d439175534fd8e6763
--- /dev/null
+++ b/cv-node/lib/elas/filter.cpp
@@ -0,0 +1,468 @@
+/*
+Copyright 2011. All rights reserved.
+Institute of Measurement and Control Systems
+Karlsruhe Institute of Technology, Germany
+
+This file is part of libelas.
+Authors: Julius Ziegler, Andreas Geiger
+
+libelas is free software; you can redistribute it and/or modify it under the
+terms of the GNU General Public License as published by the Free Software
+Foundation; either version 3 of the License, or any later version.
+
+libelas is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+libelas; if not, write to the Free Software Foundation, Inc., 51 Franklin
+Street, Fifth Floor, Boston, MA 02110-1301, USA
+*/
+
+#include <stdio.h>
+#include <string.h>
+#include <cassert>
+
+#include "filter.h"
+
+// define fixed-width datatypes for Visual Studio projects
+#ifndef _MSC_VER
+ #include <stdint.h>
+#else
+ typedef __int8 int8_t;
+ typedef __int16 int16_t;
+ typedef __int32 int32_t;
+ typedef __int64 int64_t;
+ typedef unsigned __int8 uint8_t;
+ typedef unsigned __int16 uint16_t;
+ typedef unsigned __int32 uint32_t;
+ typedef unsigned __int64 uint64_t;
+#endif
+
+// fast filters: implements 3x3 and 5x5 sobel filters and
+// 5x5 blob and corner filters based on SSE2/3 instructions
+namespace filter {
+
+ // private namespace, public user functions at the bottom of this file
+ namespace detail {
+ void integral_image( const uint8_t* in, int32_t* out, int w, int h ) {
+ int32_t* out_top = out;
+ const uint8_t* line_end = in + w;
+ const uint8_t* in_end = in + w*h;
+ int32_t line_sum = 0;
+ for( ; in != line_end; in++, out++ ) {
+ line_sum += *in;
+ *out = line_sum;
+ }
+ for( ; in != in_end; ) {
+ int32_t line_sum = 0;
+ const uint8_t* line_end = in + w;
+ for( ; in != line_end; in++, out++, out_top++ ) {
+ line_sum += *in;
+ *out = *out_top + line_sum;
+ }
+ }
+ }
+
+ void unpack_8bit_to_16bit( const __m128i a, __m128i& b0, __m128i& b1 ) {
+ __m128i zero = _mm_setzero_si128();
+ b0 = _mm_unpacklo_epi8( a, zero );
+ b1 = _mm_unpackhi_epi8( a, zero );
+ }
+
+ void pack_16bit_to_8bit_saturate( const __m128i a0, const __m128i a1, __m128i& b ) {
+ b = _mm_packus_epi16( a0, a1 );
+ }
+
+ // convolve image with a (1,4,6,4,1) row vector. Result is accumulated into output.
+ // output is scaled by 1/128, then clamped to [-128,128], and finally shifted to [0,255].
+ void convolve_14641_row_5x5_16bit( const int16_t* in, uint8_t* out, int w, int h ) {
+ assert( w % 16 == 0 && "width must be multiple of 16!" );
+ const __m128i* i0 = (const __m128i*)(in);
+ const int16_t* i1 = in+1;
+ const int16_t* i2 = in+2;
+ const int16_t* i3 = in+3;
+ const int16_t* i4 = in+4;
+ uint8_t* result = out + 2;
+ const int16_t* const end_input = in + w*h;
+ __m128i offs = _mm_set1_epi16( 128 );
+ for( ; i4 < end_input; i0 += 1, i1 += 8, i2 += 8, i3 += 8, i4 += 8, result += 16 ) {
+ __m128i result_register_lo;
+ __m128i result_register_hi;
+ for( int i=0; i<2; i++ ) {
+ __m128i* result_register;
+ if( i==0 ) result_register = &result_register_lo;
+ else result_register = &result_register_hi;
+ __m128i i0_register = *i0;
+ __m128i i1_register = _mm_loadu_si128( (__m128i*)( i1 ) );
+ __m128i i2_register = _mm_loadu_si128( (__m128i*)( i2 ) );
+ __m128i i3_register = _mm_loadu_si128( (__m128i*)( i3 ) );
+ __m128i i4_register = _mm_loadu_si128( (__m128i*)( i4 ) );
+ *result_register = _mm_setzero_si128();
+ *result_register = _mm_add_epi16( i0_register, *result_register );
+ i1_register = _mm_add_epi16( i1_register, i1_register );
+ i1_register = _mm_add_epi16( i1_register, i1_register );
+ *result_register = _mm_add_epi16( i1_register, *result_register );
+ i2_register = _mm_add_epi16( i2_register, i2_register );
+ *result_register = _mm_add_epi16( i2_register, *result_register );
+ i2_register = _mm_add_epi16( i2_register, i2_register );
+ *result_register = _mm_add_epi16( i2_register, *result_register );
+ i3_register = _mm_add_epi16( i3_register, i3_register );
+ i3_register = _mm_add_epi16( i3_register, i3_register );
+ *result_register = _mm_add_epi16( i3_register, *result_register );
+ *result_register = _mm_add_epi16( i4_register, *result_register );
+ *result_register = _mm_srai_epi16( *result_register, 7 );
+ *result_register = _mm_add_epi16( *result_register, offs );
+ if( i==0 ) {
+ i0 += 1;
+ i1 += 8;
+ i2 += 8;
+ i3 += 8;
+ i4 += 8;
+ }
+ }
+ pack_16bit_to_8bit_saturate( result_register_lo, result_register_hi, result_register_lo );
+ _mm_storeu_si128( ((__m128i*)( result )), result_register_lo );
+ }
+ }
+
+ // convolve image with a (1,2,0,-2,-1) row vector. Result is accumulated into output.
+ // This one works on 16bit input and 8bit output.
+ // output is scaled by 1/128, then clamped to [-128,128], and finally shifted to [0,255].
+ void convolve_12021_row_5x5_16bit( const int16_t* in, uint8_t* out, int w, int h ) {
+ assert( w % 16 == 0 && "width must be multiple of 16!" );
+ const __m128i* i0 = (const __m128i*)(in);
+ const int16_t* i1 = in+1;
+ const int16_t* i3 = in+3;
+ const int16_t* i4 = in+4;
+ uint8_t* result = out + 2;
+ const int16_t* const end_input = in + w*h;
+ __m128i offs = _mm_set1_epi16( 128 );
+ for( ; i4 < end_input; i0 += 1, i1 += 8, i3 += 8, i4 += 8, result += 16 ) {
+ __m128i result_register_lo;
+ __m128i result_register_hi;
+ for( int i=0; i<2; i++ ) {
+ __m128i* result_register;
+ if( i==0 ) result_register = &result_register_lo;
+ else result_register = &result_register_hi;
+ __m128i i0_register = *i0;
+ __m128i i1_register = _mm_loadu_si128( (__m128i*)( i1 ) );
+ __m128i i3_register = _mm_loadu_si128( (__m128i*)( i3 ) );
+ __m128i i4_register = _mm_loadu_si128( (__m128i*)( i4 ) );
+ *result_register = _mm_setzero_si128();
+ *result_register = _mm_add_epi16( i0_register, *result_register );
+ i1_register = _mm_add_epi16( i1_register, i1_register );
+ *result_register = _mm_add_epi16( i1_register, *result_register );
+ i3_register = _mm_add_epi16( i3_register, i3_register );
+ *result_register = _mm_sub_epi16( *result_register, i3_register );
+ *result_register = _mm_sub_epi16( *result_register, i4_register );
+ *result_register = _mm_srai_epi16( *result_register, 7 );
+ *result_register = _mm_add_epi16( *result_register, offs );
+ if( i==0 ) {
+ i0 += 1;
+ i1 += 8;
+ i3 += 8;
+ i4 += 8;
+ }
+ }
+ pack_16bit_to_8bit_saturate( result_register_lo, result_register_hi, result_register_lo );
+ _mm_storeu_si128( ((__m128i*)( result )), result_register_lo );
+ }
+ }
+
+ // convolve image with a (1,2,1) row vector. Result is accumulated into output.
+ // This one works on 16bit input and 8bit output.
+ // output is scaled by 1/4, then clamped to [-128,128], and finally shifted to [0,255].
+ void convolve_121_row_3x3_16bit( const int16_t* in, uint8_t* out, int w, int h ) {
+ assert( w % 16 == 0 && "width must be multiple of 16!" );
+ const __m128i* i0 = (const __m128i*)(in);
+ const int16_t* i1 = in+1;
+ const int16_t* i2 = in+2;
+ uint8_t* result = out + 1;
+ const int16_t* const end_input = in + w*h;
+ const size_t blocked_loops = (w*h-2)/16;
+ __m128i offs = _mm_set1_epi16( 128 );
+ for( size_t i=0; i != blocked_loops; i++ ) {
+ __m128i result_register_lo;
+ __m128i result_register_hi;
+ __m128i i1_register;
+ __m128i i2_register;
+
+ i1_register = _mm_loadu_si128( (__m128i*)( i1 ) );
+ i2_register = _mm_loadu_si128( (__m128i*)( i2 ) );
+ result_register_lo = *i0;
+ i1_register = _mm_add_epi16( i1_register, i1_register );
+ result_register_lo = _mm_add_epi16( i1_register, result_register_lo );
+ result_register_lo = _mm_add_epi16( i2_register, result_register_lo );
+ result_register_lo = _mm_srai_epi16( result_register_lo, 2 );
+ result_register_lo = _mm_add_epi16( result_register_lo, offs );
+
+ i0++;
+ i1+=8;
+ i2+=8;
+
+ i1_register = _mm_loadu_si128( (__m128i*)( i1 ) );
+ i2_register = _mm_loadu_si128( (__m128i*)( i2 ) );
+ result_register_hi = *i0;
+ i1_register = _mm_add_epi16( i1_register, i1_register );
+ result_register_hi = _mm_add_epi16( i1_register, result_register_hi );
+ result_register_hi = _mm_add_epi16( i2_register, result_register_hi );
+ result_register_hi = _mm_srai_epi16( result_register_hi, 2 );
+ result_register_hi = _mm_add_epi16( result_register_hi, offs );
+
+ i0++;
+ i1+=8;
+ i2+=8;
+
+ pack_16bit_to_8bit_saturate( result_register_lo, result_register_hi, result_register_lo );
+ _mm_storeu_si128( ((__m128i*)( result )), result_register_lo );
+
+ result += 16;
+ }
+ }
+
+ // convolve image with a (1,0,-1) row vector. Result is accumulated into output.
+ // This one works on 16bit input and 8bit output.
+ // output is scaled by 1/4, then clamped to [-128,128], and finally shifted to [0,255].
+ void convolve_101_row_3x3_16bit( const int16_t* in, uint8_t* out, int w, int h ) {
+ assert( w % 16 == 0 && "width must be multiple of 16!" );
+ const __m128i* i0 = (const __m128i*)(in);
+ const int16_t* i2 = in+2;
+ uint8_t* result = out + 1;
+ const int16_t* const end_input = in + w*h;
+ const size_t blocked_loops = (w*h-2)/16;
+ __m128i offs = _mm_set1_epi16( 128 );
+ for( size_t i=0; i != blocked_loops; i++ ) {
+ __m128i result_register_lo;
+ __m128i result_register_hi;
+ __m128i i2_register;
+
+ i2_register = _mm_loadu_si128( (__m128i*)( i2 ) );
+ result_register_lo = *i0;
+ result_register_lo = _mm_sub_epi16( result_register_lo, i2_register );
+ result_register_lo = _mm_srai_epi16( result_register_lo, 2 );
+ result_register_lo = _mm_add_epi16( result_register_lo, offs );
+
+ i0 += 1;
+ i2 += 8;
+
+ i2_register = _mm_loadu_si128( (__m128i*)( i2 ) );
+ result_register_hi = *i0;
+ result_register_hi = _mm_sub_epi16( result_register_hi, i2_register );
+ result_register_hi = _mm_srai_epi16( result_register_hi, 2 );
+ result_register_hi = _mm_add_epi16( result_register_hi, offs );
+
+ i0 += 1;
+ i2 += 8;
+
+ pack_16bit_to_8bit_saturate( result_register_lo, result_register_hi, result_register_lo );
+ _mm_storeu_si128( ((__m128i*)( result )), result_register_lo );
+
+ result += 16;
+ }
+
+ for( ; i2 < end_input; i2++, result++) {
+ *result = ((*(i2-2) - *i2)>>2)+128;
+ }
+ }
+
+ void convolve_cols_5x5( const unsigned char* in, int16_t* out_v, int16_t* out_h, int w, int h ) {
+ using namespace std;
+ memset( out_h, 0, w*h*sizeof(int16_t) );
+ memset( out_v, 0, w*h*sizeof(int16_t) );
+ assert( w % 16 == 0 && "width must be multiple of 16!" );
+ const int w_chunk = w/16;
+ __m128i* i0 = (__m128i*)( in );
+ __m128i* i1 = (__m128i*)( in ) + w_chunk*1;
+ __m128i* i2 = (__m128i*)( in ) + w_chunk*2;
+ __m128i* i3 = (__m128i*)( in ) + w_chunk*3;
+ __m128i* i4 = (__m128i*)( in ) + w_chunk*4;
+ __m128i* result_h = (__m128i*)( out_h ) + 4*w_chunk;
+ __m128i* result_v = (__m128i*)( out_v ) + 4*w_chunk;
+ __m128i* end_input = (__m128i*)( in ) + w_chunk*h;
+ __m128i sixes = _mm_set1_epi16( 6 );
+ __m128i fours = _mm_set1_epi16( 4 );
+ for( ; i4 != end_input; i0++, i1++, i2++, i3++, i4++, result_v+=2, result_h+=2 ) {
+ __m128i ilo, ihi;
+ unpack_8bit_to_16bit( *i0, ihi, ilo );
+ *result_h = _mm_add_epi16( ihi, *result_h );
+ *(result_h+1) = _mm_add_epi16( ilo, *(result_h+1) );
+ *result_v = _mm_add_epi16( *result_v, ihi );
+ *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
+ unpack_8bit_to_16bit( *i1, ihi, ilo );
+ *result_h = _mm_add_epi16( ihi, *result_h );
+ *result_h = _mm_add_epi16( ihi, *result_h );
+ *(result_h+1) = _mm_add_epi16( ilo, *(result_h+1) );
+ *(result_h+1) = _mm_add_epi16( ilo, *(result_h+1) );
+ ihi = _mm_mullo_epi16( ihi, fours );
+ ilo = _mm_mullo_epi16( ilo, fours );
+ *result_v = _mm_add_epi16( *result_v, ihi );
+ *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
+ unpack_8bit_to_16bit( *i2, ihi, ilo );
+ ihi = _mm_mullo_epi16( ihi, sixes );
+ ilo = _mm_mullo_epi16( ilo, sixes );
+ *result_v = _mm_add_epi16( *result_v, ihi );
+ *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
+ unpack_8bit_to_16bit( *i3, ihi, ilo );
+ *result_h = _mm_sub_epi16( *result_h, ihi );
+ *result_h = _mm_sub_epi16( *result_h, ihi );
+ *(result_h+1) = _mm_sub_epi16( *(result_h+1), ilo );
+ *(result_h+1) = _mm_sub_epi16( *(result_h+1), ilo );
+ ihi = _mm_mullo_epi16( ihi, fours );
+ ilo = _mm_mullo_epi16( ilo, fours );
+ *result_v = _mm_add_epi16( *result_v, ihi );
+ *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
+ unpack_8bit_to_16bit( *i4, ihi, ilo );
+ *result_h = _mm_sub_epi16( *result_h, ihi );
+ *(result_h+1) = _mm_sub_epi16( *(result_h+1), ilo );
+ *result_v = _mm_add_epi16( *result_v, ihi );
+ *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
+ }
+ }
+
+ void convolve_col_p1p1p0m1m1_5x5( const unsigned char* in, int16_t* out, int w, int h ) {
+ memset( out, 0, w*h*sizeof(int16_t) );
+ using namespace std;
+ assert( w % 16 == 0 && "width must be multiple of 16!" );
+ const int w_chunk = w/16;
+ __m128i* i0 = (__m128i*)( in );
+ __m128i* i1 = (__m128i*)( in ) + w_chunk*1;
+ __m128i* i3 = (__m128i*)( in ) + w_chunk*3;
+ __m128i* i4 = (__m128i*)( in ) + w_chunk*4;
+ __m128i* result = (__m128i*)( out ) + 4*w_chunk;
+ __m128i* end_input = (__m128i*)( in ) + w_chunk*h;
+ for( ; i4 != end_input; i0++, i1++, i3++, i4++, result+=2 ) {
+ __m128i ilo0, ihi0;
+ unpack_8bit_to_16bit( *i0, ihi0, ilo0 );
+ __m128i ilo1, ihi1;
+ unpack_8bit_to_16bit( *i1, ihi1, ilo1 );
+ *result = _mm_add_epi16( ihi0, ihi1 );
+ *(result+1) = _mm_add_epi16( ilo0, ilo1 );
+ __m128i ilo, ihi;
+ unpack_8bit_to_16bit( *i3, ihi, ilo );
+ *result = _mm_sub_epi16( *result, ihi );
+ *(result+1) = _mm_sub_epi16( *(result+1), ilo );
+ unpack_8bit_to_16bit( *i4, ihi, ilo );
+ *result = _mm_sub_epi16( *result, ihi );
+ *(result+1) = _mm_sub_epi16( *(result+1), ilo );
+ }
+ }
+
+ void convolve_row_p1p1p0m1m1_5x5( const int16_t* in, int16_t* out, int w, int h ) {
+ assert( w % 16 == 0 && "width must be multiple of 16!" );
+ const __m128i* i0 = (const __m128i*)(in);
+ const int16_t* i1 = in+1;
+ const int16_t* i3 = in+3;
+ const int16_t* i4 = in+4;
+ int16_t* result = out + 2;
+ const int16_t* const end_input = in + w*h;
+ for( ; i4+8 < end_input; i0 += 1, i1 += 8, i3 += 8, i4 += 8, result += 8 ) {
+ __m128i result_register;
+ __m128i i0_register = *i0;
+ __m128i i1_register = _mm_loadu_si128( (__m128i*)( i1 ) );
+ __m128i i3_register = _mm_loadu_si128( (__m128i*)( i3 ) );
+ __m128i i4_register = _mm_loadu_si128( (__m128i*)( i4 ) );
+ result_register = _mm_add_epi16( i0_register, i1_register );
+ result_register = _mm_sub_epi16( result_register, i3_register );
+ result_register = _mm_sub_epi16( result_register, i4_register );
+ _mm_storeu_si128( ((__m128i*)( result )), result_register );
+ }
+ }
+
+ void convolve_cols_3x3( const unsigned char* in, int16_t* out_v, int16_t* out_h, int w, int h ) {
+ using namespace std;
+ assert( w % 16 == 0 && "width must be multiple of 16!" );
+ const int w_chunk = w/16;
+ __m128i* i0 = (__m128i*)( in );
+ __m128i* i1 = (__m128i*)( in ) + w_chunk*1;
+ __m128i* i2 = (__m128i*)( in ) + w_chunk*2;
+ __m128i* result_h = (__m128i*)( out_h ) + 2*w_chunk;
+ __m128i* result_v = (__m128i*)( out_v ) + 2*w_chunk;
+ __m128i* end_input = (__m128i*)( in ) + w_chunk*h;
+ for( ; i2 != end_input; i0++, i1++, i2++, result_v+=2, result_h+=2 ) {
+ *result_h = _mm_setzero_si128();
+ *(result_h+1) = _mm_setzero_si128();
+ *result_v = _mm_setzero_si128();
+ *(result_v+1) = _mm_setzero_si128();
+ __m128i ilo, ihi;
+ unpack_8bit_to_16bit( *i0, ihi, ilo );
+ unpack_8bit_to_16bit( *i0, ihi, ilo );
+ *result_h = _mm_add_epi16( ihi, *result_h );
+ *(result_h+1) = _mm_add_epi16( ilo, *(result_h+1) );
+ *result_v = _mm_add_epi16( *result_v, ihi );
+ *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
+ unpack_8bit_to_16bit( *i1, ihi, ilo );
+ *result_v = _mm_add_epi16( *result_v, ihi );
+ *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
+ *result_v = _mm_add_epi16( *result_v, ihi );
+ *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
+ unpack_8bit_to_16bit( *i2, ihi, ilo );
+ *result_h = _mm_sub_epi16( *result_h, ihi );
+ *(result_h+1) = _mm_sub_epi16( *(result_h+1), ilo );
+ *result_v = _mm_add_epi16( *result_v, ihi );
+ *(result_v+1) = _mm_add_epi16( *(result_v+1), ilo );
+ }
+ }
+ };
+
+ void sobel3x3( const uint8_t* in, uint8_t* out_v, uint8_t* out_h, int w, int h ) {
+ int16_t* temp_h = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
+ int16_t* temp_v = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
+ detail::convolve_cols_3x3( in, temp_v, temp_h, w, h );
+ detail::convolve_101_row_3x3_16bit( temp_v, out_v, w, h );
+ detail::convolve_121_row_3x3_16bit( temp_h, out_h, w, h );
+ _mm_free( temp_h );
+ _mm_free( temp_v );
+ }
+
+ void sobel5x5( const uint8_t* in, uint8_t* out_v, uint8_t* out_h, int w, int h ) {
+ int16_t* temp_h = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
+ int16_t* temp_v = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
+ detail::convolve_cols_5x5( in, temp_v, temp_h, w, h );
+ detail::convolve_12021_row_5x5_16bit( temp_v, out_v, w, h );
+ detail::convolve_14641_row_5x5_16bit( temp_h, out_h, w, h );
+ _mm_free( temp_h );
+ _mm_free( temp_v );
+ }
+
+ // -1 -1 0 1 1
+ // -1 -1 0 1 1
+ // 0 0 0 0 0
+ // 1 1 0 -1 -1
+ // 1 1 0 -1 -1
+ void checkerboard5x5( const uint8_t* in, int16_t* out, int w, int h ) {
+ int16_t* temp = (int16_t*)( _mm_malloc( w*h*sizeof( int16_t ), 16 ) );
+ detail::convolve_col_p1p1p0m1m1_5x5( in, temp, w, h );
+ detail::convolve_row_p1p1p0m1m1_5x5( temp, out, w, h );
+ _mm_free( temp );
+ }
+
+ // -1 -1 -1 -1 -1
+ // -1 1 1 1 -1
+ // -1 1 8 1 -1
+ // -1 1 1 1 -1
+ // -1 -1 -1 -1 -1
+ void blob5x5( const uint8_t* in, int16_t* out, int w, int h ) {
+ int32_t* integral = (int32_t*)( _mm_malloc( w*h*sizeof( int32_t ), 16 ) );
+ detail::integral_image( in, integral, w, h );
+ int16_t* out_ptr = out + 3 + 3*w;
+ int16_t* out_end = out + w * h - 2 - 2*w;
+ const int32_t* i00 = integral;
+ const int32_t* i50 = integral + 5;
+ const int32_t* i05 = integral + 5*w;
+ const int32_t* i55 = integral + 5 + 5*w;
+ const int32_t* i11 = integral + 1 + 1*w;
+ const int32_t* i41 = integral + 4 + 1*w;
+ const int32_t* i14 = integral + 1 + 4*w;
+ const int32_t* i44 = integral + 4 + 4*w;
+ const uint8_t* im22 = in + 3 + 3*w;
+ for( ; out_ptr != out_end; out_ptr++, i00++, i50++, i05++, i55++, i11++, i41++, i14++, i44++, im22++ ) {
+ int32_t result = 0;
+ result = -( *i55 - *i50 - *i05 + *i00 );
+ result += 2*( *i44 - *i41 - *i14 + *i11 );
+ result += 7* *im22;
+ *out_ptr = result;
+ }
+ _mm_free( integral );
+ }
+};
diff --git a/cv-node/lib/elas/filter.h b/cv-node/lib/elas/filter.h
new file mode 100644
index 0000000000000000000000000000000000000000..59af83ef06067dd9d4a3ee22184b2abf33938f17
--- /dev/null
+++ b/cv-node/lib/elas/filter.h
@@ -0,0 +1,99 @@
+/*
+Copyright 2011. All rights reserved.
+Institute of Measurement and Control Systems
+Karlsruhe Institute of Technology, Germany
+
+This file is part of libelas.
+Authors: Julius Ziegler, Andreas Geiger
+
+libelas is free software; you can redistribute it and/or modify it under the
+terms of the GNU General Public License as published by the Free Software
+Foundation; either version 3 of the License, or any later version.
+
+libelas is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+libelas; if not, write to the Free Software Foundation, Inc., 51 Franklin
+Street, Fifth Floor, Boston, MA 02110-1301, USA
+*/
+
+#ifndef __FILTER_H__
+#define __FILTER_H__
+
+#include <emmintrin.h>
+#include <pmmintrin.h>
+
+// define fixed-width datatypes for Visual Studio projects
+#ifndef _MSC_VER
+ #include <stdint.h>
+#else
+ typedef __int8 int8_t;
+ typedef __int16 int16_t;
+ typedef __int32 int32_t;
+ typedef __int64 int64_t;
+ typedef unsigned __int8 uint8_t;
+ typedef unsigned __int16 uint16_t;
+ typedef unsigned __int32 uint32_t;
+ typedef unsigned __int64 uint64_t;
+#endif
+
+// fast filters: implements 3x3 and 5x5 sobel filters and
+// 5x5 blob and corner filters based on SSE2/3 instructions
+namespace filter {
+
+ // private namespace, public user functions at the bottom of this file
+ namespace detail {
+ void integral_image( const uint8_t* in, int32_t* out, int w, int h );
+ void unpack_8bit_to_16bit( const __m128i a, __m128i& b0, __m128i& b1 );
+ void pack_16bit_to_8bit_saturate( const __m128i a0, const __m128i a1, __m128i& b );
+
+ // convolve image with a (1,4,6,4,1) row vector. Result is accumulated into output.
+ // output is scaled by 1/128, then clamped to [-128,128], and finally shifted to [0,255].
+ void convolve_14641_row_5x5_16bit( const int16_t* in, uint8_t* out, int w, int h );
+
+ // convolve image with a (1,2,0,-2,-1) row vector. Result is accumulated into output.
+ // This one works on 16bit input and 8bit output.
+ // output is scaled by 1/128, then clamped to [-128,128], and finally shifted to [0,255].
+ void convolve_12021_row_5x5_16bit( const int16_t* in, uint8_t* out, int w, int h );
+
+ // convolve image with a (1,2,1) row vector. Result is accumulated into output.
+ // This one works on 16bit input and 8bit output.
+ // output is scaled by 1/4, then clamped to [-128,128], and finally shifted to [0,255].
+ void convolve_121_row_3x3_16bit( const int16_t* in, uint8_t* out, int w, int h );
+
+ // convolve image with a (1,0,-1) row vector. Result is accumulated into output.
+ // This one works on 16bit input and 8bit output.
+ // output is scaled by 1/4, then clamped to [-128,128], and finally shifted to [0,255].
+ void convolve_101_row_3x3_16bit( const int16_t* in, uint8_t* out, int w, int h );
+
+ void convolve_cols_5x5( const unsigned char* in, int16_t* out_v, int16_t* out_h, int w, int h );
+
+ void convolve_col_p1p1p0m1m1_5x5( const unsigned char* in, int16_t* out, int w, int h );
+
+ void convolve_row_p1p1p0m1m1_5x5( const int16_t* in, int16_t* out, int w, int h );
+
+ void convolve_cols_3x3( const unsigned char* in, int16_t* out_v, int16_t* out_h, int w, int h );
+ }
+
+ void sobel3x3( const uint8_t* in, uint8_t* out_v, uint8_t* out_h, int w, int h );
+
+ void sobel5x5( const uint8_t* in, uint8_t* out_v, uint8_t* out_h, int w, int h );
+
+ // -1 -1 0 1 1
+ // -1 -1 0 1 1
+ // 0 0 0 0 0
+ // 1 1 0 -1 -1
+ // 1 1 0 -1 -1
+ void checkerboard5x5( const uint8_t* in, int16_t* out, int w, int h );
+
+ // -1 -1 -1 -1 -1
+ // -1 1 1 1 -1
+ // -1 1 8 1 -1
+ // -1 1 1 1 -1
+ // -1 -1 -1 -1 -1
+ void blob5x5( const uint8_t* in, int16_t* out, int w, int h );
+};
+
+#endif
diff --git a/cv-node/lib/elas/matrix.cpp b/cv-node/lib/elas/matrix.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..3201dd5b5ecd74eafcbb155eabc426d247120e77
--- /dev/null
+++ b/cv-node/lib/elas/matrix.cpp
@@ -0,0 +1,851 @@
+/*
+Copyright 2011. All rights reserved.
+Institute of Measurement and Control Systems
+Karlsruhe Institute of Technology, Germany
+
+This file is part of libviso2.
+Authors: Andreas Geiger
+
+libviso2 is free software; you can redistribute it and/or modify it under the
+terms of the GNU General Public License as published by the Free Software
+Foundation; either version 2 of the License, or any later version.
+
+libviso2 is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+libviso2; if not, write to the Free Software Foundation, Inc., 51 Franklin
+Street, Fifth Floor, Boston, MA 02110-1301, USA
+*/
+
+#include "matrix.h"
+#include <algorithm>
+#include <math.h>
+
+#define SWAP(a,b) {temp=a;a=b;b=temp;}
+#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
+static FLOAT sqrarg;
+#define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 : sqrarg*sqrarg)
+static FLOAT maxarg1,maxarg2;
+#define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1) > (maxarg2) ? (maxarg1) : (maxarg2))
+static int32_t iminarg1,iminarg2;
+#define IMIN(a,b) (iminarg1=(a),iminarg2=(b),(iminarg1) < (iminarg2) ? (iminarg1) : (iminarg2))
+
+
+using namespace std;
+
+Matrix::Matrix () {
+ m = 0;
+ n = 0;
+ val = 0;
+}
+
+Matrix::Matrix (const int32_t m_,const int32_t n_) {
+ allocateMemory(m_,n_);
+}
+
+Matrix::Matrix (const int32_t m_,const int32_t n_,const FLOAT* val_) {
+ allocateMemory(m_,n_);
+ int32_t k=0;
+ for (int32_t i=0; i<m_; i++)
+ for (int32_t j=0; j<n_; j++)
+ val[i][j] = val_[k++];
+}
+
+Matrix::Matrix (const Matrix &M) {
+ allocateMemory(M.m,M.n);
+ for (int32_t i=0; i<M.m; i++)
+ memcpy(val[i],M.val[i],M.n*sizeof(FLOAT));
+}
+
+Matrix::~Matrix () {
+ releaseMemory();
+}
+
+Matrix& Matrix::operator= (const Matrix &M) {
+ if (this!=&M) {
+ if (M.m!=m || M.n!=n) {
+ releaseMemory();
+ allocateMemory(M.m,M.n);
+ }
+ if (M.n>0)
+ for (int32_t i=0; i<M.m; i++)
+ memcpy(val[i],M.val[i],M.n*sizeof(FLOAT));
+ }
+ return *this;
+}
+
+void Matrix::getData(FLOAT* val_,int32_t i1,int32_t j1,int32_t i2,int32_t j2) {
+ if (i2==-1) i2 = m-1;
+ if (j2==-1) j2 = n-1;
+ int32_t k=0;
+ for (int32_t i=i1; i<=i2; i++)
+ for (int32_t j=j1; j<=j2; j++)
+ val_[k++] = val[i][j];
+}
+
+Matrix Matrix::getMat(int32_t i1,int32_t j1,int32_t i2,int32_t j2) {
+ if (i2==-1) i2 = m-1;
+ if (j2==-1) j2 = n-1;
+ if (i1<0 || i2>=m || j1<0 || j2>=n || i2<i1 || j2<j1) {
+ cerr << "ERROR: Cannot get submatrix [" << i1 << ".." << i2 <<
+ "] x [" << j1 << ".." << j2 << "]" <<
+ " of a (" << m << "x" << n << ") matrix." << endl;
+ exit(0);
+ }
+ Matrix M(i2-i1+1,j2-j1+1);
+ for (int32_t i=0; i<M.m; i++)
+ for (int32_t j=0; j<M.n; j++)
+ M.val[i][j] = val[i1+i][j1+j];
+ return M;
+}
+
+void Matrix::setMat(const Matrix &M,const int32_t i1,const int32_t j1) {
+ if (i1<0 || j1<0 || i1+M.m>m || j1+M.n>n) {
+ cerr << "ERROR: Cannot set submatrix [" << i1 << ".." << i1+M.m-1 <<
+ "] x [" << j1 << ".." << j1+M.n-1 << "]" <<
+ " of a (" << m << "x" << n << ") matrix." << endl;
+ exit(0);
+ }
+ for (int32_t i=0; i<M.m; i++)
+ for (int32_t j=0; j<M.n; j++)
+ val[i1+i][j1+j] = M.val[i][j];
+}
+
+void Matrix::setVal(FLOAT s,int32_t i1,int32_t j1,int32_t i2,int32_t j2) {
+ if (i2==-1) i2 = m-1;
+ if (j2==-1) j2 = n-1;
+ if (i2<i1 || j2<j1) {
+ cerr << "ERROR in setVal: Indices must be ordered (i1<=i2, j1<=j2)." << endl;
+ exit(0);
+ }
+ for (int32_t i=i1; i<=i2; i++)
+ for (int32_t j=j1; j<=j2; j++)
+ val[i][j] = s;
+}
+
+void Matrix::setDiag(FLOAT s,int32_t i1,int32_t i2) {
+ if (i2==-1) i2 = min(m-1,n-1);
+ for (int32_t i=i1; i<=i2; i++)
+ val[i][i] = s;
+}
+
+void Matrix::zero() {
+ setVal(0);
+}
+
+Matrix Matrix::extractCols (vector<int> idx) {
+ Matrix M(m,idx.size());
+ for (int32_t j=0; j<M.n; j++)
+ if (idx[j]<n)
+ for (int32_t i=0; i<m; i++)
+ M.val[i][j] = val[i][idx[j]];
+ return M;
+}
+
+Matrix Matrix::eye (const int32_t m) {
+ Matrix M(m,m);
+ for (int32_t i=0; i<m; i++)
+ M.val[i][i] = 1;
+ return M;
+}
+
+void Matrix::eye () {
+ for (int32_t i=0; i<m; i++)
+ for (int32_t j=0; j<n; j++)
+ val[i][j] = 0;
+ for (int32_t i=0; i<min(m,n); i++)
+ val[i][i] = 1;
+}
+
+Matrix Matrix::diag (const Matrix &M) {
+ if (M.m>1 && M.n==1) {
+ Matrix D(M.m,M.m);
+ for (int32_t i=0; i<M.m; i++)
+ D.val[i][i] = M.val[i][0];
+ return D;
+ } else if (M.m==1 && M.n>1) {
+ Matrix D(M.n,M.n);
+ for (int32_t i=0; i<M.n; i++)
+ D.val[i][i] = M.val[0][i];
+ return D;
+ }
+ cout << "ERROR: Trying to create diagonal matrix from vector of size (" << M.m << "x" << M.n << ")" << endl;
+ exit(0);
+}
+
+Matrix Matrix::reshape(const Matrix &M,int32_t m_,int32_t n_) {
+ if (M.m*M.n != m_*n_) {
+ cerr << "ERROR: Trying to reshape a matrix of size (" << M.m << "x" << M.n <<
+ ") to size (" << m_ << "x" << n_ << ")" << endl;
+ exit(0);
+ }
+ Matrix M2(m_,n_);
+ for (int32_t k=0; k<m_*n_; k++) {
+ int32_t i1 = k/M.n;
+ int32_t j1 = k%M.n;
+ int32_t i2 = k/n_;
+ int32_t j2 = k%n_;
+ M2.val[i2][j2] = M.val[i1][j1];
+ }
+ return M2;
+}
+
+Matrix Matrix::rotMatX (const FLOAT &angle) {
+ FLOAT s = sin(angle);
+ FLOAT c = cos(angle);
+ Matrix R(3,3);
+ R.val[0][0] = +1;
+ R.val[1][1] = +c;
+ R.val[1][2] = -s;
+ R.val[2][1] = +s;
+ R.val[2][2] = +c;
+ return R;
+}
+
+Matrix Matrix::rotMatY (const FLOAT &angle) {
+ FLOAT s = sin(angle);
+ FLOAT c = cos(angle);
+ Matrix R(3,3);
+ R.val[0][0] = +c;
+ R.val[0][2] = +s;
+ R.val[1][1] = +1;
+ R.val[2][0] = -s;
+ R.val[2][2] = +c;
+ return R;
+}
+
+Matrix Matrix::rotMatZ (const FLOAT &angle) {
+ FLOAT s = sin(angle);
+ FLOAT c = cos(angle);
+ Matrix R(3,3);
+ R.val[0][0] = +c;
+ R.val[0][1] = -s;
+ R.val[1][0] = +s;
+ R.val[1][1] = +c;
+ R.val[2][2] = +1;
+ return R;
+}
+
+Matrix Matrix::operator+ (const Matrix &M) {
+ const Matrix &A = *this;
+ const Matrix &B = M;
+ if (A.m!=B.m || A.n!=B.n) {
+ cerr << "ERROR: Trying to add matrices of size (" << A.m << "x" << A.n <<
+ ") and (" << B.m << "x" << B.n << ")" << endl;
+ exit(0);
+ }
+ Matrix C(A.m,A.n);
+ for (int32_t i=0; i<m; i++)
+ for (int32_t j=0; j<n; j++)
+ C.val[i][j] = A.val[i][j]+B.val[i][j];
+ return C;
+}
+
+Matrix Matrix::operator- (const Matrix &M) {
+ const Matrix &A = *this;
+ const Matrix &B = M;
+ if (A.m!=B.m || A.n!=B.n) {
+ cerr << "ERROR: Trying to subtract matrices of size (" << A.m << "x" << A.n <<
+ ") and (" << B.m << "x" << B.n << ")" << endl;
+ exit(0);
+ }
+ Matrix C(A.m,A.n);
+ for (int32_t i=0; i<m; i++)
+ for (int32_t j=0; j<n; j++)
+ C.val[i][j] = A.val[i][j]-B.val[i][j];
+ return C;
+}
+
+Matrix Matrix::operator* (const Matrix &M) {
+ const Matrix &A = *this;
+ const Matrix &B = M;
+ if (A.n!=B.m) {
+ cerr << "ERROR: Trying to multiply matrices of size (" << A.m << "x" << A.n <<
+ ") and (" << B.m << "x" << B.n << ")" << endl;
+ exit(0);
+ }
+ Matrix C(A.m,B.n);
+ for (int32_t i=0; i<A.m; i++)
+ for (int32_t j=0; j<B.n; j++)
+ for (int32_t k=0; k<A.n; k++)
+ C.val[i][j] += A.val[i][k]*B.val[k][j];
+ return C;
+}
+
+Matrix Matrix::operator* (const FLOAT &s) {
+ Matrix C(m,n);
+ for (int32_t i=0; i<m; i++)
+ for (int32_t j=0; j<n; j++)
+ C.val[i][j] = val[i][j]*s;
+ return C;
+}
+
+Matrix Matrix::operator/ (const Matrix &M) {
+ const Matrix &A = *this;
+ const Matrix &B = M;
+
+ if (A.m==B.m && A.n==B.n) {
+ Matrix C(A.m,A.n);
+ for (int32_t i=0; i<A.m; i++)
+ for (int32_t j=0; j<A.n; j++)
+ if (B.val[i][j]!=0)
+ C.val[i][j] = A.val[i][j]/B.val[i][j];
+ return C;
+
+ } else if (A.m==B.m && B.n==1) {
+ Matrix C(A.m,A.n);
+ for (int32_t i=0; i<A.m; i++)
+ for (int32_t j=0; j<A.n; j++)
+ if (B.val[i][0]!=0)
+ C.val[i][j] = A.val[i][j]/B.val[i][0];
+ return C;
+
+ } else if (A.n==B.n && B.m==1) {
+ Matrix C(A.m,A.n);
+ for (int32_t i=0; i<A.m; i++)
+ for (int32_t j=0; j<A.n; j++)
+ if (B.val[0][j]!=0)
+ C.val[i][j] = A.val[i][j]/B.val[0][j];
+ return C;
+
+ } else {
+ cerr << "ERROR: Trying to divide matrices of size (" << A.m << "x" << A.n <<
+ ") and (" << B.m << "x" << B.n << ")" << endl;
+ exit(0);
+ }
+}
+
+Matrix Matrix::operator/ (const FLOAT &s) {
+ if (fabs(s)<1e-20) {
+ cerr << "ERROR: Trying to divide by zero!" << endl;
+ exit(0);
+ }
+ Matrix C(m,n);
+ for (int32_t i=0; i<m; i++)
+ for (int32_t j=0; j<n; j++)
+ C.val[i][j] = val[i][j]/s;
+ return C;
+}
+
+Matrix Matrix::operator- () {
+ Matrix C(m,n);
+ for (int32_t i=0; i<m; i++)
+ for (int32_t j=0; j<n; j++)
+ C.val[i][j] = -val[i][j];
+ return C;
+}
+
+Matrix Matrix::operator~ () {
+ Matrix C(n,m);
+ for (int32_t i=0; i<m; i++)
+ for (int32_t j=0; j<n; j++)
+ C.val[j][i] = val[i][j];
+ return C;
+}
+
+FLOAT Matrix::l2norm () {
+ FLOAT norm = 0;
+ for (int32_t i=0; i<m; i++)
+ for (int32_t j=0; j<n; j++)
+ norm += val[i][j]*val[i][j];
+ return sqrt(norm);
+}
+
+FLOAT Matrix::mean () {
+ FLOAT mean = 0;
+ for (int32_t i=0; i<m; i++)
+ for (int32_t j=0; j<n; j++)
+ mean += val[i][j];
+ return mean/(FLOAT)(m*n);
+}
+
+Matrix Matrix::cross (const Matrix &a, const Matrix &b) {
+ if (a.m!=3 || a.n!=1 || b.m!=3 || b.n!=1) {
+ cerr << "ERROR: Cross product vectors must be of size (3x1)" << endl;
+ exit(0);
+ }
+ Matrix c(3,1);
+ c.val[0][0] = a.val[1][0]*b.val[2][0]-a.val[2][0]*b.val[1][0];
+ c.val[1][0] = a.val[2][0]*b.val[0][0]-a.val[0][0]*b.val[2][0];
+ c.val[2][0] = a.val[0][0]*b.val[1][0]-a.val[1][0]*b.val[0][0];
+ return c;
+}
+
+Matrix Matrix::inv (const Matrix &M) {
+ if (M.m!=M.n) {
+ cerr << "ERROR: Trying to invert matrix of size (" << M.m << "x" << M.n << ")" << endl;
+ exit(0);
+ }
+ Matrix A(M);
+ Matrix B = eye(M.m);
+ B.solve(A);
+ return B;
+}
+
+bool Matrix::inv () {
+ if (m!=n) {
+ cerr << "ERROR: Trying to invert matrix of size (" << m << "x" << n << ")" << endl;
+ exit(0);
+ }
+ Matrix A(*this);
+ eye();
+ solve(A);
+ return true;
+}
+
+FLOAT Matrix::det () {
+
+ if (m != n) {
+ cerr << "ERROR: Trying to compute determinant of a matrix of size (" << m << "x" << n << ")" << endl;
+ exit(0);
+ }
+
+ Matrix A(*this);
+ int32_t *idx = (int32_t*)malloc(m*sizeof(int32_t));
+ FLOAT d;
+ A.lu(idx,d);
+ for( int32_t i=0; i<m; i++)
+ d *= A.val[i][i];
+ free(idx);
+}
+
+bool Matrix::solve (const Matrix &M, FLOAT eps) {
+
+ // substitutes
+ const Matrix &A = M;
+ Matrix &B = *this;
+
+ if (A.m != A.n || A.m != B.m || A.m<1 || B.n<1) {
+ cerr << "ERROR: Trying to eliminate matrices of size (" << A.m << "x" << A.n <<
+ ") and (" << B.m << "x" << B.n << ")" << endl;
+ exit(0);
+ }
+
+ // index vectors for bookkeeping on the pivoting
+ int32_t* indxc = new int32_t[m];
+ int32_t* indxr = new int32_t[m];
+ int32_t* ipiv = new int32_t[m];
+
+ // loop variables
+ int32_t i, icol, irow, j, k, l, ll;
+ FLOAT big, dum, pivinv, temp;
+
+ // initialize pivots to zero
+ for (j=0;j<m;j++) ipiv[j]=0;
+
+ // main loop over the columns to be reduced
+ for (i=0;i<m;i++) {
+
+ big=0.0;
+
+ // search for a pivot element
+ for (j=0;j<m;j++)
+ if (ipiv[j]!=1)
+ for (k=0;k<m;k++)
+ if (ipiv[k]==0)
+ if (fabs(A.val[j][k])>=big) {
+ big=fabs(A.val[j][k]);
+ irow=j;
+ icol=k;
+ }
+ ++(ipiv[icol]);
+
+ // We now have the pivot element, so we interchange rows, if needed, to put the pivot
+ // element on the diagonal. The columns are not physically interchanged, only relabeled.
+ if (irow != icol) {
+ for (l=0;l<m;l++) SWAP(A.val[irow][l], A.val[icol][l])
+ for (l=0;l<n;l++) SWAP(B.val[irow][l], B.val[icol][l])
+ }
+
+ indxr[i]=irow; // We are now ready to divide the pivot row by the
+ indxc[i]=icol; // pivot element, located at irow and icol.
+
+ // check for singularity
+ if (fabs(A.val[icol][icol]) < eps) {
+ delete[] indxc;
+ delete[] indxr;
+ delete[] ipiv;
+ return false;
+ }
+
+ pivinv=1.0/A.val[icol][icol];
+ A.val[icol][icol]=1.0;
+ for (l=0;l<m;l++) A.val[icol][l] *= pivinv;
+ for (l=0;l<n;l++) B.val[icol][l] *= pivinv;
+
+ // Next, we reduce the rows except for the pivot one
+ for (ll=0;ll<m;ll++)
+ if (ll!=icol) {
+ dum = A.val[ll][icol];
+ A.val[ll][icol] = 0.0;
+ for (l=0;l<m;l++) A.val[ll][l] -= A.val[icol][l]*dum;
+ for (l=0;l<n;l++) B.val[ll][l] -= B.val[icol][l]*dum;
+ }
+ }
+
+ // This is the end of the main loop over columns of the reduction. It only remains to unscramble
+ // the solution in view of the column interchanges. We do this by interchanging pairs of
+ // columns in the reverse order that the permutation was built up.
+ for (l=m-1;l>=0;l--) {
+ if (indxr[l]!=indxc[l])
+ for (k=0;k<m;k++)
+ SWAP(A.val[k][indxr[l]], A.val[k][indxc[l]])
+ }
+
+ // success
+ delete[] indxc;
+ delete[] indxr;
+ delete[] ipiv;
+ return true;
+}
+
+// Given a matrix a[1..n][1..n], this routine replaces it by the LU decomposition of a rowwise
+// permutation of itself. a and n are input. a is output, arranged as in equation (2.3.14) above;
+// indx[1..n] is an output vector that records the row permutation effected by the partial
+// pivoting; d is output as ±1 depending on whether the number of row interchanges was even
+// or odd, respectively. This routine is used in combination with lubksb to solve linear equations
+// or invert a matrix.
+
+bool Matrix::lu(int32_t *idx, FLOAT &d, FLOAT eps) {
+
+ if (m != n) {
+ cerr << "ERROR: Trying to LU decompose a matrix of size (" << m << "x" << n << ")" << endl;
+ exit(0);
+ }
+
+ int32_t i,imax,j,k;
+ FLOAT big,dum,sum,temp;
+ FLOAT* vv = (FLOAT*)malloc(n*sizeof(FLOAT)); // vv stores the implicit scaling of each row.
+ d = 1.0;
+ for (i=0; i<n; i++) { // Loop over rows to get the implicit scaling information.
+ big = 0.0;
+ for (j=0; j<n; j++)
+ if ((temp=fabs(val[i][j]))>big)
+ big = temp;
+ if (big == 0.0) { // No nonzero largest element.
+ free(vv);
+ return false;
+ }
+ vv[i] = 1.0/big; // Save the scaling.
+ }
+ for (j=0; j<n; j++) { // This is the loop over columns of Crout’s method.
+ for (i=0; i<j; i++) { // This is equation (2.3.12) except for i = j.
+ sum = val[i][j];
+ for (k=0; k<i; k++)
+ sum -= val[i][k]*val[k][j];
+ val[i][j] = sum;
+ }
+ big = 0.0; // Initialize the search for largest pivot element.
+ for (i=j; i<n; i++) {
+ sum = val[i][j];
+ for (k=0; k<j; k++)
+ sum -= val[i][k]*val[k][j];
+ val[i][j] = sum;
+ if ( (dum=vv[i]*fabs(sum))>=big) {
+ big = dum;
+ imax = i;
+ }
+ }
+ if (j!=imax) { // Do we need to interchange rows?
+ for (k=0; k<n; k++) { // Yes, do so...
+ dum = val[imax][k];
+ val[imax][k] = val[j][k];
+ val[j][k] = dum;
+ }
+ d = -d; // ...and change the parity of d.
+ vv[imax]=vv[j]; // Also interchange the scale factor.
+ }
+ idx[j] = imax;
+ if (j!=n-1) { // Now, finally, divide by the pivot element.
+ dum = 1.0/val[j][j];
+ for (i=j+1; i<n; i++)
+ val[i][j] *= dum;
+ }
+ } // Go back for the next column in the reduction.
+
+ // success
+ free(vv);
+ return true;
+}
+
+// Given a matrix M/A[1..m][1..n], this routine computes its singular value decomposition, M/A =
+// U·W·V T. Thematrix U replaces a on output. The diagonal matrix of singular values W is output
+// as a vector w[1..n]. Thematrix V (not the transpose V T ) is output as v[1..n][1..n].
+void Matrix::svd(Matrix &U2,Matrix &W,Matrix &V) {
+
+ Matrix U = Matrix(*this);
+ U2 = Matrix(m,m);
+ V = Matrix(n,n);
+
+ FLOAT* w = (FLOAT*)malloc(n*sizeof(FLOAT));
+ FLOAT* rv1 = (FLOAT*)malloc(n*sizeof(FLOAT));
+
+ int32_t flag,i,its,j,jj,k,l,nm;
+ FLOAT anorm,c,f,g,h,s,scale,x,y,z;
+
+ g = scale = anorm = 0.0; // Householder reduction to bidiagonal form.
+ for (i=0;i<n;i++) {
+ l = i+1;
+ rv1[i] = scale*g;
+ g = s = scale = 0.0;
+ if (i < m) {
+ for (k=i;k<m;k++) scale += fabs(U.val[k][i]);
+ if (scale) {
+ for (k=i;k<m;k++) {
+ U.val[k][i] /= scale;
+ s += U.val[k][i]*U.val[k][i];
+ }
+ f = U.val[i][i];
+ g = -SIGN(sqrt(s),f);
+ h = f*g-s;
+ U.val[i][i] = f-g;
+ for (j=l;j<n;j++) {
+ for (s=0.0,k=i;k<m;k++) s += U.val[k][i]*U.val[k][j];
+ f = s/h;
+ for (k=i;k<m;k++) U.val[k][j] += f*U.val[k][i];
+ }
+ for (k=i;k<m;k++) U.val[k][i] *= scale;
+ }
+ }
+ w[i] = scale*g;
+ g = s = scale = 0.0;
+ if (i<m && i!=n-1) {
+ for (k=l;k<n;k++) scale += fabs(U.val[i][k]);
+ if (scale) {
+ for (k=l;k<n;k++) {
+ U.val[i][k] /= scale;
+ s += U.val[i][k]*U.val[i][k];
+ }
+ f = U.val[i][l];
+ g = -SIGN(sqrt(s),f);
+ h = f*g-s;
+ U.val[i][l] = f-g;
+ for (k=l;k<n;k++) rv1[k] = U.val[i][k]/h;
+ for (j=l;j<m;j++) {
+ for (s=0.0,k=l;k<n;k++) s += U.val[j][k]*U.val[i][k];
+ for (k=l;k<n;k++) U.val[j][k] += s*rv1[k];
+ }
+ for (k=l;k<n;k++) U.val[i][k] *= scale;
+ }
+ }
+ anorm = FMAX(anorm,(fabs(w[i])+fabs(rv1[i])));
+ }
+ for (i=n-1;i>=0;i--) { // Accumulation of right-hand transformations.
+ if (i<n-1) {
+ if (g) {
+ for (j=l;j<n;j++) // Double division to avoid possible underflow.
+ V.val[j][i]=(U.val[i][j]/U.val[i][l])/g;
+ for (j=l;j<n;j++) {
+ for (s=0.0,k=l;k<n;k++) s += U.val[i][k]*V.val[k][j];
+ for (k=l;k<n;k++) V.val[k][j] += s*V.val[k][i];
+ }
+ }
+ for (j=l;j<n;j++) V.val[i][j] = V.val[j][i] = 0.0;
+ }
+ V.val[i][i] = 1.0;
+ g = rv1[i];
+ l = i;
+ }
+ for (i=IMIN(m,n)-1;i>=0;i--) { // Accumulation of left-hand transformations.
+ l = i+1;
+ g = w[i];
+ for (j=l;j<n;j++) U.val[i][j] = 0.0;
+ if (g) {
+ g = 1.0/g;
+ for (j=l;j<n;j++) {
+ for (s=0.0,k=l;k<m;k++) s += U.val[k][i]*U.val[k][j];
+ f = (s/U.val[i][i])*g;
+ for (k=i;k<m;k++) U.val[k][j] += f*U.val[k][i];
+ }
+ for (j=i;j<m;j++) U.val[j][i] *= g;
+ } else for (j=i;j<m;j++) U.val[j][i]=0.0;
+ ++U.val[i][i];
+ }
+ for (k=n-1;k>=0;k--) { // Diagonalization of the bidiagonal form: Loop over singular values,
+ for (its=0;its<30;its++) { // and over allowed iterations.
+ flag = 1;
+ for (l=k;l>=0;l--) { // Test for splitting.
+ nm = l-1;
+ if ((FLOAT)(fabs(rv1[l])+anorm) == anorm) { flag = 0; break; }
+ if ((FLOAT)(fabs( w[nm])+anorm) == anorm) { break; }
+ }
+ if (flag) {
+ c = 0.0; // Cancellation of rv1[l], if l > 1.
+ s = 1.0;
+ for (i=l;i<=k;i++) {
+ f = s*rv1[i];
+ rv1[i] = c*rv1[i];
+ if ((FLOAT)(fabs(f)+anorm) == anorm) break;
+ g = w[i];
+ h = pythag(f,g);
+ w[i] = h;
+ h = 1.0/h;
+ c = g*h;
+ s = -f*h;
+ for (j=0;j<m;j++) {
+ y = U.val[j][nm];
+ z = U.val[j][i];
+ U.val[j][nm] = y*c+z*s;
+ U.val[j][i] = z*c-y*s;
+ }
+ }
+ }
+ z = w[k];
+ if (l==k) { // Convergence.
+ if (z<0.0) { // Singular value is made nonnegative.
+ w[k] = -z;
+ for (j=0;j<n;j++) V.val[j][k] = -V.val[j][k];
+ }
+ break;
+ }
+ if (its == 29)
+ cerr << "ERROR in SVD: No convergence in 30 iterations" << endl;
+ x = w[l]; // Shift from bottom 2-by-2 minor.
+ nm = k-1;
+ y = w[nm];
+ g = rv1[nm];
+ h = rv1[k];
+ f = ((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
+ g = pythag(f,1.0);
+ f = ((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
+ c = s = 1.0; // Next QR transformation:
+ for (j=l;j<=nm;j++) {
+ i = j+1;
+ g = rv1[i];
+ y = w[i];
+ h = s*g;
+ g = c*g;
+ z = pythag(f,h);
+ rv1[j] = z;
+ c = f/z;
+ s = h/z;
+ f = x*c+g*s;
+ g = g*c-x*s;
+ h = y*s;
+ y *= c;
+ for (jj=0;jj<n;jj++) {
+ x = V.val[jj][j];
+ z = V.val[jj][i];
+ V.val[jj][j] = x*c+z*s;
+ V.val[jj][i] = z*c-x*s;
+ }
+ z = pythag(f,h);
+ w[j] = z; // Rotation can be arbitrary if z = 0.
+ if (z) {
+ z = 1.0/z;
+ c = f*z;
+ s = h*z;
+ }
+ f = c*g+s*y;
+ x = c*y-s*g;
+ for (jj=0;jj<m;jj++) {
+ y = U.val[jj][j];
+ z = U.val[jj][i];
+ U.val[jj][j] = y*c+z*s;
+ U.val[jj][i] = z*c-y*s;
+ }
+ }
+ rv1[l] = 0.0;
+ rv1[k] = f;
+ w[k] = x;
+ }
+ }
+
+ // sort singular values and corresponding columns of u and v
+ // by decreasing magnitude. Also, signs of corresponding columns are
+ // flipped so as to maximize the number of positive elements.
+ int32_t s2,inc=1;
+ FLOAT sw;
+ FLOAT* su = (FLOAT*)malloc(m*sizeof(FLOAT));
+ FLOAT* sv = (FLOAT*)malloc(n*sizeof(FLOAT));
+ do { inc *= 3; inc++; } while (inc <= n);
+ do {
+ inc /= 3;
+ for (i=inc;i<n;i++) {
+ sw = w[i];
+ for (k=0;k<m;k++) su[k] = U.val[k][i];
+ for (k=0;k<n;k++) sv[k] = V.val[k][i];
+ j = i;
+ while (w[j-inc] < sw) {
+ w[j] = w[j-inc];
+ for (k=0;k<m;k++) U.val[k][j] = U.val[k][j-inc];
+ for (k=0;k<n;k++) V.val[k][j] = V.val[k][j-inc];
+ j -= inc;
+ if (j < inc) break;
+ }
+ w[j] = sw;
+ for (k=0;k<m;k++) U.val[k][j] = su[k];
+ for (k=0;k<n;k++) V.val[k][j] = sv[k];
+ }
+ } while (inc > 1);
+ for (k=0;k<n;k++) { // flip signs
+ s2=0;
+ for (i=0;i<m;i++) if (U.val[i][k] < 0.0) s2++;
+ for (j=0;j<n;j++) if (V.val[j][k] < 0.0) s2++;
+ if (s2 > (m+n)/2) {
+ for (i=0;i<m;i++) U.val[i][k] = -U.val[i][k];
+ for (j=0;j<n;j++) V.val[j][k] = -V.val[j][k];
+ }
+ }
+
+ // create vector and copy singular values
+ W = Matrix(min(m,n),1,w);
+
+ // extract mxm submatrix U
+ U2.setMat(U.getMat(0,0,m-1,min(m-1,n-1)),0,0);
+
+ // release temporary memory
+ free(w);
+ free(rv1);
+ free(su);
+ free(sv);
+}
+
+ostream& operator<< (ostream& out,const Matrix& M) {
+ if (M.m==0 || M.n==0) {
+ out << "[empty matrix]";
+ } else {
+ char buffer[1024];
+ for (int32_t i=0; i<M.m; i++) {
+ for (int32_t j=0; j<M.n; j++) {
+ sprintf(buffer,"%12.7f ",M.val[i][j]);
+ out << buffer;
+ }
+ if (i<M.m-1)
+ out << endl;
+ }
+ }
+ return out;
+}
+
+void Matrix::allocateMemory (const int32_t m_,const int32_t n_) {
+ m = abs(m_); n = abs(n_);
+ if (m==0 || n==0) {
+ val = 0;
+ return;
+ }
+ val = (FLOAT**)malloc(m*sizeof(FLOAT*));
+ val[0] = (FLOAT*)calloc(m*n,sizeof(FLOAT));
+ for(int32_t i=1; i<m; i++)
+ val[i] = val[i-1]+n;
+}
+
+void Matrix::releaseMemory () {
+ if (val!=0) {
+ free(val[0]);
+ free(val);
+ }
+}
+
+FLOAT Matrix::pythag(FLOAT a,FLOAT b) {
+ FLOAT absa,absb;
+ absa = fabs(a);
+ absb = fabs(b);
+ if (absa > absb)
+ return absa*sqrt(1.0+SQR(absb/absa));
+ else
+ return (absb == 0.0 ? 0.0 : absb*sqrt(1.0+SQR(absa/absb)));
+}
+
diff --git a/cv-node/lib/elas/matrix.h b/cv-node/lib/elas/matrix.h
new file mode 100644
index 0000000000000000000000000000000000000000..5ec306cf193450fc14d03ead87d6ec444a3d8f3e
--- /dev/null
+++ b/cv-node/lib/elas/matrix.h
@@ -0,0 +1,133 @@
+/*
+Copyright 2011. All rights reserved.
+Institute of Measurement and Control Systems
+Karlsruhe Institute of Technology, Germany
+
+This file is part of libviso2.
+Authors: Andreas Geiger
+
+libviso2 is free software; you can redistribute it and/or modify it under the
+terms of the GNU General Public License as published by the Free Software
+Foundation; either version 2 of the License, or any later version.
+
+libviso2 is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+libviso2; if not, write to the Free Software Foundation, Inc., 51 Franklin
+Street, Fifth Floor, Boston, MA 02110-1301, USA
+*/
+
+#ifndef MATRIX_H
+#define MATRIX_H
+
+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+#include <iostream>
+#include <vector>
+
+#ifndef _MSC_VER
+ #include <stdint.h>
+#else
+ typedef __int8 int8_t;
+ typedef __int16 int16_t;
+ typedef __int32 int32_t;
+ typedef __int64 int64_t;
+ typedef unsigned __int8 uint8_t;
+ typedef unsigned __int16 uint16_t;
+ typedef unsigned __int32 uint32_t;
+ typedef unsigned __int64 uint64_t;
+#endif
+
+#define endll endl << endl // double end line definition
+
+typedef double FLOAT; // double precision
+//typedef float FLOAT; // single precision
+
+class Matrix {
+
+public:
+
+ // constructor / deconstructor
+ Matrix (); // init empty 0x0 matrix
+ Matrix (const int32_t m,const int32_t n); // init empty mxn matrix
+ Matrix (const int32_t m,const int32_t n,const FLOAT* val_); // init mxn matrix with values from array 'val'
+ Matrix (const Matrix &M); // creates deepcopy of M
+ ~Matrix ();
+
+ // assignment operator, copies contents of M
+ Matrix& operator= (const Matrix &M);
+
+ // copies submatrix of M into array 'val', default values copy whole row/column/matrix
+ void getData(FLOAT* val_,int32_t i1=0,int32_t j1=0,int32_t i2=-1,int32_t j2=-1);
+
+ // set or get submatrices of current matrix
+ Matrix getMat(int32_t i1,int32_t j1,int32_t i2=-1,int32_t j2=-1);
+ void setMat(const Matrix &M,const int32_t i,const int32_t j);
+
+ // set sub-matrix to scalar (default 0), -1 as end replaces whole row/column/matrix
+ void setVal(FLOAT s,int32_t i1=0,int32_t j1=0,int32_t i2=-1,int32_t j2=-1);
+
+ // set (part of) diagonal to scalar, -1 as end replaces whole diagonal
+ void setDiag(FLOAT s,int32_t i1=0,int32_t i2=-1);
+
+ // clear matrix
+ void zero();
+
+ // extract columns with given index
+ Matrix extractCols (std::vector<int> idx);
+
+ // create identity matrix
+ static Matrix eye (const int32_t m);
+ void eye ();
+
+ // create diagonal matrix with nx1 or 1xn matrix M as elements
+ static Matrix diag(const Matrix &M);
+
+ // returns the m-by-n matrix whose elements are taken column-wise from M
+ static Matrix reshape(const Matrix &M,int32_t m,int32_t n);
+
+ // create 3x3 rotation matrices (convention: http://en.wikipedia.org/wiki/Rotation_matrix)
+ static Matrix rotMatX(const FLOAT &angle);
+ static Matrix rotMatY(const FLOAT &angle);
+ static Matrix rotMatZ(const FLOAT &angle);
+
+ // simple arithmetic operations
+ Matrix operator+ (const Matrix &M); // add matrix
+ Matrix operator- (const Matrix &M); // subtract matrix
+ Matrix operator* (const Matrix &M); // multiply with matrix
+ Matrix operator* (const FLOAT &s); // multiply with scalar
+ Matrix operator/ (const Matrix &M); // divide elementwise by matrix (or vector)
+ Matrix operator/ (const FLOAT &s); // divide by scalar
+ Matrix operator- (); // negative matrix
+ Matrix operator~ (); // transpose
+ FLOAT l2norm (); // euclidean norm (vectors) / frobenius norm (matrices)
+ FLOAT mean (); // mean of all elements in matrix
+
+ // complex arithmetic operations
+ static Matrix cross (const Matrix &a, const Matrix &b); // cross product of two vectors
+ static Matrix inv (const Matrix &M); // invert matrix M
+ bool inv (); // invert this matrix
+ FLOAT det (); // returns determinant of matrix
+ bool solve (const Matrix &M,FLOAT eps=1e-20); // solve linear system M*x=B, replaces *this and M
+ bool lu(int32_t *idx, FLOAT &d, FLOAT eps=1e-20); // replace *this by lower upper decomposition
+ void svd(Matrix &U,Matrix &W,Matrix &V); // singular value decomposition *this = U*diag(W)*V^T
+
+ // print matrix to stream
+ friend std::ostream& operator<< (std::ostream& out,const Matrix& M);
+
+ // direct data access
+ FLOAT **val;
+ int32_t m,n;
+
+private:
+
+ void allocateMemory (const int32_t m_,const int32_t n_);
+ void releaseMemory ();
+ inline FLOAT pythag(FLOAT a,FLOAT b);
+
+};
+
+#endif // MATRIX_H
diff --git a/cv-node/lib/elas/triangle.cpp b/cv-node/lib/elas/triangle.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..8de1557bc5c7192530d4594c03d0ef9e90eef72c
--- /dev/null
+++ b/cv-node/lib/elas/triangle.cpp
@@ -0,0 +1,8635 @@
+/*****************************************************************************/
+/* */
+/* 888888888 ,o, / 888 */
+/* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */
+/* 888 888 888 88b 888 888 888 888 888 d888 88b */
+/* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */
+/* 888 888 888 C888 888 888 888 / 888 q888 */
+/* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */
+/* "8oo8D */
+/* */
+/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */
+/* (triangle.c) */
+/* */
+/* Version 1.6 */
+/* July 28, 2005 */
+/* */
+/* Copyright 1993, 1995, 1997, 1998, 2002, 2005 */
+/* Jonathan Richard Shewchuk */
+/* 2360 Woolsey #H */
+/* Berkeley, California 94705-1927 */
+/* jrs@cs.berkeley.edu */
+/* */
+/* Modified by Andreas Geiger, 2011 */
+/* */
+/* This program may be freely redistributed under the condition that the */
+/* copyright notices (including this entire header and the copyright */
+/* notice printed when the `-h' switch is selected) are not removed, and */
+/* no compensation is received. Private, research, and institutional */
+/* use is free. You may distribute modified versions of this code UNDER */
+/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */
+/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */
+/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */
+/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */
+/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */
+/* WITH THE AUTHOR. (If you are not directly supplying this code to a */
+/* customer, and you are instead telling them how they can obtain it for */
+/* free, then you are not required to make any arrangement with me.) */
+/* */
+/* Hypertext instructions for Triangle are available on the Web at */
+/* */
+/* http://www.cs.cmu.edu/~quake/triangle.html */
+/* */
+/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */
+/* whatsoever. This code is provided "as-is". Use at your own risk. */
+/* */
+/* Some of the references listed below are marked with an asterisk. [*] */
+/* These references are available for downloading from the Web page */
+/* */
+/* http://www.cs.cmu.edu/~quake/triangle.research.html */
+/* */
+/* Three papers discussing aspects of Triangle are available. A short */
+/* overview appears in "Triangle: Engineering a 2D Quality Mesh */
+/* Generator and Delaunay Triangulator," in Applied Computational */
+/* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */
+/* Manocha, editors, Lecture Notes in Computer Science volume 1148, */
+/* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */
+/* Workshop on Applied Computational Geometry). [*] */
+/* */
+/* The algorithms are discussed in the greatest detail in "Delaunay */
+/* Refinement Algorithms for Triangular Mesh Generation," Computational */
+/* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */
+/* */
+/* More detail about the data structures may be found in my dissertation: */
+/* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */
+/* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */
+/* Pittsburgh, Pennsylvania, 18 May 1997. [*] */
+/* */
+/* Triangle was created as part of the Quake Project in the School of */
+/* Computer Science at Carnegie Mellon University. For further */
+/* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */
+/* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */
+/* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous */
+/* Media on Parallel Computers," Computer Methods in Applied Mechanics */
+/* and Engineering 152(1-2):85-102, 22 January 1998. */
+/* */
+/* Triangle's Delaunay refinement algorithm for quality mesh generation is */
+/* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */
+/* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */
+/* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */
+/* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */
+/* Annual Symposium on Computational Geometry (San Diego, California), */
+/* pages 274-280, Association for Computing Machinery, May 1993, */
+/* http://portal.acm.org/citation.cfm?id=161150 . */
+/* */
+/* The Delaunay refinement algorithm has been modified so that it meshes */
+/* domains with small input angles well, as described in Gary L. Miller, */
+/* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's */
+/* Algorithm Works," Twelfth International Meshing Roundtable, pages */
+/* 91-102, Sandia National Laboratories, September 2003. [*] */
+/* */
+/* My implementation of the divide-and-conquer and incremental Delaunay */
+/* triangulation algorithms follows closely the presentation of Guibas */
+/* and Stolfi, even though I use a triangle-based data structure instead */
+/* of their quad-edge data structure. (In fact, I originally implemented */
+/* Triangle using the quad-edge data structure, but the switch to a */
+/* triangle-based data structure sped Triangle by a factor of two.) The */
+/* mesh manipulation primitives and the two aforementioned Delaunay */
+/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */
+/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */
+/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */
+/* 4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/
+/* */
+/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */
+/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */
+/* Delaunay Triangulation," International Journal of Computer and */
+/* Information Science 9(3):219-242, 1980. Triangle's improvement of the */
+/* divide-and-conquer algorithm by alternating between vertical and */
+/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */
+/* Conquer Algorithm for Constructing Delaunay Triangulations," */
+/* Algorithmica 2(2):137-151, 1987. */
+/* */
+/* The incremental insertion algorithm was first proposed by C. L. Lawson, */
+/* "Software for C1 Surface Interpolation," in Mathematical Software III, */
+/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */
+/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */
+/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */
+/* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," */
+/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
+/* ACM, May 1996. [*] If I were to randomize the order of vertex */
+/* insertion (I currently don't bother), their result combined with the */
+/* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of */
+/* Random Sampling in Computational Geometry II," Discrete & */
+/* Computational Geometry 4(1):387-421, 1989, would yield an expected */
+/* O(n^{4/3}) bound on running time. */
+/* */
+/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */
+/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */
+/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */
+/* boundary of the triangulation are maintained in a splay tree for the */
+/* purpose of point location. Splay trees are described by Daniel */
+/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
+/* Trees," Journal of the ACM 32(3):652-686, July 1985, */
+/* http://portal.acm.org/citation.cfm?id=3835 . */
+/* */
+/* The algorithms for exact computation of the signs of determinants are */
+/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */
+/* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & */
+/* Computational Geometry 18(3):305-363, October 1997. (Also available */
+/* as Technical Report CMU-CS-96-140, School of Computer Science, */
+/* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] */
+/* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust */
+/* Adaptive Floating-Point Geometric Predicates," Proceedings of the */
+/* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */
+/* Many of the ideas for my exact arithmetic routines originate with */
+/* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point */
+/* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */
+/* Computer Society Press, 1991. [*] Many of the ideas for the correct */
+/* evaluation of the signs of determinants are taken from Steven Fortune */
+/* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- */
+/* tional Geometry," Proceedings of the Ninth Annual Symposium on */
+/* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven */
+/* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- */
+/* lations," International Journal of Computational Geometry & Applica- */
+/* tions 5(1-2):193-213, March-June 1995. */
+/* */
+/* The method of inserting new vertices off-center (not precisely at the */
+/* circumcenter of every poor-quality triangle) is from Alper Ungor, */
+/* "Off-centers: A New Type of Steiner Points for Computing Size-Optimal */
+/* Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN */
+/* 2004 (Buenos Aires, Argentina), April 2004. */
+/* */
+/* For definitions of and results involving Delaunay triangulations, */
+/* constrained and conforming versions thereof, and other aspects of */
+/* triangular mesh generation, see the excellent survey by Marshall Bern */
+/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */
+/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */
+/* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] */
+/* */
+/* The time for incrementally adding PSLG (planar straight line graph) */
+/* segments to create a constrained Delaunay triangulation is probably */
+/* O(t^2) per segment in the worst case and O(t) per segment in the */
+/* common case, where t is the number of triangles that intersect the */
+/* segment before it is inserted. This doesn't count point location, */
+/* which can be much more expensive. I could improve this to O(d log d) */
+/* time, but d is usually quite small, so it's not worth the bother. */
+/* (This note does not apply when the -s switch is used, invoking a */
+/* different method is used to insert segments.) */
+/* */
+/* The time for deleting a vertex from a Delaunay triangulation is O(d^2) */
+/* in the worst case and O(d) in the common case, where d is the degree */
+/* of the vertex being deleted. I could improve this to O(d log d) time, */
+/* but d is usually quite small, so it's not worth the bother. */
+/* */
+/* Ruppert's Delaunay refinement algorithm typically generates triangles */
+/* at a linear rate (constant time per triangle) after the initial */
+/* triangulation is formed. There may be pathological cases where */
+/* quadratic time is required, but these never arise in practice. */
+/* */
+/* The geometric predicates (circumcenter calculations, segment */
+/* intersection formulae, etc.) appear in my "Lecture Notes on Geometric */
+/* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh . */
+/* */
+/* If you make any improvements to this code, please please please let me */
+/* know, so that I may obtain the improvements. Even if you don't change */
+/* the code, I'd still love to hear what it's being used for. */
+/* */
+/*****************************************************************************/
+
+/* Maximum number of characters in a file name (including the null). */
+
+#define FILENAMESIZE 2048
+
+/* Maximum number of characters in a line read from a file (including the */
+/* null). */
+
+#define INPUTLINESIZE 1024
+
+/* For efficiency, a variety of data structures are allocated in bulk. The */
+/* following constants determine how many of each structure is allocated */
+/* at once. */
+
+#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */
+#define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */
+#define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */
+#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
+#define BADSUBSEGPERBLOCK 252 /* Number of encroached subsegments allocated at once. */
+#define BADTRIPERBLOCK 4092 /* Number of skinny triangles allocated at once. */
+#define FLIPSTACKERPERBLOCK 252 /* Number of flipped triangles allocated at once. */
+#define SPLAYNODEPERBLOCK 508 /* Number of splay tree nodes allocated at once. */
+
+/* The vertex types. A DEADVERTEX has been deleted entirely. An */
+/* UNDEADVERTEX is not part of the mesh, but is written to the output */
+/* .node file and affects the node indexing in the other output files. */
+
+#define INPUTVERTEX 0
+#define SEGMENTVERTEX 1
+#define FREEVERTEX 2
+#define DEADVERTEX -32768
+#define UNDEADVERTEX -32767
+
+/* Two constants for algorithms based on random sampling. Both constants */
+/* have been chosen empirically to optimize their respective algorithms. */
+
+/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */
+/* how large a random sample of triangles to inspect. */
+
+#define SAMPLEFACTOR 11
+
+/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
+/* of boundary edges should be maintained in the splay tree for point */
+/* location on the front. */
+
+#define SAMPLERATE 10
+
+/* A number that speaks for itself, every kissable digit. */
+
+#define PI 3.141592653589793238462643383279502884197169399375105820974944592308
+
+/* Another fave. */
+
+#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
+
+/* And here's one for those of you who are intimidated by math. */
+
+#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+
+#include "triangle.h"
+
+/* Labels that signify the result of point location. The result of a */
+/* search indicates that the point falls in the interior of a triangle, on */
+/* an edge, on a vertex, or outside the mesh. */
+
+enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
+
+/* Labels that signify the result of vertex insertion. The result indicates */
+/* that the vertex was inserted with complete success, was inserted but */
+/* encroaches upon a subsegment, was not inserted because it lies on a */
+/* segment, or was not inserted because another vertex occupies the same */
+/* location. */
+
+enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
+ DUPLICATEVERTEX};
+
+/* Labels that signify the result of direction finding. The result */
+/* indicates that a segment connecting the two query points falls within */
+/* the direction triangle, along the left edge of the direction triangle, */
+/* or along the right edge of the direction triangle. */
+
+enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
+
+/*****************************************************************************/
+/* */
+/* The basic mesh data structures */
+/* */
+/* There are three: vertices, triangles, and subsegments (abbreviated */
+/* `subseg'). These three data structures, linked by pointers, comprise */
+/* the mesh. A vertex simply represents a mesh vertex and its properties. */
+/* A triangle is a triangle. A subsegment is a special data structure used */
+/* to represent an impenetrable edge of the mesh (perhaps on the outer */
+/* boundary, on the boundary of a hole, or part of an internal boundary */
+/* separating two triangulated regions). Subsegments represent boundaries, */
+/* defined by the user, that triangles may not lie across. */
+/* */
+/* A triangle consists of a list of three vertices, a list of three */
+/* adjoining triangles, a list of three adjoining subsegments (when */
+/* segments exist), an arbitrary number of optional user-defined */
+/* floating-point attributes, and an optional area constraint. The latter */
+/* is an upper bound on the permissible area of each triangle in a region, */
+/* used for mesh refinement. */
+/* */
+/* For a triangle on a boundary of the mesh, some or all of the neighboring */
+/* triangles may not be present. For a triangle in the interior of the */
+/* mesh, often no neighboring subsegments are present. Such absent */
+/* triangles and subsegments are never represented by NULL pointers; they */
+/* are represented by two special records: `dummytri', the triangle that */
+/* fills "outer space", and `dummysub', the omnipresent subsegment. */
+/* `dummytri' and `dummysub' are used for several reasons; for instance, */
+/* they can be dereferenced and their contents examined without violating */
+/* protected memory. */
+/* */
+/* However, it is important to understand that a triangle includes other */
+/* information as well. The pointers to adjoining vertices, triangles, and */
+/* subsegments are ordered in a way that indicates their geometric relation */
+/* to each other. Furthermore, each of these pointers contains orientation */
+/* information. Each pointer to an adjoining triangle indicates which face */
+/* of that triangle is contacted. Similarly, each pointer to an adjoining */
+/* subsegment indicates which side of that subsegment is contacted, and how */
+/* the subsegment is oriented relative to the triangle. */
+/* */
+/* The data structure representing a subsegment may be thought to be */
+/* abutting the edge of one or two triangle data structures: either */
+/* sandwiched between two triangles, or resting against one triangle on an */
+/* exterior boundary or hole boundary. */
+/* */
+/* A subsegment consists of a list of four vertices--the vertices of the */
+/* subsegment, and the vertices of the segment it is a part of--a list of */
+/* two adjoining subsegments, and a list of two adjoining triangles. One */
+/* of the two adjoining triangles may not be present (though there should */
+/* always be one), and neighboring subsegments might not be present. */
+/* Subsegments also store a user-defined integer "boundary marker". */
+/* Typically, this integer is used to indicate what boundary conditions are */
+/* to be applied at that location in a finite element simulation. */
+/* */
+/* Like triangles, subsegments maintain information about the relative */
+/* orientation of neighboring objects. */
+/* */
+/* Vertices are relatively simple. A vertex is a list of floating-point */
+/* numbers, starting with the x, and y coordinates, followed by an */
+/* arbitrary number of optional user-defined floating-point attributes, */
+/* followed by an integer boundary marker. During the segment insertion */
+/* phase, there is also a pointer from each vertex to a triangle that may */
+/* contain it. Each pointer is not always correct, but when one is, it */
+/* speeds up segment insertion. These pointers are assigned values once */
+/* at the beginning of the segment insertion phase, and are not used or */
+/* updated except during this phase. Edge flipping during segment */
+/* insertion will render some of them incorrect. Hence, don't rely upon */
+/* them for anything. */
+/* */
+/* Other than the exception mentioned above, vertices have no information */
+/* about what triangles, subfacets, or subsegments they are linked to. */
+/* */
+/*****************************************************************************/
+
+/*****************************************************************************/
+/* */
+/* Handles */
+/* */
+/* The oriented triangle (`otri') and oriented subsegment (`osub') data */
+/* structures defined below do not themselves store any part of the mesh. */
+/* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */
+/* */
+/* Oriented triangles and oriented subsegments will usually be referred to */
+/* as "handles." A handle is essentially a pointer into the mesh; it */
+/* allows you to "hold" one particular part of the mesh. Handles are used */
+/* to specify the regions in which one is traversing and modifying the mesh.*/
+/* A single `triangle' may be held by many handles, or none at all. (The */
+/* latter case is not a memory leak, because the triangle is still */
+/* connected to other triangles in the mesh.) */
+/* */
+/* An `otri' is a handle that holds a triangle. It holds a specific edge */
+/* of the triangle. An `osub' is a handle that holds a subsegment. It */
+/* holds either the left or right side of the subsegment. */
+/* */
+/* Navigation about the mesh is accomplished through a set of mesh */
+/* manipulation primitives, further below. Many of these primitives take */
+/* a handle and produce a new handle that holds the mesh near the first */
+/* handle. Other primitives take two handles and glue the corresponding */
+/* parts of the mesh together. The orientation of the handles is */
+/* important. For instance, when two triangles are glued together by the */
+/* bond() primitive, they are glued at the edges on which the handles lie. */
+/* */
+/* Because vertices have no information about which triangles they are */
+/* attached to, I commonly represent a vertex by use of a handle whose */
+/* origin is the vertex. A single handle can simultaneously represent a */
+/* triangle, an edge, and a vertex. */
+/* */
+/*****************************************************************************/
+
+/* The triangle data structure. Each triangle contains three pointers to */
+/* adjoining triangles, plus three pointers to vertices, plus three */
+/* pointers to subsegments (declared below; these pointers are usually */
+/* `dummysub'). It may or may not also contain user-defined attributes */
+/* and/or a floating-point "area constraint." It may also contain extra */
+/* pointers for nodes, when the user asks for high-order elements. */
+/* Because the size and structure of a `triangle' is not decided until */
+/* runtime, I haven't simply declared the type `triangle' as a struct. */
+
+typedef float **triangle; /* Really: typedef triangle *triangle */
+
+/* An oriented triangle: includes a pointer to a triangle and orientation. */
+/* The orientation denotes an edge of the triangle. Hence, there are */
+/* three possible orientations. By convention, each edge always points */
+/* counterclockwise about the corresponding triangle. */
+
+struct otri {
+ triangle *tri;
+ int orient; /* Ranges from 0 to 2. */
+};
+
+/* The subsegment data structure. Each subsegment contains two pointers to */
+/* adjoining subsegments, plus four pointers to vertices, plus two */
+/* pointers to adjoining triangles, plus one boundary marker, plus one */
+/* segment number. */
+
+typedef float **subseg; /* Really: typedef subseg *subseg */
+
+/* An oriented subsegment: includes a pointer to a subsegment and an */
+/* orientation. The orientation denotes a side of the edge. Hence, there */
+/* are two possible orientations. By convention, the edge is always */
+/* directed so that the "side" denoted is the right side of the edge. */
+
+struct osub {
+ subseg *ss;
+ int ssorient; /* Ranges from 0 to 1. */
+};
+
+/* The vertex data structure. Each vertex is actually an array of floats. */
+/* The number of floats is unknown until runtime. An integer boundary */
+/* marker, and sometimes a pointer to a triangle, is appended after the */
+/* floats. */
+
+typedef float *vertex;
+
+/* A queue used to store encroached subsegments. Each subsegment's vertices */
+/* are stored so that we can check whether a subsegment is still the same. */
+
+struct badsubseg {
+ subseg encsubseg; /* An encroached subsegment. */
+ vertex subsegorg, subsegdest; /* Its two vertices. */
+};
+
+/* A queue used to store bad triangles. The key is the square of the cosine */
+/* of the smallest angle of the triangle. Each triangle's vertices are */
+/* stored so that one can check whether a triangle is still the same. */
+
+struct badtriang {
+ triangle poortri; /* A skinny or too-large triangle. */
+ float key; /* cos^2 of smallest (apical) angle. */
+ vertex triangorg, triangdest, triangapex; /* Its three vertices. */
+ struct badtriang *nexttriang; /* Pointer to next bad triangle. */
+};
+
+/* A stack of triangles flipped during the most recent vertex insertion. */
+/* The stack is used to undo the vertex insertion if the vertex encroaches */
+/* upon a subsegment. */
+
+struct flipstacker {
+ triangle flippedtri; /* A recently flipped triangle. */
+ struct flipstacker *prevflip; /* Previous flip in the stack. */
+};
+
+/* A node in a heap used to store events for the sweepline Delaunay */
+/* algorithm. Nodes do not point directly to their parents or children in */
+/* the heap. Instead, each node knows its position in the heap, and can */
+/* look up its parent and children in a separate array. The `eventptr' */
+/* points either to a `vertex' or to a triangle (in encoded format, so */
+/* that an orientation is included). In the latter case, the origin of */
+/* the oriented triangle is the apex of a "circle event" of the sweepline */
+/* algorithm. To distinguish site events from circle events, all circle */
+/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */
+
+struct event {
+ float xkey, ykey; /* Coordinates of the event. */
+ int *eventptr; /* Can be a vertex or the location of a circle event. */
+ int heapposition; /* Marks this event's position in the heap. */
+};
+
+/* A node in the splay tree. Each node holds an oriented ghost triangle */
+/* that represents a boundary edge of the growing triangulation. When a */
+/* circle event covers two boundary edges with a triangle, so that they */
+/* are no longer boundary edges, those edges are not immediately deleted */
+/* from the tree; rather, they are lazily deleted when they are next */
+/* encountered. (Since only a random sample of boundary edges are kept */
+/* in the tree, lazy deletion is faster.) `keydest' is used to verify */
+/* that a triangle is still the same as when it entered the splay tree; if */
+/* it has been rotated (due to a circle event), it no longer represents a */
+/* boundary edge and should be deleted. */
+
+struct splaynode {
+ struct otri keyedge; /* Lprev of an edge on the front. */
+ vertex keydest; /* Used to verify that splay node is still live. */
+ struct splaynode *lchild, *rchild; /* Children in splay tree. */
+};
+
+/* A type used to allocate memory. firstblock is the first block of items. */
+/* nowblock is the block from which items are currently being allocated. */
+/* nextitem points to the next slab of free memory for an item. */
+/* deaditemstack is the head of a linked list (stack) of deallocated items */
+/* that can be recycled. unallocateditems is the number of items that */
+/* remain to be allocated from nowblock. */
+/* */
+/* Traversal is the process of walking through the entire list of items, and */
+/* is separate from allocation. Note that a traversal will visit items on */
+/* the "deaditemstack" stack as well as live items. pathblock points to */
+/* the block currently being traversed. pathitem points to the next item */
+/* to be traversed. pathitemsleft is the number of items that remain to */
+/* be traversed in pathblock. */
+/* */
+/* alignbytes determines how new records should be aligned in memory. */
+/* itembytes is the length of a record in bytes (after rounding up). */
+/* itemsperblock is the number of items allocated at once in a single */
+/* block. itemsfirstblock is the number of items in the first block, */
+/* which can vary from the others. items is the number of currently */
+/* allocated items. maxitems is the maximum number of items that have */
+/* been allocated at once; it is the current number of items plus the */
+/* number of records kept on deaditemstack. */
+
+struct memorypool {
+ int **firstblock, **nowblock;
+ int *nextitem;
+ int *deaditemstack;
+ int **pathblock;
+ int *pathitem;
+ int alignbytes;
+ int itembytes;
+ int itemsperblock;
+ int itemsfirstblock;
+ long items, maxitems;
+ int unallocateditems;
+ int pathitemsleft;
+};
+
+
+/* Global constants. */
+
+float splitter; /* Used to split float factors for exact multiplication. */
+float epsilon; /* Floating-point machine epsilon. */
+float resulterrbound;
+float ccwerrboundA, ccwerrboundB, ccwerrboundC;
+float iccerrboundA, iccerrboundB, iccerrboundC;
+float o3derrboundA, o3derrboundB, o3derrboundC;
+
+/* Random number seed is not constant, but I've made it global anyway. */
+
+unsigned long long randomseed; /* Current random number seed. */
+
+
+/* Mesh data structure. Triangle operates on only one mesh, but the mesh */
+/* structure is used (instead of global variables) to allow reentrancy. */
+
+struct mesh {
+
+/* Variables used to allocate memory for triangles, subsegments, vertices, */
+/* viri (triangles being eaten), encroached segments, bad (skinny or too */
+/* large) triangles, and splay tree nodes. */
+
+ struct memorypool triangles;
+ struct memorypool subsegs;
+ struct memorypool vertices;
+ struct memorypool viri;
+ struct memorypool badsubsegs;
+ struct memorypool badtriangles;
+ struct memorypool flipstackers;
+ struct memorypool splaynodes;
+
+/* Variables that maintain the bad triangle queues. The queues are */
+/* ordered from 4095 (highest priority) to 0 (lowest priority). */
+
+ struct badtriang *queuefront[4096];
+ struct badtriang *queuetail[4096];
+ int nextnonemptyq[4096];
+ int firstnonemptyq;
+
+/* Variable that maintains the stack of recently flipped triangles. */
+
+ struct flipstacker *lastflip;
+
+/* Other variables. */
+
+ float xmin, xmax, ymin, ymax; /* x and y bounds. */
+ float xminextreme; /* Nonexistent x value used as a flag in sweepline. */
+ int invertices; /* Number of input vertices. */
+ int inelements; /* Number of input triangles. */
+ int insegments; /* Number of input segments. */
+ int holes; /* Number of input holes. */
+ int regions; /* Number of input regions. */
+ int undeads; /* Number of input vertices that don't appear in the mesh. */
+ long edges; /* Number of output edges. */
+ int mesh_dim; /* Dimension (ought to be 2). */
+ int nextras; /* Number of attributes per vertex. */
+ int eextras; /* Number of attributes per triangle. */
+ long hullsize; /* Number of edges in convex hull. */
+ int steinerleft; /* Number of Steiner points not yet used. */
+ int vertexmarkindex; /* Index to find boundary marker of a vertex. */
+ int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */
+ int highorderindex; /* Index to find extra nodes for high-order elements. */
+ int elemattribindex; /* Index to find attributes of a triangle. */
+ int areaboundindex; /* Index to find area bound of a triangle. */
+ int checksegments; /* Are there segments in the triangulation yet? */
+ int checkquality; /* Has quality triangulation begun yet? */
+ int readnodefile; /* Has a .node file been read? */
+ long samples; /* Number of random samples for point location. */
+
+ long incirclecount; /* Number of incircle tests performed. */
+ long counterclockcount; /* Number of counterclockwise tests performed. */
+ long orient3dcount; /* Number of 3D orientation tests performed. */
+ long hyperbolacount; /* Number of right-of-hyperbola tests performed. */
+ long circumcentercount; /* Number of circumcenter calculations performed. */
+ long circletopcount; /* Number of circle top calculations performed. */
+
+/* Triangular bounding box vertices. */
+
+ vertex infvertex1, infvertex2, infvertex3;
+
+/* Pointer to the `triangle' that occupies all of "outer space." */
+
+ triangle *dummytri;
+ triangle *dummytribase; /* Keep base address so we can free() it later. */
+
+/* Pointer to the omnipresent subsegment. Referenced by any triangle or */
+/* subsegment that isn't really connected to a subsegment at that */
+/* location. */
+
+ subseg *dummysub;
+ subseg *dummysubbase; /* Keep base address so we can free() it later. */
+
+/* Pointer to a recently visited triangle. Improves point location if */
+/* proximate vertices are inserted sequentially. */
+
+ struct otri recenttri;
+
+}; /* End of `struct mesh'. */
+
+
+/* Data structure for command line switches and file names. This structure */
+/* is used (instead of global variables) to allow reentrancy. */
+
+struct behavior {
+
+/* Switches for the triangulator. */
+/* poly: -p switch. refine: -r switch. */
+/* quality: -q switch. */
+/* minangle: minimum angle bound, specified after -q switch. */
+/* goodangle: cosine squared of minangle. */
+/* offconstant: constant used to place off-center Steiner points. */
+/* vararea: -a switch without number. */
+/* fixedarea: -a switch with number. */
+/* maxarea: maximum area bound, specified after -a switch. */
+/* usertest: -u switch. */
+/* regionattrib: -A switch. convex: -c switch. */
+/* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */
+/* firstnumber: inverse of -z switch. All items are numbered starting */
+/* from `firstnumber'. */
+/* edgesout: -e switch. voronoi: -v switch. */
+/* neighbors: -n switch. geomview: -g switch. */
+/* nobound: -B switch. nopolywritten: -P switch. */
+/* nonodewritten: -N switch. noelewritten: -E switch. */
+/* noiterationnum: -I switch. noholes: -O switch. */
+/* noexact: -X switch. */
+/* order: element order, specified after -o switch. */
+/* nobisect: count of how often -Y switch is selected. */
+/* steiner: maximum number of Steiner points, specified after -S switch. */
+/* incremental: -i switch. sweepline: -F switch. */
+/* dwyer: inverse of -l switch. */
+/* splitseg: -s switch. */
+/* conformdel: -D switch. docheck: -C switch. */
+/* quiet: -Q switch. verbose: count of how often -V switch is selected. */
+/* usesegments: -p, -r, -q, or -c switch; determines whether segments are */
+/* used at all. */
+/* */
+/* Read the instructions to find out the meaning of these switches. */
+
+ int poly, refine, quality, vararea, fixedarea, usertest;
+ int regionattrib, convex, weighted, jettison;
+ int firstnumber;
+ int edgesout, voronoi, neighbors, geomview;
+ int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
+ int noholes, noexact, conformdel;
+ int incremental, sweepline, dwyer;
+ int splitseg;
+ int docheck;
+ int quiet, verbose;
+ int usesegments;
+ int order;
+ int nobisect;
+ int steiner;
+ float minangle, goodangle, offconstant;
+ float maxarea;
+
+/* Variables for file names. */
+
+}; /* End of `struct behavior'. */
+
+
+/*****************************************************************************/
+/* */
+/* Mesh manipulation primitives. Each triangle contains three pointers to */
+/* other triangles, with orientations. Each pointer points not to the */
+/* first byte of a triangle, but to one of the first three bytes of a */
+/* triangle. It is necessary to extract both the triangle itself and the */
+/* orientation. To save memory, I keep both pieces of information in one */
+/* pointer. To make this possible, I assume that all triangles are aligned */
+/* to four-byte boundaries. The decode() routine below decodes a pointer, */
+/* extracting an orientation (in the range 0 to 2) and a pointer to the */
+/* beginning of a triangle. The encode() routine compresses a pointer to a */
+/* triangle and an orientation into a single pointer. My assumptions that */
+/* triangles are four-byte-aligned and that the `unsigned long' type is */
+/* long enough to hold a pointer are two of the few kludges in this program.*/
+/* */
+/* Subsegments are manipulated similarly. A pointer to a subsegment */
+/* carries both an address and an orientation in the range 0 to 1. */
+/* */
+/* The other primitives take an oriented triangle or oriented subsegment, */
+/* and return an oriented triangle or oriented subsegment or vertex; or */
+/* they change the connections in the data structure. */
+/* */
+/* Below, triangles and subsegments are denoted by their vertices. The */
+/* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */
+/* c. These vertices occur in counterclockwise order about the triangle. */
+/* The handle abc may simultaneously denote vertex a, edge ab, and triangle */
+/* abc. */
+/* */
+/* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
+/* b. If ab is thought to be directed upward (with b directly above a), */
+/* then the handle ab is thought to grasp the right side of ab, and may */
+/* simultaneously denote vertex a and edge ab. */
+/* */
+/* An asterisk (*) denotes a vertex whose identity is unknown. */
+/* */
+/* Given this notation, a partial list of mesh manipulation primitives */
+/* follows. */
+/* */
+/* */
+/* For triangles: */
+/* */
+/* sym: Find the abutting triangle; same edge. */
+/* sym(abc) -> ba* */
+/* */
+/* lnext: Find the next edge (counterclockwise) of a triangle. */
+/* lnext(abc) -> bca */
+/* */
+/* lprev: Find the previous edge (clockwise) of a triangle. */
+/* lprev(abc) -> cab */
+/* */
+/* onext: Find the next edge counterclockwise with the same origin. */
+/* onext(abc) -> ac* */
+/* */
+/* oprev: Find the next edge clockwise with the same origin. */
+/* oprev(abc) -> a*b */
+/* */
+/* dnext: Find the next edge counterclockwise with the same destination. */
+/* dnext(abc) -> *ba */
+/* */
+/* dprev: Find the next edge clockwise with the same destination. */
+/* dprev(abc) -> cb* */
+/* */
+/* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */
+/* rnext(abc) -> *a* */
+/* */
+/* rprev: Find the previous edge (clockwise) of the adjacent triangle. */
+/* rprev(abc) -> b** */
+/* */
+/* org: Origin dest: Destination apex: Apex */
+/* org(abc) -> a dest(abc) -> b apex(abc) -> c */
+/* */
+/* bond: Bond two triangles together at the resepective handles. */
+/* bond(abc, bad) */
+/* */
+/* */
+/* For subsegments: */
+/* */
+/* ssym: Reverse the orientation of a subsegment. */
+/* ssym(ab) -> ba */
+/* */
+/* spivot: Find adjoining subsegment with the same origin. */
+/* spivot(ab) -> a* */
+/* */
+/* snext: Find next subsegment in sequence. */
+/* snext(ab) -> b* */
+/* */
+/* sorg: Origin sdest: Destination */
+/* sorg(ab) -> a sdest(ab) -> b */
+/* */
+/* sbond: Bond two subsegments together at the respective origins. */
+/* sbond(ab, ac) */
+/* */
+/* */
+/* For interacting tetrahedra and subfacets: */
+/* */
+/* tspivot: Find a subsegment abutting a triangle. */
+/* tspivot(abc) -> ba */
+/* */
+/* stpivot: Find a triangle abutting a subsegment. */
+/* stpivot(ab) -> ba* */
+/* */
+/* tsbond: Bond a triangle to a subsegment. */
+/* tsbond(abc, ba) */
+/* */
+/*****************************************************************************/
+
+/********* Mesh manipulation primitives begin here *********/
+/** **/
+/** **/
+
+/* Fast lookup arrays to speed some of the mesh manipulation primitives. */
+
+int plus1mod3[3] = {1, 2, 0};
+int minus1mod3[3] = {2, 0, 1};
+
+/********* Primitives for triangles *********/
+/* */
+/* */
+
+/* decode() converts a pointer to an oriented triangle. The orientation is */
+/* extracted from the two least significant bits of the pointer. */
+
+#define decode(ptr, otri) \
+ (otri).orient = (int) ((unsigned long long) (ptr) & (unsigned long long) 3l); \
+ (otri).tri = (triangle *) \
+ ((unsigned long long) (ptr) ^ (unsigned long long) (otri).orient)
+
+/* encode() compresses an oriented triangle into a single pointer. It */
+/* relies on the assumption that all triangles are aligned to four-byte */
+/* boundaries, so the two least significant bits of (otri).tri are zero. */
+
+#define encode(otri) \
+ (triangle) ((unsigned long long) (otri).tri | (unsigned long long) (otri).orient)
+
+/* The following handle manipulation primitives are all described by Guibas */
+/* and Stolfi. However, Guibas and Stolfi use an edge-based data */
+/* structure, whereas I use a triangle-based data structure. */
+
+/* sym() finds the abutting triangle, on the same edge. Note that the edge */
+/* direction is necessarily reversed, because the handle specified by an */
+/* oriented triangle is directed counterclockwise around the triangle. */
+
+#define sym(otri1, otri2) \
+ ptr = (otri1).tri[(otri1).orient]; \
+ decode(ptr, otri2);
+
+#define symself(otri) \
+ ptr = (otri).tri[(otri).orient]; \
+ decode(ptr, otri);
+
+/* lnext() finds the next edge (counterclockwise) of a triangle. */
+
+#define lnext(otri1, otri2) \
+ (otri2).tri = (otri1).tri; \
+ (otri2).orient = plus1mod3[(otri1).orient]
+
+#define lnextself(otri) \
+ (otri).orient = plus1mod3[(otri).orient]
+
+/* lprev() finds the previous edge (clockwise) of a triangle. */
+
+#define lprev(otri1, otri2) \
+ (otri2).tri = (otri1).tri; \
+ (otri2).orient = minus1mod3[(otri1).orient]
+
+#define lprevself(otri) \
+ (otri).orient = minus1mod3[(otri).orient]
+
+/* onext() spins counterclockwise around a vertex; that is, it finds the */
+/* next edge with the same origin in the counterclockwise direction. This */
+/* edge is part of a different triangle. */
+
+#define onext(otri1, otri2) \
+ lprev(otri1, otri2); \
+ symself(otri2);
+
+#define onextself(otri) \
+ lprevself(otri); \
+ symself(otri);
+
+/* oprev() spins clockwise around a vertex; that is, it finds the next edge */
+/* with the same origin in the clockwise direction. This edge is part of */
+/* a different triangle. */
+
+#define oprev(otri1, otri2) \
+ sym(otri1, otri2); \
+ lnextself(otri2);
+
+#define oprevself(otri) \
+ symself(otri); \
+ lnextself(otri);
+
+/* dnext() spins counterclockwise around a vertex; that is, it finds the */
+/* next edge with the same destination in the counterclockwise direction. */
+/* This edge is part of a different triangle. */
+
+#define dnext(otri1, otri2) \
+ sym(otri1, otri2); \
+ lprevself(otri2);
+
+#define dnextself(otri) \
+ symself(otri); \
+ lprevself(otri);
+
+/* dprev() spins clockwise around a vertex; that is, it finds the next edge */
+/* with the same destination in the clockwise direction. This edge is */
+/* part of a different triangle. */
+
+#define dprev(otri1, otri2) \
+ lnext(otri1, otri2); \
+ symself(otri2);
+
+#define dprevself(otri) \
+ lnextself(otri); \
+ symself(otri);
+
+/* rnext() moves one edge counterclockwise about the adjacent triangle. */
+/* (It's best understood by reading Guibas and Stolfi. It involves */
+/* changing triangles twice.) */
+
+#define rnext(otri1, otri2) \
+ sym(otri1, otri2); \
+ lnextself(otri2); \
+ symself(otri2);
+
+#define rnextself(otri) \
+ symself(otri); \
+ lnextself(otri); \
+ symself(otri);
+
+/* rprev() moves one edge clockwise about the adjacent triangle. */
+/* (It's best understood by reading Guibas and Stolfi. It involves */
+/* changing triangles twice.) */
+
+#define rprev(otri1, otri2) \
+ sym(otri1, otri2); \
+ lprevself(otri2); \
+ symself(otri2);
+
+#define rprevself(otri) \
+ symself(otri); \
+ lprevself(otri); \
+ symself(otri);
+
+/* These primitives determine or set the origin, destination, or apex of a */
+/* triangle. */
+
+#define org(otri, vertexptr) \
+ vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]
+
+#define dest(otri, vertexptr) \
+ vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]
+
+#define apex(otri, vertexptr) \
+ vertexptr = (vertex) (otri).tri[(otri).orient + 3]
+
+#define setorg(otri, vertexptr) \
+ (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr
+
+#define setdest(otri, vertexptr) \
+ (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr
+
+#define setapex(otri, vertexptr) \
+ (otri).tri[(otri).orient + 3] = (triangle) vertexptr
+
+/* Bond two triangles together. */
+
+#define bond(otri1, otri2) \
+ (otri1).tri[(otri1).orient] = encode(otri2); \
+ (otri2).tri[(otri2).orient] = encode(otri1)
+
+/* Dissolve a bond (from one side). Note that the other triangle will still */
+/* think it's connected to this triangle. Usually, however, the other */
+/* triangle is being deleted entirely, or bonded to another triangle, so */
+/* it doesn't matter. */
+
+#define dissolve(otri) \
+ (otri).tri[(otri).orient] = (triangle) m->dummytri
+
+/* Copy an oriented triangle. */
+
+#define otricopy(otri1, otri2) \
+ (otri2).tri = (otri1).tri; \
+ (otri2).orient = (otri1).orient
+
+/* Test for equality of oriented triangles. */
+
+#define otriequal(otri1, otri2) \
+ (((otri1).tri == (otri2).tri) && \
+ ((otri1).orient == (otri2).orient))
+
+/* Primitives to infect or cure a triangle with the virus. These rely on */
+/* the assumption that all subsegments are aligned to four-byte boundaries.*/
+
+#define infect(otri) \
+ (otri).tri[6] = (triangle) \
+ ((unsigned long long) (otri).tri[6] | (unsigned long long) 2l)
+
+#define uninfect(otri) \
+ (otri).tri[6] = (triangle) \
+ ((unsigned long long) (otri).tri[6] & ~ (unsigned long long) 2l)
+
+/* Test a triangle for viral infection. */
+
+#define infected(otri) \
+ (((unsigned long long) (otri).tri[6] & (unsigned long long) 2l) != 0l)
+
+/* Check or set a triangle's attributes. */
+
+#define elemattribute(otri, attnum) \
+ ((float *) (otri).tri)[m->elemattribindex + (attnum)]
+
+#define setelemattribute(otri, attnum, value) \
+ ((float *) (otri).tri)[m->elemattribindex + (attnum)] = value
+
+/* Check or set a triangle's maximum area bound. */
+
+#define areabound(otri) ((float *) (otri).tri)[m->areaboundindex]
+
+#define setareabound(otri, value) \
+ ((float *) (otri).tri)[m->areaboundindex] = value
+
+/* Check or set a triangle's deallocation. Its second pointer is set to */
+/* NULL to indicate that it is not allocated. (Its first pointer is used */
+/* for the stack of dead items.) Its fourth pointer (its first vertex) */
+/* is set to NULL in case a `badtriang' structure points to it. */
+
+#define deadtri(tria) ((tria)[1] == (triangle) NULL)
+
+#define killtri(tria) \
+ (tria)[1] = (triangle) NULL; \
+ (tria)[3] = (triangle) NULL
+
+/********* Primitives for subsegments *********/
+/* */
+/* */
+
+/* sdecode() converts a pointer to an oriented subsegment. The orientation */
+/* is extracted from the least significant bit of the pointer. The two */
+/* least significant bits (one for orientation, one for viral infection) */
+/* are masked out to produce the real pointer. */
+
+#define sdecode(sptr, osub) \
+ (osub).ssorient = (int) ((unsigned long long) (sptr) & (unsigned long long) 1l); \
+ (osub).ss = (subseg *) \
+ ((unsigned long long) (sptr) & ~ (unsigned long long) 3l)
+
+/* sencode() compresses an oriented subsegment into a single pointer. It */
+/* relies on the assumption that all subsegments are aligned to two-byte */
+/* boundaries, so the least significant bit of (osub).ss is zero. */
+
+#define sencode(osub) \
+ (subseg) ((unsigned long long) (osub).ss | (unsigned long long) (osub).ssorient)
+
+/* ssym() toggles the orientation of a subsegment. */
+
+#define ssym(osub1, osub2) \
+ (osub2).ss = (osub1).ss; \
+ (osub2).ssorient = 1 - (osub1).ssorient
+
+#define ssymself(osub) \
+ (osub).ssorient = 1 - (osub).ssorient
+
+/* spivot() finds the other subsegment (from the same segment) that shares */
+/* the same origin. */
+
+#define spivot(osub1, osub2) \
+ sptr = (osub1).ss[(osub1).ssorient]; \
+ sdecode(sptr, osub2)
+
+#define spivotself(osub) \
+ sptr = (osub).ss[(osub).ssorient]; \
+ sdecode(sptr, osub)
+
+/* snext() finds the next subsegment (from the same segment) in sequence; */
+/* one whose origin is the input subsegment's destination. */
+
+#define snext(osub1, osub2) \
+ sptr = (osub1).ss[1 - (osub1).ssorient]; \
+ sdecode(sptr, osub2)
+
+#define snextself(osub) \
+ sptr = (osub).ss[1 - (osub).ssorient]; \
+ sdecode(sptr, osub)
+
+/* These primitives determine or set the origin or destination of a */
+/* subsegment or the segment that includes it. */
+
+#define sorg(osub, vertexptr) \
+ vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]
+
+#define sdest(osub, vertexptr) \
+ vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]
+
+#define setsorg(osub, vertexptr) \
+ (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr
+
+#define setsdest(osub, vertexptr) \
+ (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr
+
+#define segorg(osub, vertexptr) \
+ vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]
+
+#define segdest(osub, vertexptr) \
+ vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]
+
+#define setsegorg(osub, vertexptr) \
+ (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr
+
+#define setsegdest(osub, vertexptr) \
+ (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr
+
+/* These primitives read or set a boundary marker. Boundary markers are */
+/* used to hold user-defined tags for setting boundary conditions in */
+/* finite element solvers. */
+
+#define mark(osub) (* (int *) ((osub).ss + 8))
+
+#define setmark(osub, value) \
+ * (int *) ((osub).ss + 8) = value
+
+/* Bond two subsegments together. */
+
+#define sbond(osub1, osub2) \
+ (osub1).ss[(osub1).ssorient] = sencode(osub2); \
+ (osub2).ss[(osub2).ssorient] = sencode(osub1)
+
+/* Dissolve a subsegment bond (from one side). Note that the other */
+/* subsegment will still think it's connected to this subsegment. */
+
+#define sdissolve(osub) \
+ (osub).ss[(osub).ssorient] = (subseg) m->dummysub
+
+/* Copy a subsegment. */
+
+#define subsegcopy(osub1, osub2) \
+ (osub2).ss = (osub1).ss; \
+ (osub2).ssorient = (osub1).ssorient
+
+/* Test for equality of subsegments. */
+
+#define subsegequal(osub1, osub2) \
+ (((osub1).ss == (osub2).ss) && \
+ ((osub1).ssorient == (osub2).ssorient))
+
+/* Check or set a subsegment's deallocation. Its second pointer is set to */
+/* NULL to indicate that it is not allocated. (Its first pointer is used */
+/* for the stack of dead items.) Its third pointer (its first vertex) */
+/* is set to NULL in case a `badsubseg' structure points to it. */
+
+#define deadsubseg(sub) ((sub)[1] == (subseg) NULL)
+
+#define killsubseg(sub) \
+ (sub)[1] = (subseg) NULL; \
+ (sub)[2] = (subseg) NULL
+
+/********* Primitives for interacting triangles and subsegments *********/
+/* */
+/* */
+
+/* tspivot() finds a subsegment abutting a triangle. */
+
+#define tspivot(otri, osub) \
+ sptr = (subseg) (otri).tri[6 + (otri).orient]; \
+ sdecode(sptr, osub)
+
+/* stpivot() finds a triangle abutting a subsegment. It requires that the */
+/* variable `ptr' of type `triangle' be defined. */
+
+#define stpivot(osub, otri) \
+ ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \
+ decode(ptr, otri)
+
+/* Bond a triangle to a subsegment. */
+
+#define tsbond(otri, osub) \
+ (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \
+ (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)
+
+/* Dissolve a bond (from the triangle side). */
+
+#define tsdissolve(otri) \
+ (otri).tri[6 + (otri).orient] = (triangle) m->dummysub
+
+/* Dissolve a bond (from the subsegment side). */
+
+#define stdissolve(osub) \
+ (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri
+
+/********* Primitives for vertices *********/
+/* */
+/* */
+
+#define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex]
+
+#define setvertexmark(vx, value) \
+ ((int *) (vx))[m->vertexmarkindex] = value
+
+#define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1]
+
+#define setvertextype(vx, value) \
+ ((int *) (vx))[m->vertexmarkindex + 1] = value
+
+#define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex]
+
+#define setvertex2tri(vx, value) \
+ ((triangle *) (vx))[m->vertex2triindex] = value
+
+/** **/
+/** **/
+/********* Mesh manipulation primitives end here *********/
+
+/********* Memory allocation and program exit wrappers begin here *********/
+/** **/
+/** **/
+
+void triexit(int status)
+{
+ exit(status);
+}
+
+int *trimalloc(int size)
+{
+ int *memptr;
+
+ memptr = (int *) malloc((unsigned int) size);
+ if (memptr == (int *) NULL) {
+ printf("Error: Out of memory.\n");
+ triexit(1);
+ }
+ return(memptr);
+}
+
+void trifree(int *memptr)
+{
+ free(memptr);
+}
+
+/** **/
+/** **/
+/********* Memory allocation and program exit wrappers end here *********/
+
+/*****************************************************************************/
+/* */
+/* internalerror() Ask the user to send me the defective product. Exit. */
+/* */
+/*****************************************************************************/
+
+void internalerror()
+{
+ printf(" Please report this bug to jrs@cs.berkeley.edu\n");
+ printf(" Include the message above, your input data set, and the exact\n");
+ printf(" command line you used to run Triangle.\n");
+ triexit(1);
+}
+
+/*****************************************************************************/
+/* */
+/* parsecommandline() Read the command line, identify switches, and set */
+/* up options and file names. */
+/* */
+/*****************************************************************************/
+
+void parsecommandline(int argc, char **argv, struct behavior *b) {
+ int i, j, k;
+ char workstring[FILENAMESIZE];
+
+ b->poly = b->refine = b->quality = 0;
+ b->vararea = b->fixedarea = b->usertest = 0;
+ b->regionattrib = b->convex = b->weighted = b->jettison = 0;
+ b->firstnumber = 1;
+ b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
+ b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
+ b->noiterationnum = 0;
+ b->noholes = b->noexact = 0;
+ b->incremental = b->sweepline = 0;
+ b->dwyer = 1;
+ b->splitseg = 0;
+ b->docheck = 0;
+ b->nobisect = 0;
+ b->conformdel = 0;
+ b->steiner = -1;
+ b->order = 1;
+ b->minangle = 0.0;
+ b->maxarea = -1.0;
+ b->quiet = b->verbose = 0;
+
+ for (i = 0; i < argc; i++) {
+ for (j = 0; argv[i][j] != '\0'; j++) {
+ if (argv[i][j] == 'p') {
+ b->poly = 1;
+ }
+ if (argv[i][j] == 'A') {
+ b->regionattrib = 1;
+ }
+ if (argv[i][j] == 'c') {
+ b->convex = 1;
+ }
+ if (argv[i][j] == 'w') {
+ b->weighted = 1;
+ }
+ if (argv[i][j] == 'W') {
+ b->weighted = 2;
+ }
+ if (argv[i][j] == 'j') {
+ b->jettison = 1;
+ }
+ if (argv[i][j] == 'z') {
+ b->firstnumber = 0;
+ }
+ if (argv[i][j] == 'e') {
+ b->edgesout = 1;
+ }
+ if (argv[i][j] == 'v') {
+ b->voronoi = 1;
+ }
+ if (argv[i][j] == 'n') {
+ b->neighbors = 1;
+ }
+ if (argv[i][j] == 'g') {
+ b->geomview = 1;
+ }
+ if (argv[i][j] == 'B') {
+ b->nobound = 1;
+ }
+ if (argv[i][j] == 'P') {
+ b->nopolywritten = 1;
+ }
+ if (argv[i][j] == 'N') {
+ b->nonodewritten = 1;
+ }
+ if (argv[i][j] == 'E') {
+ b->noelewritten = 1;
+ }
+ if (argv[i][j] == 'O') {
+ b->noholes = 1;
+ }
+ if (argv[i][j] == 'X') {
+ b->noexact = 1;
+ }
+ if (argv[i][j] == 'o') {
+ if (argv[i][j + 1] == '2') {
+ j++;
+ b->order = 2;
+ }
+ }
+ if (argv[i][j] == 'l') {
+ b->dwyer = 0;
+ }
+ if (argv[i][j] == 'Q') {
+ b->quiet = 1;
+ }
+ if (argv[i][j] == 'V') {
+ b->verbose++;
+ }
+ }
+ }
+ b->usesegments = b->poly || b->refine || b->quality || b->convex;
+ b->goodangle = cos(b->minangle * PI / 180.0);
+ if (b->goodangle == 1.0) {
+ b->offconstant = 0.0;
+ } else {
+ b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
+ }
+ b->goodangle *= b->goodangle;
+ if (b->refine && b->noiterationnum) {
+ printf(
+ "Error: You cannot use the -I switch when refining a triangulation.\n");
+ triexit(1);
+ }
+ /* Be careful not to allocate space for element area constraints that */
+ /* will never be assigned any value (other than the default -1.0). */
+ if (!b->refine && !b->poly) {
+ b->vararea = 0;
+ }
+ /* Be careful not to add an extra attribute to each element unless the */
+ /* input supports it (PSLG in, but not refining a preexisting mesh). */
+ if (b->refine || !b->poly) {
+ b->regionattrib = 0;
+ }
+ /* Regular/weighted triangulations are incompatible with PSLGs */
+ /* and meshing. */
+ if (b->weighted && (b->poly || b->quality)) {
+ b->weighted = 0;
+ if (!b->quiet) {
+ printf("Warning: weighted triangulations (-w, -W) are incompatible\n");
+ printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n"
+ );
+ }
+ }
+ if (b->jettison && b->nonodewritten && !b->quiet) {
+ printf("Warning: -j and -N switches are somewhat incompatible.\n");
+ printf(" If any vertices are jettisoned, you will need the output\n");
+ printf(" .node file to reconstruct the new node indices.");
+ }
+}
+
+/** **/
+/** **/
+/********* User interaction routines begin here *********/
+
+/********* Debugging routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* printtriangle() Print out the details of an oriented triangle. */
+/* */
+/* I originally wrote this procedure to simplify debugging; it can be */
+/* called directly from the debugger, and presents information about an */
+/* oriented triangle in digestible form. It's also used when the */
+/* highest level of verbosity (`-VVV') is specified. */
+/* */
+/*****************************************************************************/
+
+void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
+{
+ struct otri printtri;
+ struct osub printsh;
+ vertex printvertex;
+
+ printf("triangle x%lx with orientation %d:\n", (unsigned long long) t->tri,
+ t->orient);
+ decode(t->tri[0], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [0] = Outer space\n");
+ } else {
+ printf(" [0] = x%lx %d\n", (unsigned long long) printtri.tri,
+ printtri.orient);
+ }
+ decode(t->tri[1], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [1] = Outer space\n");
+ } else {
+ printf(" [1] = x%lx %d\n", (unsigned long long) printtri.tri,
+ printtri.orient);
+ }
+ decode(t->tri[2], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [2] = Outer space\n");
+ } else {
+ printf(" [2] = x%lx %d\n", (unsigned long long) printtri.tri,
+ printtri.orient);
+ }
+
+ org(*t, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
+ else
+ printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
+ (t->orient + 1) % 3 + 3, (unsigned long long) printvertex,
+ printvertex[0], printvertex[1]);
+ dest(*t, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3);
+ else
+ printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
+ (t->orient + 2) % 3 + 3, (unsigned long long) printvertex,
+ printvertex[0], printvertex[1]);
+ apex(*t, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Apex [%d] = NULL\n", t->orient + 3);
+ else
+ printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
+ t->orient + 3, (unsigned long long) printvertex,
+ printvertex[0], printvertex[1]);
+
+ if (b->usesegments) {
+ sdecode(t->tri[6], printsh);
+ if (printsh.ss != m->dummysub) {
+ printf(" [6] = x%lx %d\n", (unsigned long long) printsh.ss,
+ printsh.ssorient);
+ }
+ sdecode(t->tri[7], printsh);
+ if (printsh.ss != m->dummysub) {
+ printf(" [7] = x%lx %d\n", (unsigned long long) printsh.ss,
+ printsh.ssorient);
+ }
+ sdecode(t->tri[8], printsh);
+ if (printsh.ss != m->dummysub) {
+ printf(" [8] = x%lx %d\n", (unsigned long long) printsh.ss,
+ printsh.ssorient);
+ }
+ }
+
+ if (b->vararea) {
+ printf(" Area constraint: %.4g\n", areabound(*t));
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* printsubseg() Print out the details of an oriented subsegment. */
+/* */
+/* I originally wrote this procedure to simplify debugging; it can be */
+/* called directly from the debugger, and presents information about an */
+/* oriented subsegment in digestible form. It's also used when the highest */
+/* level of verbosity (`-VVV') is specified. */
+/* */
+/*****************************************************************************/
+
+void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
+{
+ struct osub printsh;
+ struct otri printtri;
+ vertex printvertex;
+
+ printf("subsegment x%lx with orientation %d and mark %d:\n",
+ (unsigned long long) s->ss, s->ssorient, mark(*s));
+ sdecode(s->ss[0], printsh);
+ if (printsh.ss == m->dummysub) {
+ printf(" [0] = No subsegment\n");
+ } else {
+ printf(" [0] = x%lx %d\n", (unsigned long long) printsh.ss,
+ printsh.ssorient);
+ }
+ sdecode(s->ss[1], printsh);
+ if (printsh.ss == m->dummysub) {
+ printf(" [1] = No subsegment\n");
+ } else {
+ printf(" [1] = x%lx %d\n", (unsigned long long) printsh.ss,
+ printsh.ssorient);
+ }
+
+ sorg(*s, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Origin[%d] = NULL\n", 2 + s->ssorient);
+ else
+ printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
+ 2 + s->ssorient, (unsigned long long) printvertex,
+ printvertex[0], printvertex[1]);
+ sdest(*s, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Dest [%d] = NULL\n", 3 - s->ssorient);
+ else
+ printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
+ 3 - s->ssorient, (unsigned long long) printvertex,
+ printvertex[0], printvertex[1]);
+
+ decode(s->ss[6], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [6] = Outer space\n");
+ } else {
+ printf(" [6] = x%lx %d\n", (unsigned long long) printtri.tri,
+ printtri.orient);
+ }
+ decode(s->ss[7], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [7] = Outer space\n");
+ } else {
+ printf(" [7] = x%lx %d\n", (unsigned long long) printtri.tri,
+ printtri.orient);
+ }
+
+ segorg(*s, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient);
+ else
+ printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n",
+ 4 + s->ssorient, (unsigned long long) printvertex,
+ printvertex[0], printvertex[1]);
+ segdest(*s, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient);
+ else
+ printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n",
+ 5 - s->ssorient, (unsigned long long) printvertex,
+ printvertex[0], printvertex[1]);
+}
+
+/** **/
+/** **/
+/********* Debugging routines end here *********/
+
+/********* Memory management routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* poolzero() Set all of a pool's fields to zero. */
+/* */
+/* This procedure should never be called on a pool that has any memory */
+/* allocated to it, as that memory would leak. */
+/* */
+/*****************************************************************************/
+
+void poolzero(struct memorypool *pool)
+{
+ pool->firstblock = (int **) NULL;
+ pool->nowblock = (int **) NULL;
+ pool->nextitem = (int *) NULL;
+ pool->deaditemstack = (int *) NULL;
+ pool->pathblock = (int **) NULL;
+ pool->pathitem = (int *) NULL;
+ pool->alignbytes = 0;
+ pool->itembytes = 0;
+ pool->itemsperblock = 0;
+ pool->itemsfirstblock = 0;
+ pool->items = 0;
+ pool->maxitems = 0;
+ pool->unallocateditems = 0;
+ pool->pathitemsleft = 0;
+}
+
+/*****************************************************************************/
+/* */
+/* poolrestart() Deallocate all items in a pool. */
+/* */
+/* The pool is returned to its starting state, except that no memory is */
+/* freed to the operating system. Rather, the previously allocated blocks */
+/* are ready to be reused. */
+/* */
+/*****************************************************************************/
+
+void poolrestart(struct memorypool *pool)
+{
+ unsigned long long alignptr;
+
+ pool->items = 0;
+ pool->maxitems = 0;
+
+ /* Set the currently active block. */
+ pool->nowblock = pool->firstblock;
+ /* Find the first item in the pool. Increment by the size of (int *). */
+ alignptr = (unsigned long long) (pool->nowblock + 1);
+ /* Align the item on an `alignbytes'-byte boundary. */
+ pool->nextitem = (int *)
+ (alignptr + (unsigned long long) pool->alignbytes -
+ (alignptr % (unsigned long long) pool->alignbytes));
+ /* There are lots of unallocated items left in this block. */
+ pool->unallocateditems = pool->itemsfirstblock;
+ /* The stack of deallocated items is empty. */
+ pool->deaditemstack = (int *) NULL;
+}
+
+/*****************************************************************************/
+/* */
+/* poolinit() Initialize a pool of memory for allocation of items. */
+/* */
+/* This routine initializes the machinery for allocating items. A `pool' */
+/* is created whose records have size at least `bytecount'. Items will be */
+/* allocated in `itemcount'-item blocks. Each item is assumed to be a */
+/* collection of words, and either pointers or floating-point values are */
+/* assumed to be the "primary" word type. (The "primary" word type is used */
+/* to determine alignment of items.) If `alignment' isn't zero, all items */
+/* will be `alignment'-byte aligned in memory. `alignment' must be either */
+/* a multiple or a factor of the primary word size; powers of two are safe. */
+/* `alignment' is normally used to create a few unused bits at the bottom */
+/* of each item's pointer, in which information may be stored. */
+/* */
+/* Don't change this routine unless you understand it. */
+/* */
+/*****************************************************************************/
+
+void poolinit(struct memorypool *pool, int bytecount, int itemcount,
+ int firstitemcount, int alignment)
+{
+ /* Find the proper alignment, which must be at least as large as: */
+ /* - The parameter `alignment'. */
+ /* - sizeof(int *), so the stack of dead items can be maintained */
+ /* without unaligned accesses. */
+ if (alignment > sizeof(int *)) {
+ pool->alignbytes = alignment;
+ } else {
+ pool->alignbytes = sizeof(int *);
+ }
+ pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
+ pool->alignbytes;
+ pool->itemsperblock = itemcount;
+ if (firstitemcount == 0) {
+ pool->itemsfirstblock = itemcount;
+ } else {
+ pool->itemsfirstblock = firstitemcount;
+ }
+
+ /* Allocate a block of items. Space for `itemsfirstblock' items and one */
+ /* pointer (to point to the next block) are allocated, as well as space */
+ /* to ensure alignment of the items. */
+ pool->firstblock = (int **)
+ trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(int *) +
+ pool->alignbytes);
+ /* Set the next block pointer to NULL. */
+ *(pool->firstblock) = (int *) NULL;
+ poolrestart(pool);
+}
+
+/*****************************************************************************/
+/* */
+/* pooldeinit() Free to the operating system all memory taken by a pool. */
+/* */
+/*****************************************************************************/
+
+void pooldeinit(struct memorypool *pool)
+{
+ while (pool->firstblock != (int **) NULL) {
+ pool->nowblock = (int **) *(pool->firstblock);
+ trifree((int *) pool->firstblock);
+ pool->firstblock = pool->nowblock;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* poolalloc() Allocate space for an item. */
+/* */
+/*****************************************************************************/
+
+int *poolalloc(struct memorypool *pool)
+{
+ int *newitem;
+ int **newblock;
+ unsigned long long alignptr;
+
+ /* First check the linked list of dead items. If the list is not */
+ /* empty, allocate an item from the list rather than a fresh one. */
+ if (pool->deaditemstack != (int *) NULL) {
+ newitem = pool->deaditemstack; /* Take first item in list. */
+ pool->deaditemstack = * (int **) pool->deaditemstack;
+ } else {
+ /* Check if there are any free items left in the current block. */
+ if (pool->unallocateditems == 0) {
+ /* Check if another block must be allocated. */
+ if (*(pool->nowblock) == (int *) NULL) {
+ /* Allocate a new block of items, pointed to by the previous block. */
+ newblock = (int **) trimalloc(pool->itemsperblock * pool->itembytes +
+ (int) sizeof(int *) +
+ pool->alignbytes);
+ *(pool->nowblock) = (int *) newblock;
+ /* The next block pointer is NULL. */
+ *newblock = (int *) NULL;
+ }
+
+ /* Move to the new block. */
+ pool->nowblock = (int **) *(pool->nowblock);
+ /* Find the first item in the block. */
+ /* Increment by the size of (int *). */
+ alignptr = (unsigned long long) (pool->nowblock + 1);
+ /* Align the item on an `alignbytes'-byte boundary. */
+ pool->nextitem = (int *)
+ (alignptr + (unsigned long long) pool->alignbytes -
+ (alignptr % (unsigned long long) pool->alignbytes));
+ /* There are lots of unallocated items left in this block. */
+ pool->unallocateditems = pool->itemsperblock;
+ }
+
+ /* Allocate a new item. */
+ newitem = pool->nextitem;
+ /* Advance `nextitem' pointer to next free item in block. */
+ pool->nextitem = (int *) ((char *) pool->nextitem + pool->itembytes);
+ pool->unallocateditems--;
+ pool->maxitems++;
+ }
+ pool->items++;
+ return newitem;
+}
+
+/*****************************************************************************/
+/* */
+/* pooldealloc() Deallocate space for an item. */
+/* */
+/* The deallocated space is stored in a queue for later reuse. */
+/* */
+/*****************************************************************************/
+
+void pooldealloc(struct memorypool *pool, int *dyingitem)
+{
+ /* Push freshly killed item onto stack. */
+ *((int **) dyingitem) = pool->deaditemstack;
+ pool->deaditemstack = dyingitem;
+ pool->items--;
+}
+
+/*****************************************************************************/
+/* */
+/* traversalinit() Prepare to traverse the entire list of items. */
+/* */
+/* This routine is used in conjunction with traverse(). */
+/* */
+/*****************************************************************************/
+
+void traversalinit(struct memorypool *pool)
+{
+ unsigned long long alignptr;
+
+ /* Begin the traversal in the first block. */
+ pool->pathblock = pool->firstblock;
+ /* Find the first item in the block. Increment by the size of (int *). */
+ alignptr = (unsigned long long) (pool->pathblock + 1);
+ /* Align with item on an `alignbytes'-byte boundary. */
+ pool->pathitem = (int *)
+ (alignptr + (unsigned long long) pool->alignbytes -
+ (alignptr % (unsigned long long) pool->alignbytes));
+ /* Set the number of items left in the current block. */
+ pool->pathitemsleft = pool->itemsfirstblock;
+}
+
+/*****************************************************************************/
+/* */
+/* traverse() Find the next item in the list. */
+/* */
+/* This routine is used in conjunction with traversalinit(). Be forewarned */
+/* that this routine successively returns all items in the list, including */
+/* deallocated ones on the deaditemqueue. It's up to you to figure out */
+/* which ones are actually dead. Why? I don't want to allocate extra */
+/* space just to demarcate dead items. It can usually be done more */
+/* space-efficiently by a routine that knows something about the structure */
+/* of the item. */
+/* */
+/*****************************************************************************/
+
+int *traverse(struct memorypool *pool)
+{
+ int *newitem;
+ unsigned long long alignptr;
+
+ /* Stop upon exhausting the list of items. */
+ if (pool->pathitem == pool->nextitem) {
+ return (int *) NULL;
+ }
+
+ /* Check whether any untraversed items remain in the current block. */
+ if (pool->pathitemsleft == 0) {
+ /* Find the next block. */
+ pool->pathblock = (int **) *(pool->pathblock);
+ /* Find the first item in the block. Increment by the size of (int *). */
+ alignptr = (unsigned long long) (pool->pathblock + 1);
+ /* Align with item on an `alignbytes'-byte boundary. */
+ pool->pathitem = (int *)
+ (alignptr + (unsigned long long) pool->alignbytes -
+ (alignptr % (unsigned long long) pool->alignbytes));
+ /* Set the number of items left in the current block. */
+ pool->pathitemsleft = pool->itemsperblock;
+ }
+
+ newitem = pool->pathitem;
+ /* Find the next item in the block. */
+ pool->pathitem = (int *) ((char *) pool->pathitem + pool->itembytes);
+ pool->pathitemsleft--;
+ return newitem;
+}
+
+/*****************************************************************************/
+/* */
+/* dummyinit() Initialize the triangle that fills "outer space" and the */
+/* omnipresent subsegment. */
+/* */
+/* The triangle that fills "outer space," called `dummytri', is pointed to */
+/* by every triangle and subsegment on a boundary (be it outer or inner) of */
+/* the triangulation. Also, `dummytri' points to one of the triangles on */
+/* the convex hull (until the holes and concavities are carved), making it */
+/* possible to find a starting triangle for point location. */
+/* */
+/* The omnipresent subsegment, `dummysub', is pointed to by every triangle */
+/* or subsegment that doesn't have a full complement of real subsegments */
+/* to point to. */
+/* */
+/* `dummytri' and `dummysub' are generally required to fulfill only a few */
+/* invariants: their vertices must remain NULL and `dummytri' must always */
+/* be bonded (at offset zero) to some triangle on the convex hull of the */
+/* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */
+/* `dummysub' may change willy-nilly. This makes it possible to avoid */
+/* writing a good deal of special-case code (in the edge flip, for example) */
+/* for dealing with the boundary of the mesh, places where no subsegment is */
+/* present, and so forth. Other entities are frequently bonded to */
+/* `dummytri' and `dummysub' as if they were real mesh entities, with no */
+/* harm done. */
+/* */
+/*****************************************************************************/
+
+void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
+ int subsegbytes)
+{
+ unsigned long long alignptr;
+
+ /* Set up `dummytri', the `triangle' that occupies "outer space." */
+ m->dummytribase = (triangle *) trimalloc(trianglebytes +
+ m->triangles.alignbytes);
+ /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
+ alignptr = (unsigned long long) m->dummytribase;
+ m->dummytri = (triangle *)
+ (alignptr + (unsigned long long) m->triangles.alignbytes -
+ (alignptr % (unsigned long long) m->triangles.alignbytes));
+ /* Initialize the three adjoining triangles to be "outer space." These */
+ /* will eventually be changed by various bonding operations, but their */
+ /* values don't really matter, as long as they can legally be */
+ /* dereferenced. */
+ m->dummytri[0] = (triangle) m->dummytri;
+ m->dummytri[1] = (triangle) m->dummytri;
+ m->dummytri[2] = (triangle) m->dummytri;
+ /* Three NULL vertices. */
+ m->dummytri[3] = (triangle) NULL;
+ m->dummytri[4] = (triangle) NULL;
+ m->dummytri[5] = (triangle) NULL;
+
+ if (b->usesegments) {
+ /* Set up `dummysub', the omnipresent subsegment pointed to by any */
+ /* triangle side or subsegment end that isn't attached to a real */
+ /* subsegment. */
+ m->dummysubbase = (subseg *) trimalloc(subsegbytes +
+ m->subsegs.alignbytes);
+ /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
+ alignptr = (unsigned long long) m->dummysubbase;
+ m->dummysub = (subseg *)
+ (alignptr + (unsigned long long) m->subsegs.alignbytes -
+ (alignptr % (unsigned long long) m->subsegs.alignbytes));
+ /* Initialize the two adjoining subsegments to be the omnipresent */
+ /* subsegment. These will eventually be changed by various bonding */
+ /* operations, but their values don't really matter, as long as they */
+ /* can legally be dereferenced. */
+ m->dummysub[0] = (subseg) m->dummysub;
+ m->dummysub[1] = (subseg) m->dummysub;
+ /* Four NULL vertices. */
+ m->dummysub[2] = (subseg) NULL;
+ m->dummysub[3] = (subseg) NULL;
+ m->dummysub[4] = (subseg) NULL;
+ m->dummysub[5] = (subseg) NULL;
+ /* Initialize the two adjoining triangles to be "outer space." */
+ m->dummysub[6] = (subseg) m->dummytri;
+ m->dummysub[7] = (subseg) m->dummytri;
+ /* Set the boundary marker to zero. */
+ * (int *) (m->dummysub + 8) = 0;
+
+ /* Initialize the three adjoining subsegments of `dummytri' to be */
+ /* the omnipresent subsegment. */
+ m->dummytri[6] = (triangle) m->dummysub;
+ m->dummytri[7] = (triangle) m->dummysub;
+ m->dummytri[8] = (triangle) m->dummysub;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* initializevertexpool() Calculate the size of the vertex data structure */
+/* and initialize its memory pool. */
+/* */
+/* This routine also computes the `vertexmarkindex' and `vertex2triindex' */
+/* indices used to find values within each vertex. */
+/* */
+/*****************************************************************************/
+
+void initializevertexpool(struct mesh *m, struct behavior *b)
+{
+ int vertexsize;
+
+ /* The index within each vertex at which the boundary marker is found, */
+ /* followed by the vertex type. Ensure the vertex marker is aligned to */
+ /* a sizeof(int)-byte address. */
+ m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(float) +
+ sizeof(int) - 1) /
+ sizeof(int);
+ vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
+ if (b->poly) {
+ /* The index within each vertex at which a triangle pointer is found. */
+ /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
+ m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
+ sizeof(triangle);
+ vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
+ }
+
+ /* Initialize the pool of vertices. */
+ poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
+ m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
+ sizeof(float));
+}
+
+/*****************************************************************************/
+/* */
+/* initializetrisubpools() Calculate the sizes of the triangle and */
+/* subsegment data structures and initialize */
+/* their memory pools. */
+/* */
+/* This routine also computes the `highorderindex', `elemattribindex', and */
+/* `areaboundindex' indices used to find values within each triangle. */
+/* */
+/*****************************************************************************/
+
+void initializetrisubpools(struct mesh *m, struct behavior *b)
+{
+ int trisize;
+
+ /* The index within each triangle at which the extra nodes (above three) */
+ /* associated with high order elements are found. There are three */
+ /* pointers to other triangles, three pointers to corners, and possibly */
+ /* three pointers to subsegments before the extra nodes. */
+ m->highorderindex = 6 + (b->usesegments * 3);
+ /* The number of bytes occupied by a triangle. */
+ trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
+ sizeof(triangle);
+ /* The index within each triangle at which its attributes are found, */
+ /* where the index is measured in floats. */
+ m->elemattribindex = (trisize + sizeof(float) - 1) / sizeof(float);
+ /* The index within each triangle at which the maximum area constraint */
+ /* is found, where the index is measured in floats. Note that if the */
+ /* `regionattrib' flag is set, an additional attribute will be added. */
+ m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
+ /* If triangle attributes or an area bound are needed, increase the number */
+ /* of bytes occupied by a triangle. */
+ if (b->vararea) {
+ trisize = (m->areaboundindex + 1) * sizeof(float);
+ } else if (m->eextras + b->regionattrib > 0) {
+ trisize = m->areaboundindex * sizeof(float);
+ }
+ /* If a Voronoi diagram or triangle neighbor graph is requested, make */
+ /* sure there's room to store an integer index in each triangle. This */
+ /* integer index can occupy the same space as the subsegment pointers */
+ /* or attributes or area constraint or extra nodes. */
+ if ((b->voronoi || b->neighbors) &&
+ (trisize < 6 * sizeof(triangle) + sizeof(int))) {
+ trisize = 6 * sizeof(triangle) + sizeof(int);
+ }
+
+ /* Having determined the memory size of a triangle, initialize the pool. */
+ poolinit(&m->triangles, trisize, TRIPERBLOCK,
+ (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
+ TRIPERBLOCK, 4);
+
+ if (b->usesegments) {
+ /* Initialize the pool of subsegments. Take into account all eight */
+ /* pointers and one boundary marker. */
+ poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
+ SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
+
+ /* Initialize the "outer space" triangle and omnipresent subsegment. */
+ dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
+ } else {
+ /* Initialize the "outer space" triangle. */
+ dummyinit(m, b, m->triangles.itembytes, 0);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* triangledealloc() Deallocate space for a triangle, marking it dead. */
+/* */
+/*****************************************************************************/
+
+void triangledealloc(struct mesh *m, triangle *dyingtriangle)
+{
+ /* Mark the triangle as dead. This makes it possible to detect dead */
+ /* triangles when traversing the list of all triangles. */
+ killtri(dyingtriangle);
+ pooldealloc(&m->triangles, (int *) dyingtriangle);
+}
+
+/*****************************************************************************/
+/* */
+/* triangletraverse() Traverse the triangles, skipping dead ones. */
+/* */
+/*****************************************************************************/
+
+triangle *triangletraverse(struct mesh *m)
+{
+ triangle *newtriangle;
+
+ do {
+ newtriangle = (triangle *) traverse(&m->triangles);
+ if (newtriangle == (triangle *) NULL) {
+ return (triangle *) NULL;
+ }
+ } while (deadtri(newtriangle)); /* Skip dead ones. */
+ return newtriangle;
+}
+
+/*****************************************************************************/
+/* */
+/* subsegdealloc() Deallocate space for a subsegment, marking it dead. */
+/* */
+/*****************************************************************************/
+
+void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
+{
+ /* Mark the subsegment as dead. This makes it possible to detect dead */
+ /* subsegments when traversing the list of all subsegments. */
+ killsubseg(dyingsubseg);
+ pooldealloc(&m->subsegs, (int *) dyingsubseg);
+}
+
+/*****************************************************************************/
+/* */
+/* subsegtraverse() Traverse the subsegments, skipping dead ones. */
+/* */
+/*****************************************************************************/
+
+subseg *subsegtraverse(struct mesh *m)
+{
+ subseg *newsubseg;
+
+ do {
+ newsubseg = (subseg *) traverse(&m->subsegs);
+ if (newsubseg == (subseg *) NULL) {
+ return (subseg *) NULL;
+ }
+ } while (deadsubseg(newsubseg)); /* Skip dead ones. */
+ return newsubseg;
+}
+
+/*****************************************************************************/
+/* */
+/* vertexdealloc() Deallocate space for a vertex, marking it dead. */
+/* */
+/*****************************************************************************/
+
+void vertexdealloc(struct mesh *m, vertex dyingvertex)
+{
+ /* Mark the vertex as dead. This makes it possible to detect dead */
+ /* vertices when traversing the list of all vertices. */
+ setvertextype(dyingvertex, DEADVERTEX);
+ pooldealloc(&m->vertices, (int *) dyingvertex);
+}
+
+/*****************************************************************************/
+/* */
+/* vertextraverse() Traverse the vertices, skipping dead ones. */
+/* */
+/*****************************************************************************/
+
+vertex vertextraverse(struct mesh *m)
+{
+ vertex newvertex;
+
+ do {
+ newvertex = (vertex) traverse(&m->vertices);
+ if (newvertex == (vertex) NULL) {
+ return (vertex) NULL;
+ }
+ } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */
+ return newvertex;
+}
+
+/*****************************************************************************/
+/* */
+/* getvertex() Get a specific vertex, by number, from the list. */
+/* */
+/* The first vertex is number 'firstnumber'. */
+/* */
+/* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
+/* is large). I don't care to take the trouble to make it work in constant */
+/* time. */
+/* */
+/*****************************************************************************/
+
+vertex getvertex(struct mesh *m, struct behavior *b, int number)
+{
+ int **getblock;
+ char *foundvertex;
+ unsigned long long alignptr;
+ int current;
+
+ getblock = m->vertices.firstblock;
+ current = b->firstnumber;
+
+ /* Find the right block. */
+ if (current + m->vertices.itemsfirstblock <= number) {
+ getblock = (int **) *getblock;
+ current += m->vertices.itemsfirstblock;
+ while (current + m->vertices.itemsperblock <= number) {
+ getblock = (int **) *getblock;
+ current += m->vertices.itemsperblock;
+ }
+ }
+
+ /* Now find the right vertex. */
+ alignptr = (unsigned long long) (getblock + 1);
+ foundvertex = (char *) (alignptr + (unsigned long long) m->vertices.alignbytes -
+ (alignptr % (unsigned long long) m->vertices.alignbytes));
+ return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
+}
+
+/*****************************************************************************/
+/* */
+/* triangledeinit() Free all remaining allocated memory. */
+/* */
+/*****************************************************************************/
+
+void triangledeinit(struct mesh *m, struct behavior *b)
+{
+ pooldeinit(&m->triangles);
+ trifree((int *) m->dummytribase);
+ if (b->usesegments) {
+ pooldeinit(&m->subsegs);
+ trifree((int *) m->dummysubbase);
+ }
+ pooldeinit(&m->vertices);
+}
+
+/** **/
+/** **/
+/********* Memory management routines end here *********/
+
+/********* Constructors begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* maketriangle() Create a new triangle with orientation zero. */
+/* */
+/*****************************************************************************/
+
+void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
+{
+ int i;
+
+ newotri->tri = (triangle *) poolalloc(&m->triangles);
+ /* Initialize the three adjoining triangles to be "outer space". */
+ newotri->tri[0] = (triangle) m->dummytri;
+ newotri->tri[1] = (triangle) m->dummytri;
+ newotri->tri[2] = (triangle) m->dummytri;
+ /* Three NULL vertices. */
+ newotri->tri[3] = (triangle) NULL;
+ newotri->tri[4] = (triangle) NULL;
+ newotri->tri[5] = (triangle) NULL;
+ if (b->usesegments) {
+ /* Initialize the three adjoining subsegments to be the omnipresent */
+ /* subsegment. */
+ newotri->tri[6] = (triangle) m->dummysub;
+ newotri->tri[7] = (triangle) m->dummysub;
+ newotri->tri[8] = (triangle) m->dummysub;
+ }
+ for (i = 0; i < m->eextras; i++) {
+ setelemattribute(*newotri, i, 0.0);
+ }
+ if (b->vararea) {
+ setareabound(*newotri, -1.0);
+ }
+
+ newotri->orient = 0;
+}
+
+/*****************************************************************************/
+/* */
+/* makesubseg() Create a new subsegment with orientation zero. */
+/* */
+/*****************************************************************************/
+
+void makesubseg(struct mesh *m, struct osub *newsubseg)
+{
+ newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
+ /* Initialize the two adjoining subsegments to be the omnipresent */
+ /* subsegment. */
+ newsubseg->ss[0] = (subseg) m->dummysub;
+ newsubseg->ss[1] = (subseg) m->dummysub;
+ /* Four NULL vertices. */
+ newsubseg->ss[2] = (subseg) NULL;
+ newsubseg->ss[3] = (subseg) NULL;
+ newsubseg->ss[4] = (subseg) NULL;
+ newsubseg->ss[5] = (subseg) NULL;
+ /* Initialize the two adjoining triangles to be "outer space." */
+ newsubseg->ss[6] = (subseg) m->dummytri;
+ newsubseg->ss[7] = (subseg) m->dummytri;
+ /* Set the boundary marker to zero. */
+ setmark(*newsubseg, 0);
+
+ newsubseg->ssorient = 0;
+}
+
+/** **/
+/** **/
+/********* Constructors end here *********/
+
+/********* Geometric primitives begin here *********/
+/** **/
+/** **/
+
+/* The adaptive exact arithmetic geometric predicates implemented herein are */
+/* described in detail in my paper, "Adaptive Precision Floating-Point */
+/* Arithmetic and Fast Robust Geometric Predicates." See the header for a */
+/* full citation. */
+
+/* Which of the following two methods of finding the absolute values is */
+/* fastest is compiler-dependent. A few compilers can inline and optimize */
+/* the fabs() call; but most will incur the overhead of a function call, */
+/* which is disastrously slow. A faster way on IEEE machines might be to */
+/* mask the appropriate bit, but that's difficult to do in C without */
+/* forcing the value to be stored to memory (rather than be kept in the */
+/* register to which the optimizer assigned it). */
+
+#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
+/* #define Absolute(a) fabs(a) */
+
+/* Many of the operations are broken up into two pieces, a main part that */
+/* performs an approximate operation, and a "tail" that computes the */
+/* roundoff error of that operation. */
+/* */
+/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
+/* Split(), and Two_Product() are all implemented as described in the */
+/* reference. Each of these macros requires certain variables to be */
+/* defined in the calling routine. The variables `bvirt', `c', `abig', */
+/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
+/* they store the result of an operation that may incur roundoff error. */
+/* The input parameter `x' (or the highest numbered `x_' parameter) must */
+/* also be declared `INEXACT'. */
+
+#define Fast_Two_Sum_Tail(a, b, x, y) \
+ bvirt = x - a; \
+ y = b - bvirt
+
+#define Fast_Two_Sum(a, b, x, y) \
+ x = (float) (a + b); \
+ Fast_Two_Sum_Tail(a, b, x, y)
+
+#define Two_Sum_Tail(a, b, x, y) \
+ bvirt = (float) (x - a); \
+ avirt = x - bvirt; \
+ bround = b - bvirt; \
+ around = a - avirt; \
+ y = around + bround
+
+#define Two_Sum(a, b, x, y) \
+ x = (float) (a + b); \
+ Two_Sum_Tail(a, b, x, y)
+
+#define Two_Diff_Tail(a, b, x, y) \
+ bvirt = (float) (a - x); \
+ avirt = x + bvirt; \
+ bround = bvirt - b; \
+ around = a - avirt; \
+ y = around + bround
+
+#define Two_Diff(a, b, x, y) \
+ x = (float) (a - b); \
+ Two_Diff_Tail(a, b, x, y)
+
+#define Split(a, ahi, alo) \
+ c = (float) (splitter * a); \
+ abig = (float) (c - a); \
+ ahi = c - abig; \
+ alo = a - ahi
+
+#define Two_Product_Tail(a, b, x, y) \
+ Split(a, ahi, alo); \
+ Split(b, bhi, blo); \
+ err1 = x - (ahi * bhi); \
+ err2 = err1 - (alo * bhi); \
+ err3 = err2 - (ahi * blo); \
+ y = (alo * blo) - err3
+
+#define Two_Product(a, b, x, y) \
+ x = (float) (a * b); \
+ Two_Product_Tail(a, b, x, y)
+
+/* Two_Product_Presplit() is Two_Product() where one of the inputs has */
+/* already been split. Avoids redundant splitting. */
+
+#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
+ x = (float) (a * b); \
+ Split(a, ahi, alo); \
+ err1 = x - (ahi * bhi); \
+ err2 = err1 - (alo * bhi); \
+ err3 = err2 - (ahi * blo); \
+ y = (alo * blo) - err3
+
+/* Square() can be done more quickly than Two_Product(). */
+
+#define Square_Tail(a, x, y) \
+ Split(a, ahi, alo); \
+ err1 = x - (ahi * ahi); \
+ err3 = err1 - ((ahi + ahi) * alo); \
+ y = (alo * alo) - err3
+
+#define Square(a, x, y) \
+ x = (float) (a * a); \
+ Square_Tail(a, x, y)
+
+/* Macros for summing expansions of various fixed lengths. These are all */
+/* unrolled versions of Expansion_Sum(). */
+
+#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
+ Two_Sum(a0, b , _i, x0); \
+ Two_Sum(a1, _i, x2, x1)
+
+#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
+ Two_Diff(a0, b , _i, x0); \
+ Two_Sum( a1, _i, x2, x1)
+
+#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
+ Two_One_Sum(a1, a0, b0, _j, _0, x0); \
+ Two_One_Sum(_j, _0, b1, x3, x2, x1)
+
+#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
+ Two_One_Diff(a1, a0, b0, _j, _0, x0); \
+ Two_One_Diff(_j, _0, b1, x3, x2, x1)
+
+/* Macro for multiplying a two-component expansion by a single component. */
+
+#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
+ Split(b, bhi, blo); \
+ Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
+ Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
+ Two_Sum(_i, _0, _k, x1); \
+ Fast_Two_Sum(_j, _k, x3, x2)
+
+/*****************************************************************************/
+/* */
+/* exactinit() Initialize the variables used for exact arithmetic. */
+/* */
+/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */
+/* floating-point arithmetic. `epsilon' bounds the relative roundoff */
+/* error. It is used for floating-point error analysis. */
+/* */
+/* `splitter' is used to split floating-point numbers into two half- */
+/* length significands for exact multiplication. */
+/* */
+/* I imagine that a highly optimizing compiler might be too smart for its */
+/* own good, and somehow cause this routine to fail, if it pretends that */
+/* floating-point arithmetic is too much like real arithmetic. */
+/* */
+/* Don't change this routine unless you fully understand it. */
+/* */
+/*****************************************************************************/
+
+void exactinit()
+{
+ float half;
+ float check, lastcheck;
+ int every_other;
+ every_other = 1;
+ half = 0.5;
+ epsilon = 1.0;
+ splitter = 1.0;
+ check = 1.0;
+ /* Repeatedly divide `epsilon' by two until it is too small to add to */
+ /* one without causing roundoff. (Also check if the sum is equal to */
+ /* the previous sum, for machines that round up instead of using exact */
+ /* rounding. Not that these routines will work on such machines.) */
+ do {
+ lastcheck = check;
+ epsilon *= half;
+ if (every_other) {
+ splitter *= 2.0;
+ }
+ every_other = !every_other;
+ check = 1.0 + epsilon;
+ } while ((check != 1.0) && (check != lastcheck));
+ splitter += 1.0;
+ /* Error bounds for orientation and incircle tests. */
+ resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
+ ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
+ ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
+ ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
+ iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
+ iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
+ iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
+ o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
+ o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
+ o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
+}
+
+/*****************************************************************************/
+/* */
+/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
+/* components from the output expansion. */
+/* */
+/* Sets h = e + f. See my Robust Predicates paper for details. */
+/* */
+/* If round-to-even is used (as with IEEE 754), maintains the strongly */
+/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
+/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
+/* properties. */
+/* */
+/*****************************************************************************/
+
+int fast_expansion_sum_zeroelim(int elen, float *e, int flen, float *f, float *h)
+{
+ float Q;
+ float Qnew;
+ float hh;
+ float bvirt;
+ float avirt, bround, around;
+ int eindex, findex, hindex;
+ float enow, fnow;
+
+ enow = e[0];
+ fnow = f[0];
+ eindex = findex = 0;
+ if ((fnow > enow) == (fnow > -enow)) {
+ Q = enow;
+ enow = e[++eindex];
+ } else {
+ Q = fnow;
+ fnow = f[++findex];
+ }
+ hindex = 0;
+ if ((eindex < elen) && (findex < flen)) {
+ if ((fnow > enow) == (fnow > -enow)) {
+ Fast_Two_Sum(enow, Q, Qnew, hh);
+ enow = e[++eindex];
+ } else {
+ Fast_Two_Sum(fnow, Q, Qnew, hh);
+ fnow = f[++findex];
+ }
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ while ((eindex < elen) && (findex < flen)) {
+ if ((fnow > enow) == (fnow > -enow)) {
+ Two_Sum(Q, enow, Qnew, hh);
+ enow = e[++eindex];
+ } else {
+ Two_Sum(Q, fnow, Qnew, hh);
+ fnow = f[++findex];
+ }
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ }
+ }
+ while (eindex < elen) {
+ Two_Sum(Q, enow, Qnew, hh);
+ enow = e[++eindex];
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ }
+ while (findex < flen) {
+ Two_Sum(Q, fnow, Qnew, hh);
+ fnow = f[++findex];
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ }
+ if ((Q != 0.0) || (hindex == 0)) {
+ h[hindex++] = Q;
+ }
+ return hindex;
+}
+
+/*****************************************************************************/
+/* */
+/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */
+/* eliminating zero components from the */
+/* output expansion. */
+/* */
+/* Sets h = be. See my Robust Predicates paper for details. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
+/* properties as well. (That is, if e has one of these properties, so */
+/* will h.) */
+/* */
+/*****************************************************************************/
+
+int scale_expansion_zeroelim(int elen, float *e, float b, float *h)
+{
+ float Q, sum;
+ float hh;
+ float product1;
+ float product0;
+ int eindex, hindex;
+ float enow;
+ float bvirt;
+ float avirt, bround, around;
+ float c;
+ float abig;
+ float ahi, alo, bhi, blo;
+ float err1, err2, err3;
+
+ Split(b, bhi, blo);
+ Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
+ hindex = 0;
+ if (hh != 0) {
+ h[hindex++] = hh;
+ }
+ for (eindex = 1; eindex < elen; eindex++) {
+ enow = e[eindex];
+ Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
+ Two_Sum(Q, product0, sum, hh);
+ if (hh != 0) {
+ h[hindex++] = hh;
+ }
+ Fast_Two_Sum(product1, sum, Q, hh);
+ if (hh != 0) {
+ h[hindex++] = hh;
+ }
+ }
+ if ((Q != 0.0) || (hindex == 0)) {
+ h[hindex++] = Q;
+ }
+ return hindex;
+}
+
+/*****************************************************************************/
+/* */
+/* estimate() Produce a one-word estimate of an expansion's value. */
+/* */
+/* See my Robust Predicates paper for details. */
+/* */
+/*****************************************************************************/
+
+float estimate(int elen, float *e)
+{
+ float Q;
+ int eindex;
+ Q = e[0];
+ for (eindex = 1; eindex < elen; eindex++) {
+ Q += e[eindex];
+ }
+ return Q;
+}
+
+/*****************************************************************************/
+/* */
+/* counterclockwise() Return a positive value if the points pa, pb, and */
+/* pc occur in counterclockwise order; a negative */
+/* value if they occur in clockwise order; and zero */
+/* if they are collinear. The result is also a rough */
+/* approximation of twice the signed area of the */
+/* triangle defined by the three points. */
+/* */
+/* Uses exact arithmetic if necessary to ensure a correct answer. The */
+/* result returned is the determinant of a matrix. This determinant is */
+/* computed adaptively, in the sense that exact arithmetic is used only to */
+/* the degree it is needed to ensure that the returned value has the */
+/* correct sign. Hence, this function is usually quite fast, but will run */
+/* more slowly when the input points are collinear or nearly so. */
+/* */
+/* See my Robust Predicates paper for details. */
+/* */
+/*****************************************************************************/
+
+float counterclockwiseadapt(vertex pa, vertex pb, vertex pc, float detsum)
+{
+ float acx, acy, bcx, bcy;
+ float acxtail, acytail, bcxtail, bcytail;
+ float detleft, detright;
+ float detlefttail, detrighttail;
+ float det, errbound;
+ float B[4], C1[8], C2[12], D[16];
+ float B3;
+ int C1length, C2length, Dlength;
+ float u[4];
+ float u3;
+ float s1, t1;
+ float s0, t0;
+
+ float bvirt;
+ float avirt, bround, around;
+ float c;
+ float abig;
+ float ahi, alo, bhi, blo;
+ float err1, err2, err3;
+ float _i, _j;
+ float _0;
+
+ acx = (float) (pa[0] - pc[0]);
+ bcx = (float) (pb[0] - pc[0]);
+ acy = (float) (pa[1] - pc[1]);
+ bcy = (float) (pb[1] - pc[1]);
+
+ Two_Product(acx, bcy, detleft, detlefttail);
+ Two_Product(acy, bcx, detright, detrighttail);
+
+ Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
+ B3, B[2], B[1], B[0]);
+ B[3] = B3;
+
+ det = estimate(4, B);
+ errbound = ccwerrboundB * detsum;
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
+ Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
+ Two_Diff_Tail(pa[1], pc[1], acy, acytail);
+ Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
+
+ if ((acxtail == 0.0) && (acytail == 0.0)
+ && (bcxtail == 0.0) && (bcytail == 0.0)) {
+ return det;
+ }
+
+ errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
+ det += (acx * bcytail + bcy * acxtail)
+ - (acy * bcxtail + bcx * acytail);
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ Two_Product(acxtail, bcy, s1, s0);
+ Two_Product(acytail, bcx, t1, t0);
+ Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
+
+ Two_Product(acx, bcytail, s1, s0);
+ Two_Product(acy, bcxtail, t1, t0);
+ Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
+
+ Two_Product(acxtail, bcytail, s1, s0);
+ Two_Product(acytail, bcxtail, t1, t0);
+ Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
+
+ return(D[Dlength - 1]);
+}
+
+float counterclockwise(struct mesh *m, struct behavior *b,
+ vertex pa, vertex pb, vertex pc)
+{
+ float detleft, detright, det;
+ float detsum, errbound;
+
+ m->counterclockcount++;
+
+ detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
+ detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
+ det = detleft - detright;
+
+ if (b->noexact) {
+ return det;
+ }
+
+ if (detleft > 0.0) {
+ if (detright <= 0.0) {
+ return det;
+ } else {
+ detsum = detleft + detright;
+ }
+ } else if (detleft < 0.0) {
+ if (detright >= 0.0) {
+ return det;
+ } else {
+ detsum = -detleft - detright;
+ }
+ } else {
+ return det;
+ }
+
+ errbound = ccwerrboundA * detsum;
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ return counterclockwiseadapt(pa, pb, pc, detsum);
+}
+
+/*****************************************************************************/
+/* */
+/* incircle() Return a positive value if the point pd lies inside the */
+/* circle passing through pa, pb, and pc; a negative value if */
+/* it lies outside; and zero if the four points are cocircular.*/
+/* The points pa, pb, and pc must be in counterclockwise */
+/* order, or the sign of the result will be reversed. */
+/* */
+/* Uses exact arithmetic if necessary to ensure a correct answer. The */
+/* result returned is the determinant of a matrix. This determinant is */
+/* computed adaptively, in the sense that exact arithmetic is used only to */
+/* the degree it is needed to ensure that the returned value has the */
+/* correct sign. Hence, this function is usually quite fast, but will run */
+/* more slowly when the input points are cocircular or nearly so. */
+/* */
+/* See my Robust Predicates paper for details. */
+/* */
+/*****************************************************************************/
+
+float incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, float permanent)
+{
+ float adx, bdx, cdx, ady, bdy, cdy;
+ float det, errbound;
+
+ float bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
+ float bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
+ float bc[4], ca[4], ab[4];
+ float bc3, ca3, ab3;
+ float axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
+ int axbclen, axxbclen, aybclen, ayybclen, alen;
+ float bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
+ int bxcalen, bxxcalen, bycalen, byycalen, blen;
+ float cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
+ int cxablen, cxxablen, cyablen, cyyablen, clen;
+ float abdet[64];
+ int ablen;
+ float fin1[1152], fin2[1152];
+ float *finnow, *finother, *finswap;
+ int finlength;
+
+ float adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
+ float adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
+ float adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
+ float aa[4], bb[4], cc[4];
+ float aa3, bb3, cc3;
+ float ti1, tj1;
+ float ti0, tj0;
+ float u[4], v[4];
+ float u3, v3;
+ float temp8[8], temp16a[16], temp16b[16], temp16c[16];
+ float temp32a[32], temp32b[32], temp48[48], temp64[64];
+ int temp8len, temp16alen, temp16blen, temp16clen;
+ int temp32alen, temp32blen, temp48len, temp64len;
+ float axtbb[8], axtcc[8], aytbb[8], aytcc[8];
+ int axtbblen, axtcclen, aytbblen, aytcclen;
+ float bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
+ int bxtaalen, bxtcclen, bytaalen, bytcclen;
+ float cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
+ int cxtaalen, cxtbblen, cytaalen, cytbblen;
+ float axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
+ int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
+ float axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
+ int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
+ float axtbctt[8], aytbctt[8], bxtcatt[8];
+ float bytcatt[8], cxtabtt[8], cytabtt[8];
+ int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
+ float abt[8], bct[8], cat[8];
+ int abtlen, bctlen, catlen;
+ float abtt[4], bctt[4], catt[4];
+ int abttlen, bcttlen, cattlen;
+ float abtt3, bctt3, catt3;
+ float negate;
+
+ float bvirt;
+ float avirt, bround, around;
+ float c;
+ float abig;
+ float ahi, alo, bhi, blo;
+ float err1, err2, err3;
+ float _i, _j;
+ float _0;
+
+ adx = (float) (pa[0] - pd[0]);
+ bdx = (float) (pb[0] - pd[0]);
+ cdx = (float) (pc[0] - pd[0]);
+ ady = (float) (pa[1] - pd[1]);
+ bdy = (float) (pb[1] - pd[1]);
+ cdy = (float) (pc[1] - pd[1]);
+
+ Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
+ Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
+ Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
+ bc[3] = bc3;
+ axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
+ axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
+ aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
+ ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
+ alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
+
+ Two_Product(cdx, ady, cdxady1, cdxady0);
+ Two_Product(adx, cdy, adxcdy1, adxcdy0);
+ Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
+ ca[3] = ca3;
+ bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
+ bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
+ bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
+ byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
+ blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
+
+ Two_Product(adx, bdy, adxbdy1, adxbdy0);
+ Two_Product(bdx, ady, bdxady1, bdxady0);
+ Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
+ ab[3] = ab3;
+ cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
+ cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
+ cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
+ cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
+ clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
+
+ ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
+ finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
+
+ det = estimate(finlength, fin1);
+ errbound = iccerrboundB * permanent;
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
+ Two_Diff_Tail(pa[1], pd[1], ady, adytail);
+ Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
+ Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
+ Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
+ Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
+ if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
+ && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
+ return det;
+ }
+
+ errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
+ det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
+ - (bdy * cdxtail + cdx * bdytail))
+ + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
+ + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
+ - (cdy * adxtail + adx * cdytail))
+ + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
+ + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
+ - (ady * bdxtail + bdx * adytail))
+ + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ finnow = fin1;
+ finother = fin2;
+
+ if ((bdxtail != 0.0) || (bdytail != 0.0)
+ || (cdxtail != 0.0) || (cdytail != 0.0)) {
+ Square(adx, adxadx1, adxadx0);
+ Square(ady, adyady1, adyady0);
+ Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
+ aa[3] = aa3;
+ }
+ if ((cdxtail != 0.0) || (cdytail != 0.0)
+ || (adxtail != 0.0) || (adytail != 0.0)) {
+ Square(bdx, bdxbdx1, bdxbdx0);
+ Square(bdy, bdybdy1, bdybdy0);
+ Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
+ bb[3] = bb3;
+ }
+ if ((adxtail != 0.0) || (adytail != 0.0)
+ || (bdxtail != 0.0) || (bdytail != 0.0)) {
+ Square(cdx, cdxcdx1, cdxcdx0);
+ Square(cdy, cdycdy1, cdycdy0);
+ Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
+ cc[3] = cc3;
+ }
+
+ if (adxtail != 0.0) {
+ axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
+ temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
+ temp16a);
+
+ axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
+ temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
+
+ axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
+ temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (adytail != 0.0) {
+ aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
+ temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
+ temp16a);
+
+ aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
+ temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
+
+ aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
+ temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdxtail != 0.0) {
+ bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
+ temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
+ temp16a);
+
+ bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
+ temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
+
+ bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
+ temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdytail != 0.0) {
+ bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
+ temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
+ temp16a);
+
+ bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
+ temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
+
+ bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
+ temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdxtail != 0.0) {
+ cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
+ temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
+ temp16a);
+
+ cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
+ temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
+
+ cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
+ temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdytail != 0.0) {
+ cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
+ temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
+ temp16a);
+
+ cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
+ temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
+
+ cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
+ temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ if ((adxtail != 0.0) || (adytail != 0.0)) {
+ if ((bdxtail != 0.0) || (bdytail != 0.0)
+ || (cdxtail != 0.0) || (cdytail != 0.0)) {
+ Two_Product(bdxtail, cdy, ti1, ti0);
+ Two_Product(bdx, cdytail, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ negate = -bdy;
+ Two_Product(cdxtail, negate, ti1, ti0);
+ negate = -bdytail;
+ Two_Product(cdx, negate, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
+ v[3] = v3;
+ bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
+
+ Two_Product(bdxtail, cdytail, ti1, ti0);
+ Two_Product(cdxtail, bdytail, tj1, tj0);
+ Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
+ bctt[3] = bctt3;
+ bcttlen = 4;
+ } else {
+ bct[0] = 0.0;
+ bctlen = 1;
+ bctt[0] = 0.0;
+ bcttlen = 1;
+ }
+
+ if (adxtail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
+ axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
+ temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (bdytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
+ temp32a);
+ axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
+ temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (adytail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
+ aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
+ temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+
+ temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
+ temp32a);
+ aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
+ temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if ((bdxtail != 0.0) || (bdytail != 0.0)) {
+ if ((cdxtail != 0.0) || (cdytail != 0.0)
+ || (adxtail != 0.0) || (adytail != 0.0)) {
+ Two_Product(cdxtail, ady, ti1, ti0);
+ Two_Product(cdx, adytail, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ negate = -cdy;
+ Two_Product(adxtail, negate, ti1, ti0);
+ negate = -cdytail;
+ Two_Product(adx, negate, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
+ v[3] = v3;
+ catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
+
+ Two_Product(cdxtail, adytail, ti1, ti0);
+ Two_Product(adxtail, cdytail, tj1, tj0);
+ Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
+ catt[3] = catt3;
+ cattlen = 4;
+ } else {
+ cat[0] = 0.0;
+ catlen = 1;
+ catt[0] = 0.0;
+ cattlen = 1;
+ }
+
+ if (bdxtail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
+ bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
+ temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (cdytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (adytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
+ temp32a);
+ bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
+ temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdytail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
+ bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
+ temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+
+ temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
+ temp32a);
+ bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
+ temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if ((cdxtail != 0.0) || (cdytail != 0.0)) {
+ if ((adxtail != 0.0) || (adytail != 0.0)
+ || (bdxtail != 0.0) || (bdytail != 0.0)) {
+ Two_Product(adxtail, bdy, ti1, ti0);
+ Two_Product(adx, bdytail, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ negate = -ady;
+ Two_Product(bdxtail, negate, ti1, ti0);
+ negate = -adytail;
+ Two_Product(bdx, negate, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
+ v[3] = v3;
+ abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
+
+ Two_Product(adxtail, bdytail, ti1, ti0);
+ Two_Product(bdxtail, adytail, tj1, tj0);
+ Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
+ abtt[3] = abtt3;
+ abttlen = 4;
+ } else {
+ abt[0] = 0.0;
+ abtlen = 1;
+ abtt[0] = 0.0;
+ abttlen = 1;
+ }
+
+ if (cdxtail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
+ cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
+ temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (adytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
+ temp32a);
+ cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
+ temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdytail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
+ cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
+ temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+
+ temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
+ temp32a);
+ cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
+ temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+
+ return finnow[finlength - 1];
+}
+
+float incircle(struct mesh *m, struct behavior *b,
+ vertex pa, vertex pb, vertex pc, vertex pd)
+{
+ float adx, bdx, cdx, ady, bdy, cdy;
+ float bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
+ float alift, blift, clift;
+ float det;
+ float permanent, errbound;
+
+ m->incirclecount++;
+
+ adx = pa[0] - pd[0];
+ bdx = pb[0] - pd[0];
+ cdx = pc[0] - pd[0];
+ ady = pa[1] - pd[1];
+ bdy = pb[1] - pd[1];
+ cdy = pc[1] - pd[1];
+
+ bdxcdy = bdx * cdy;
+ cdxbdy = cdx * bdy;
+ alift = adx * adx + ady * ady;
+
+ cdxady = cdx * ady;
+ adxcdy = adx * cdy;
+ blift = bdx * bdx + bdy * bdy;
+
+ adxbdy = adx * bdy;
+ bdxady = bdx * ady;
+ clift = cdx * cdx + cdy * cdy;
+
+ det = alift * (bdxcdy - cdxbdy)
+ + blift * (cdxady - adxcdy)
+ + clift * (adxbdy - bdxady);
+
+ if (b->noexact) {
+ return det;
+ }
+
+ permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
+ + (Absolute(cdxady) + Absolute(adxcdy)) * blift
+ + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
+ errbound = iccerrboundA * permanent;
+ if ((det > errbound) || (-det > errbound)) {
+ return det;
+ }
+
+ return incircleadapt(pa, pb, pc, pd, permanent);
+}
+
+/*****************************************************************************/
+/* */
+/* orient3d() Return a positive value if the point pd lies below the */
+/* plane passing through pa, pb, and pc; "below" is defined so */
+/* that pa, pb, and pc appear in counterclockwise order when */
+/* viewed from above the plane. Returns a negative value if */
+/* pd lies above the plane. Returns zero if the points are */
+/* coplanar. The result is also a rough approximation of six */
+/* times the signed volume of the tetrahedron defined by the */
+/* four points. */
+/* */
+/* Uses exact arithmetic if necessary to ensure a correct answer. The */
+/* result returned is the determinant of a matrix. This determinant is */
+/* computed adaptively, in the sense that exact arithmetic is used only to */
+/* the degree it is needed to ensure that the returned value has the */
+/* correct sign. Hence, this function is usually quite fast, but will run */
+/* more slowly when the input points are coplanar or nearly so. */
+/* */
+/* See my Robust Predicates paper for details. */
+/* */
+/*****************************************************************************/
+
+float orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
+ float aheight, float bheight, float cheight, float dheight,
+ float permanent)
+{
+ float adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
+ float det, errbound;
+
+ float bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
+ float bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
+ float bc[4], ca[4], ab[4];
+ float bc3, ca3, ab3;
+ float adet[8], bdet[8], cdet[8];
+ int alen, blen, clen;
+ float abdet[16];
+ int ablen;
+ float *finnow, *finother, *finswap;
+ float fin1[192], fin2[192];
+ int finlength;
+
+ float adxtail, bdxtail, cdxtail;
+ float adytail, bdytail, cdytail;
+ float adheighttail, bdheighttail, cdheighttail;
+ float at_blarge, at_clarge;
+ float bt_clarge, bt_alarge;
+ float ct_alarge, ct_blarge;
+ float at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
+ int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
+ float bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
+ float adxt_cdy1, adxt_bdy1, bdxt_ady1;
+ float bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
+ float adxt_cdy0, adxt_bdy0, bdxt_ady0;
+ float bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
+ float adyt_cdx1, adyt_bdx1, bdyt_adx1;
+ float bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
+ float adyt_cdx0, adyt_bdx0, bdyt_adx0;
+ float bct[8], cat[8], abt[8];
+ int bctlen, catlen, abtlen;
+ float bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
+ float adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
+ float bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
+ float adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
+ float u[4], v[12], w[16];
+ float u3;
+ int vlength, wlength;
+ float negate;
+
+ float bvirt;
+ float avirt, bround, around;
+ float c;
+ float abig;
+ float ahi, alo, bhi, blo;
+ float err1, err2, err3;
+ float _i, _j, _k;
+ float _0;
+
+ adx = (float) (pa[0] - pd[0]);
+ bdx = (float) (pb[0] - pd[0]);
+ cdx = (float) (pc[0] - pd[0]);
+ ady = (float) (pa[1] - pd[1]);
+ bdy = (float) (pb[1] - pd[1]);
+ cdy = (float) (pc[1] - pd[1]);
+ adheight = (float) (aheight - dheight);
+ bdheight = (float) (bheight - dheight);
+ cdheight = (float) (cheight - dheight);
+
+ Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
+ Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
+ Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
+ bc[3] = bc3;
+ alen = scale_expansion_zeroelim(4, bc, adheight, adet);
+
+ Two_Product(cdx, ady, cdxady1, cdxady0);
+ Two_Product(adx, cdy, adxcdy1, adxcdy0);
+ Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
+ ca[3] = ca3;
+ blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);
+
+ Two_Product(adx, bdy, adxbdy1, adxbdy0);
+ Two_Product(bdx, ady, bdxady1, bdxady0);
+ Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
+ ab[3] = ab3;
+ clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);
+
+ ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
+ finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
+
+ det = estimate(finlength, fin1);
+ errbound = o3derrboundB * permanent;
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
+ Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
+ Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
+ Two_Diff_Tail(pa[1], pd[1], ady, adytail);
+ Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
+ Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
+ Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
+ Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
+ Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
+
+ if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
+ (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
+ (adheighttail == 0.0) &&
+ (bdheighttail == 0.0) &&
+ (cdheighttail == 0.0)) {
+ return det;
+ }
+
+ errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
+ det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
+ (bdy * cdxtail + cdx * bdytail)) +
+ adheighttail * (bdx * cdy - bdy * cdx)) +
+ (bdheight * ((cdx * adytail + ady * cdxtail) -
+ (cdy * adxtail + adx * cdytail)) +
+ bdheighttail * (cdx * ady - cdy * adx)) +
+ (cdheight * ((adx * bdytail + bdy * adxtail) -
+ (ady * bdxtail + bdx * adytail)) +
+ cdheighttail * (adx * bdy - ady * bdx));
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ finnow = fin1;
+ finother = fin2;
+
+ if (adxtail == 0.0) {
+ if (adytail == 0.0) {
+ at_b[0] = 0.0;
+ at_blen = 1;
+ at_c[0] = 0.0;
+ at_clen = 1;
+ } else {
+ negate = -adytail;
+ Two_Product(negate, bdx, at_blarge, at_b[0]);
+ at_b[1] = at_blarge;
+ at_blen = 2;
+ Two_Product(adytail, cdx, at_clarge, at_c[0]);
+ at_c[1] = at_clarge;
+ at_clen = 2;
+ }
+ } else {
+ if (adytail == 0.0) {
+ Two_Product(adxtail, bdy, at_blarge, at_b[0]);
+ at_b[1] = at_blarge;
+ at_blen = 2;
+ negate = -adxtail;
+ Two_Product(negate, cdy, at_clarge, at_c[0]);
+ at_c[1] = at_clarge;
+ at_clen = 2;
+ } else {
+ Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
+ Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
+ Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
+ at_blarge, at_b[2], at_b[1], at_b[0]);
+ at_b[3] = at_blarge;
+ at_blen = 4;
+ Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
+ Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
+ Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
+ at_clarge, at_c[2], at_c[1], at_c[0]);
+ at_c[3] = at_clarge;
+ at_clen = 4;
+ }
+ }
+ if (bdxtail == 0.0) {
+ if (bdytail == 0.0) {
+ bt_c[0] = 0.0;
+ bt_clen = 1;
+ bt_a[0] = 0.0;
+ bt_alen = 1;
+ } else {
+ negate = -bdytail;
+ Two_Product(negate, cdx, bt_clarge, bt_c[0]);
+ bt_c[1] = bt_clarge;
+ bt_clen = 2;
+ Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
+ bt_a[1] = bt_alarge;
+ bt_alen = 2;
+ }
+ } else {
+ if (bdytail == 0.0) {
+ Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
+ bt_c[1] = bt_clarge;
+ bt_clen = 2;
+ negate = -bdxtail;
+ Two_Product(negate, ady, bt_alarge, bt_a[0]);
+ bt_a[1] = bt_alarge;
+ bt_alen = 2;
+ } else {
+ Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
+ Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
+ Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
+ bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
+ bt_c[3] = bt_clarge;
+ bt_clen = 4;
+ Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
+ Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
+ Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
+ bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
+ bt_a[3] = bt_alarge;
+ bt_alen = 4;
+ }
+ }
+ if (cdxtail == 0.0) {
+ if (cdytail == 0.0) {
+ ct_a[0] = 0.0;
+ ct_alen = 1;
+ ct_b[0] = 0.0;
+ ct_blen = 1;
+ } else {
+ negate = -cdytail;
+ Two_Product(negate, adx, ct_alarge, ct_a[0]);
+ ct_a[1] = ct_alarge;
+ ct_alen = 2;
+ Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
+ ct_b[1] = ct_blarge;
+ ct_blen = 2;
+ }
+ } else {
+ if (cdytail == 0.0) {
+ Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
+ ct_a[1] = ct_alarge;
+ ct_alen = 2;
+ negate = -cdxtail;
+ Two_Product(negate, bdy, ct_blarge, ct_b[0]);
+ ct_b[1] = ct_blarge;
+ ct_blen = 2;
+ } else {
+ Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
+ Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
+ Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
+ ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
+ ct_a[3] = ct_alarge;
+ ct_alen = 4;
+ Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
+ Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
+ Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
+ ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
+ ct_b[3] = ct_blarge;
+ ct_blen = 4;
+ }
+ }
+
+ bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
+ wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+ catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
+ wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+ abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
+ wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+ if (adheighttail != 0.0) {
+ vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdheighttail != 0.0) {
+ vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdheighttail != 0.0) {
+ vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ if (adxtail != 0.0) {
+ if (bdytail != 0.0) {
+ Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
+ Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (cdheighttail != 0.0) {
+ Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if (cdytail != 0.0) {
+ negate = -adxtail;
+ Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
+ Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (bdheighttail != 0.0) {
+ Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ }
+ if (bdxtail != 0.0) {
+ if (cdytail != 0.0) {
+ Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
+ Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (adheighttail != 0.0) {
+ Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if (adytail != 0.0) {
+ negate = -bdxtail;
+ Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
+ Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (cdheighttail != 0.0) {
+ Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ }
+ if (cdxtail != 0.0) {
+ if (adytail != 0.0) {
+ Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
+ Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (bdheighttail != 0.0) {
+ Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if (bdytail != 0.0) {
+ negate = -cdxtail;
+ Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
+ Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (adheighttail != 0.0) {
+ Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ }
+
+ if (adheighttail != 0.0) {
+ wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdheighttail != 0.0) {
+ wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdheighttail != 0.0) {
+ wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ return finnow[finlength - 1];
+}
+
+float orient3d(struct mesh *m, struct behavior *b,
+ vertex pa, vertex pb, vertex pc, vertex pd,
+ float aheight, float bheight, float cheight, float dheight)
+{
+ float adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
+ float bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
+ float det;
+ float permanent, errbound;
+
+ m->orient3dcount++;
+
+ adx = pa[0] - pd[0];
+ bdx = pb[0] - pd[0];
+ cdx = pc[0] - pd[0];
+ ady = pa[1] - pd[1];
+ bdy = pb[1] - pd[1];
+ cdy = pc[1] - pd[1];
+ adheight = aheight - dheight;
+ bdheight = bheight - dheight;
+ cdheight = cheight - dheight;
+
+ bdxcdy = bdx * cdy;
+ cdxbdy = cdx * bdy;
+
+ cdxady = cdx * ady;
+ adxcdy = adx * cdy;
+
+ adxbdy = adx * bdy;
+ bdxady = bdx * ady;
+
+ det = adheight * (bdxcdy - cdxbdy)
+ + bdheight * (cdxady - adxcdy)
+ + cdheight * (adxbdy - bdxady);
+
+ if (b->noexact) {
+ return det;
+ }
+
+ permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
+ + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
+ + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
+ errbound = o3derrboundA * permanent;
+ if ((det > errbound) || (-det > errbound)) {
+ return det;
+ }
+
+ return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
+ permanent);
+}
+
+/*****************************************************************************/
+/* */
+/* nonregular() Return a positive value if the point pd is incompatible */
+/* with the circle or plane passing through pa, pb, and pc */
+/* (meaning that pd is inside the circle or below the */
+/* plane); a negative value if it is compatible; and zero if */
+/* the four points are cocircular/coplanar. The points pa, */
+/* pb, and pc must be in counterclockwise order, or the sign */
+/* of the result will be reversed. */
+/* */
+/* If the -w switch is used, the points are lifted onto the parabolic */
+/* lifting map, then they are dropped according to their weights, then the */
+/* 3D orientation test is applied. If the -W switch is used, the points' */
+/* heights are already provided, so the 3D orientation test is applied */
+/* directly. If neither switch is used, the incircle test is applied. */
+/* */
+/*****************************************************************************/
+
+float nonregular(struct mesh *m, struct behavior *b,
+ vertex pa, vertex pb, vertex pc, vertex pd)
+{
+ if (b->weighted == 0) {
+ return incircle(m, b, pa, pb, pc, pd);
+ } else if (b->weighted == 1) {
+ return orient3d(m, b, pa, pb, pc, pd,
+ pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
+ pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
+ pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
+ pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
+ } else {
+ return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* findcircumcenter() Find the circumcenter of a triangle. */
+/* */
+/* The result is returned both in terms of x-y coordinates and xi-eta */
+/* (barycentric) coordinates. The xi-eta coordinate system is defined in */
+/* terms of the triangle: the origin of the triangle is the origin of the */
+/* coordinate system; the destination of the triangle is one unit along the */
+/* xi axis; and the apex of the triangle is one unit along the eta axis. */
+/* This procedure also returns the square of the length of the triangle's */
+/* shortest edge. */
+/* */
+/*****************************************************************************/
+
+void findcircumcenter(struct mesh *m, struct behavior *b,
+ vertex torg, vertex tdest, vertex tapex,
+ vertex circumcenter, float *xi, float *eta, int offcenter)
+{
+ float xdo, ydo, xao, yao;
+ float dodist, aodist, dadist;
+ float denominator;
+ float dx, dy, dxoff, dyoff;
+
+ m->circumcentercount++;
+
+ /* Compute the circumcenter of the triangle. */
+ xdo = tdest[0] - torg[0];
+ ydo = tdest[1] - torg[1];
+ xao = tapex[0] - torg[0];
+ yao = tapex[1] - torg[1];
+ dodist = xdo * xdo + ydo * ydo;
+ aodist = xao * xao + yao * yao;
+ dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
+ (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
+ if (b->noexact) {
+ denominator = 0.5 / (xdo * yao - xao * ydo);
+ } else {
+ /* Use the counterclockwise() routine to ensure a positive (and */
+ /* reasonably accurate) result, avoiding any possibility of */
+ /* division by zero. */
+ denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
+ /* Don't count the above as an orientation test. */
+ m->counterclockcount--;
+ }
+ dx = (yao * dodist - ydo * aodist) * denominator;
+ dy = (xdo * aodist - xao * dodist) * denominator;
+
+ /* Find the (squared) length of the triangle's shortest edge. This */
+ /* serves as a conservative estimate of the insertion radius of the */
+ /* circumcenter's parent. The estimate is used to ensure that */
+ /* the algorithm terminates even if very small angles appear in */
+ /* the input PSLG. */
+ if ((dodist < aodist) && (dodist < dadist)) {
+ if (offcenter && (b->offconstant > 0.0)) {
+ /* Find the position of the off-center, as described by Alper Ungor. */
+ dxoff = 0.5 * xdo - b->offconstant * ydo;
+ dyoff = 0.5 * ydo + b->offconstant * xdo;
+ /* If the off-center is closer to the origin than the */
+ /* circumcenter, use the off-center instead. */
+ if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
+ dx = dxoff;
+ dy = dyoff;
+ }
+ }
+ } else if (aodist < dadist) {
+ if (offcenter && (b->offconstant > 0.0)) {
+ dxoff = 0.5 * xao + b->offconstant * yao;
+ dyoff = 0.5 * yao - b->offconstant * xao;
+ /* If the off-center is closer to the origin than the */
+ /* circumcenter, use the off-center instead. */
+ if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
+ dx = dxoff;
+ dy = dyoff;
+ }
+ }
+ } else {
+ if (offcenter && (b->offconstant > 0.0)) {
+ dxoff = 0.5 * (tapex[0] - tdest[0]) -
+ b->offconstant * (tapex[1] - tdest[1]);
+ dyoff = 0.5 * (tapex[1] - tdest[1]) +
+ b->offconstant * (tapex[0] - tdest[0]);
+ /* If the off-center is closer to the destination than the */
+ /* circumcenter, use the off-center instead. */
+ if (dxoff * dxoff + dyoff * dyoff <
+ (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
+ dx = xdo + dxoff;
+ dy = ydo + dyoff;
+ }
+ }
+ }
+
+ circumcenter[0] = torg[0] + dx;
+ circumcenter[1] = torg[1] + dy;
+
+ /* To interpolate vertex attributes for the new vertex inserted at */
+ /* the circumcenter, define a coordinate system with a xi-axis, */
+ /* directed from the triangle's origin to its destination, and */
+ /* an eta-axis, directed from its origin to its apex. */
+ /* Calculate the xi and eta coordinates of the circumcenter. */
+ *xi = (yao * dx - xao * dy) * (2.0 * denominator);
+ *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
+}
+
+/** **/
+/** **/
+/********* Geometric primitives end here *********/
+
+/*****************************************************************************/
+/* */
+/* triangleinit() Initialize some variables. */
+/* */
+/*****************************************************************************/
+
+void triangleinit(struct mesh *m)
+{
+ poolzero(&m->vertices);
+ poolzero(&m->triangles);
+ poolzero(&m->subsegs);
+ poolzero(&m->viri);
+ poolzero(&m->badsubsegs);
+ poolzero(&m->badtriangles);
+ poolzero(&m->flipstackers);
+ poolzero(&m->splaynodes);
+
+ m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
+ m->undeads = 0; /* No eliminated input vertices yet. */
+ m->samples = 1; /* Point location should take at least one sample. */
+ m->checksegments = 0; /* There are no segments in the triangulation yet. */
+ m->checkquality = 0; /* The quality triangulation stage has not begun. */
+ m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
+ m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
+ randomseed = 1;
+
+ exactinit(); /* Initialize exact arithmetic constants. */
+}
+
+/*****************************************************************************/
+/* */
+/* randomnation() Generate a random number between 0 and `choices' - 1. */
+/* */
+/* This is a simple linear congruential random number generator. Hence, it */
+/* is a bad random number generator, but good enough for most randomized */
+/* geometric algorithms. */
+/* */
+/*****************************************************************************/
+
+unsigned long long randomnation(unsigned int choices)
+{
+ randomseed = (randomseed * 1366l + 150889l) % 714025l;
+ return randomseed / (714025l / choices + 1);
+}
+
+/********* Point location routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* makevertexmap() Construct a mapping from vertices to triangles to */
+/* improve the speed of point location for segment */
+/* insertion. */
+/* */
+/* Traverses all the triangles, and provides each corner of each triangle */
+/* with a pointer to that triangle. Of course, pointers will be */
+/* overwritten by other pointers because (almost) each vertex is a corner */
+/* of several triangles, but in the end every vertex will point to some */
+/* triangle that contains it. */
+/* */
+/*****************************************************************************/
+
+void makevertexmap(struct mesh *m, struct behavior *b)
+{
+ struct otri triangleloop;
+ vertex triorg;
+
+ if (b->verbose) {
+ printf(" Constructing mapping from vertices to triangles.\n");
+ }
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ while (triangleloop.tri != (triangle *) NULL) {
+ /* Check all three vertices of the triangle. */
+ for (triangleloop.orient = 0; triangleloop.orient < 3;
+ triangleloop.orient++) {
+ org(triangleloop, triorg);
+ setvertex2tri(triorg, encode(triangleloop));
+ }
+ triangleloop.tri = triangletraverse(m);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* preciselocate() Find a triangle or edge containing a given point. */
+/* */
+/* Begins its search from `searchtri'. It is important that `searchtri' */
+/* be a handle with the property that `searchpoint' is strictly to the left */
+/* of the edge denoted by `searchtri', or is collinear with that edge and */
+/* does not intersect that edge. (In particular, `searchpoint' should not */
+/* be the origin or destination of that edge.) */
+/* */
+/* These conditions are imposed because preciselocate() is normally used in */
+/* one of two situations: */
+/* */
+/* (1) To try to find the location to insert a new point. Normally, we */
+/* know an edge that the point is strictly to the left of. In the */
+/* incremental Delaunay algorithm, that edge is a bounding box edge. */
+/* In Ruppert's Delaunay refinement algorithm for quality meshing, */
+/* that edge is the shortest edge of the triangle whose circumcenter */
+/* is being inserted. */
+/* */
+/* (2) To try to find an existing point. In this case, any edge on the */
+/* convex hull is a good starting edge. You must screen out the */
+/* possibility that the vertex sought is an endpoint of the starting */
+/* edge before you call preciselocate(). */
+/* */
+/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
+/* */
+/* This implementation differs from that given by Guibas and Stolfi. It */
+/* walks from triangle to triangle, crossing an edge only if `searchpoint' */
+/* is on the other side of the line containing that edge. After entering */
+/* a triangle, there are two edges by which one can leave that triangle. */
+/* If both edges are valid (`searchpoint' is on the other side of both */
+/* edges), one of the two is chosen by drawing a line perpendicular to */
+/* the entry edge (whose endpoints are `forg' and `fdest') passing through */
+/* `fapex'. Depending on which side of this perpendicular `searchpoint' */
+/* falls on, an exit edge is chosen. */
+/* */
+/* This implementation is empirically faster than the Guibas and Stolfi */
+/* point location routine (which I originally used), which tends to spiral */
+/* in toward its target. */
+/* */
+/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
+/* is a handle whose origin is the existing vertex. */
+/* */
+/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
+/* handle whose primary edge is the edge on which the point lies. */
+/* */
+/* Returns INTRIANGLE if the point lies strictly within a triangle. */
+/* `searchtri' is a handle on the triangle that contains the point. */
+/* */
+/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
+/* handle whose primary edge the point is to the right of. This might */
+/* occur when the circumcenter of a triangle falls just slightly outside */
+/* the mesh due to floating-point roundoff error. It also occurs when */
+/* seeking a hole or region point that a foolish user has placed outside */
+/* the mesh. */
+/* */
+/* If `stopatsubsegment' is nonzero, the search will stop if it tries to */
+/* walk through a subsegment, and will return OUTSIDE. */
+/* */
+/* WARNING: This routine is designed for convex triangulations, and will */
+/* not generally work after the holes and concavities have been carved. */
+/* However, it can still be used to find the circumcenter of a triangle, as */
+/* long as the search is begun from the triangle in question. */
+/* */
+/*****************************************************************************/
+
+enum locateresult preciselocate(struct mesh *m, struct behavior *b,
+ vertex searchpoint, struct otri *searchtri,
+ int stopatsubsegment)
+{
+ struct otri backtracktri;
+ struct osub checkedge;
+ vertex forg, fdest, fapex;
+ float orgorient, destorient;
+ int moveleft;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (b->verbose > 2) {
+ printf(" Searching for point (%.12g, %.12g).\n",
+ searchpoint[0], searchpoint[1]);
+ }
+ /* Where are we? */
+ org(*searchtri, forg);
+ dest(*searchtri, fdest);
+ apex(*searchtri, fapex);
+ while (1) {
+ if (b->verbose > 2) {
+ printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
+ }
+ /* Check whether the apex is the point we seek. */
+ if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
+ lprevself(*searchtri);
+ return ONVERTEX;
+ }
+ /* Does the point lie on the other side of the line defined by the */
+ /* triangle edge opposite the triangle's destination? */
+ destorient = counterclockwise(m, b, forg, fapex, searchpoint);
+ /* Does the point lie on the other side of the line defined by the */
+ /* triangle edge opposite the triangle's origin? */
+ orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
+ if (destorient > 0.0) {
+ if (orgorient > 0.0) {
+ /* Move left if the inner product of (fapex - searchpoint) and */
+ /* (fdest - forg) is positive. This is equivalent to drawing */
+ /* a line perpendicular to the line (forg, fdest) and passing */
+ /* through `fapex', and determining which side of this line */
+ /* `searchpoint' falls on. */
+ moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
+ (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
+ } else {
+ moveleft = 1;
+ }
+ } else {
+ if (orgorient > 0.0) {
+ moveleft = 0;
+ } else {
+ /* The point we seek must be on the boundary of or inside this */
+ /* triangle. */
+ if (destorient == 0.0) {
+ lprevself(*searchtri);
+ return ONEDGE;
+ }
+ if (orgorient == 0.0) {
+ lnextself(*searchtri);
+ return ONEDGE;
+ }
+ return INTRIANGLE;
+ }
+ }
+
+ /* Move to another triangle. Leave a trace `backtracktri' in case */
+ /* floating-point roundoff or some such bogey causes us to walk */
+ /* off a boundary of the triangulation. */
+ if (moveleft) {
+ lprev(*searchtri, backtracktri);
+ fdest = fapex;
+ } else {
+ lnext(*searchtri, backtracktri);
+ forg = fapex;
+ }
+ sym(backtracktri, *searchtri);
+
+ if (m->checksegments && stopatsubsegment) {
+ /* Check for walking through a subsegment. */
+ tspivot(backtracktri, checkedge);
+ if (checkedge.ss != m->dummysub) {
+ /* Go back to the last triangle. */
+ otricopy(backtracktri, *searchtri);
+ return OUTSIDE;
+ }
+ }
+ /* Check for walking right out of the triangulation. */
+ if (searchtri->tri == m->dummytri) {
+ /* Go back to the last triangle. */
+ otricopy(backtracktri, *searchtri);
+ return OUTSIDE;
+ }
+
+ apex(*searchtri, fapex);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* locate() Find a triangle or edge containing a given point. */
+/* */
+/* Searching begins from one of: the input `searchtri', a recently */
+/* encountered triangle `recenttri', or from a triangle chosen from a */
+/* random sample. The choice is made by determining which triangle's */
+/* origin is closest to the point we are searching for. Normally, */
+/* `searchtri' should be a handle on the convex hull of the triangulation. */
+/* */
+/* Details on the random sampling method can be found in the Mucke, Saias, */
+/* and Zhu paper cited in the header of this code. */
+/* */
+/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
+/* */
+/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
+/* is a handle whose origin is the existing vertex. */
+/* */
+/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
+/* handle whose primary edge is the edge on which the point lies. */
+/* */
+/* Returns INTRIANGLE if the point lies strictly within a triangle. */
+/* `searchtri' is a handle on the triangle that contains the point. */
+/* */
+/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
+/* handle whose primary edge the point is to the right of. This might */
+/* occur when the circumcenter of a triangle falls just slightly outside */
+/* the mesh due to floating-point roundoff error. It also occurs when */
+/* seeking a hole or region point that a foolish user has placed outside */
+/* the mesh. */
+/* */
+/* WARNING: This routine is designed for convex triangulations, and will */
+/* not generally work after the holes and concavities have been carved. */
+/* */
+/*****************************************************************************/
+
+enum locateresult locate(struct mesh *m, struct behavior *b,
+ vertex searchpoint, struct otri *searchtri)
+{
+ int **sampleblock;
+ char *firsttri;
+ struct otri sampletri;
+ vertex torg, tdest;
+ unsigned long long alignptr;
+ float searchdist, dist;
+ float ahead;
+ long samplesperblock, totalsamplesleft, samplesleft;
+ long population, totalpopulation;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (b->verbose > 2) {
+ printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n",
+ searchpoint[0], searchpoint[1]);
+ }
+ /* Record the distance from the suggested starting triangle to the */
+ /* point we seek. */
+ org(*searchtri, torg);
+ searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
+ if (b->verbose > 2) {
+ printf(" Boundary triangle has origin (%.12g, %.12g).\n",
+ torg[0], torg[1]);
+ }
+
+ /* If a recently encountered triangle has been recorded and has not been */
+ /* deallocated, test it as a good starting point. */
+ if (m->recenttri.tri != (triangle *) NULL) {
+ if (!deadtri(m->recenttri.tri)) {
+ org(m->recenttri, torg);
+ if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
+ otricopy(m->recenttri, *searchtri);
+ return ONVERTEX;
+ }
+ dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
+ if (dist < searchdist) {
+ otricopy(m->recenttri, *searchtri);
+ searchdist = dist;
+ if (b->verbose > 2) {
+ printf(" Choosing recent triangle with origin (%.12g, %.12g).\n",
+ torg[0], torg[1]);
+ }
+ }
+ }
+ }
+
+ /* The number of random samples taken is proportional to the cube root of */
+ /* the number of triangles in the mesh. The next bit of code assumes */
+ /* that the number of triangles increases monotonically (or at least */
+ /* doesn't decrease enough to matter). */
+ while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
+ m->triangles.items) {
+ m->samples++;
+ }
+
+ /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */
+ /* from each block of triangles (except the first)--until we meet the */
+ /* sample quota. The ceiling means that blocks at the end might be */
+ /* neglected, but I don't care. */
+ samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
+ /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
+ /* from the first block of triangles. */
+ samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
+ m->triangles.maxitems + 1;
+ totalsamplesleft = m->samples;
+ population = m->triangles.itemsfirstblock;
+ totalpopulation = m->triangles.maxitems;
+ sampleblock = m->triangles.firstblock;
+ sampletri.orient = 0;
+ while (totalsamplesleft > 0) {
+ /* If we're in the last block, `population' needs to be corrected. */
+ if (population > totalpopulation) {
+ population = totalpopulation;
+ }
+ /* Find a pointer to the first triangle in the block. */
+ alignptr = (unsigned long long) (sampleblock + 1);
+ firsttri = (char *) (alignptr +
+ (unsigned long long) m->triangles.alignbytes -
+ (alignptr %
+ (unsigned long long) m->triangles.alignbytes));
+
+ /* Choose `samplesleft' randomly sampled triangles in this block. */
+ do {
+ sampletri.tri = (triangle *) (firsttri +
+ (randomnation((unsigned int) population) *
+ m->triangles.itembytes));
+ if (!deadtri(sampletri.tri)) {
+ org(sampletri, torg);
+ dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
+ if (dist < searchdist) {
+ otricopy(sampletri, *searchtri);
+ searchdist = dist;
+ if (b->verbose > 2) {
+ printf(" Choosing triangle with origin (%.12g, %.12g).\n",
+ torg[0], torg[1]);
+ }
+ }
+ }
+
+ samplesleft--;
+ totalsamplesleft--;
+ } while ((samplesleft > 0) && (totalsamplesleft > 0));
+
+ if (totalsamplesleft > 0) {
+ sampleblock = (int **) *sampleblock;
+ samplesleft = samplesperblock;
+ totalpopulation -= population;
+ population = TRIPERBLOCK;
+ }
+ }
+
+ /* Where are we? */
+ org(*searchtri, torg);
+ dest(*searchtri, tdest);
+ /* Check the starting triangle's vertices. */
+ if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
+ return ONVERTEX;
+ }
+ if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
+ lnextself(*searchtri);
+ return ONVERTEX;
+ }
+ /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
+ ahead = counterclockwise(m, b, torg, tdest, searchpoint);
+ if (ahead < 0.0) {
+ /* Turn around so that `searchpoint' is to the left of the */
+ /* edge specified by `searchtri'. */
+ symself(*searchtri);
+ } else if (ahead == 0.0) {
+ /* Check if `searchpoint' is between `torg' and `tdest'. */
+ if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
+ ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
+ return ONEDGE;
+ }
+ }
+ return preciselocate(m, b, searchpoint, searchtri, 0);
+}
+
+/** **/
+/** **/
+/********* Point location routines end here *********/
+
+/********* Mesh transformation routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* insertsubseg() Create a new subsegment and insert it between two */
+/* triangles. */
+/* */
+/* The new subsegment is inserted at the edge described by the handle */
+/* `tri'. Its vertices are properly initialized. The marker `subsegmark' */
+/* is applied to the subsegment and, if appropriate, its vertices. */
+/* */
+/*****************************************************************************/
+
+void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
+ int subsegmark)
+{
+ struct otri oppotri;
+ struct osub newsubseg;
+ vertex triorg, tridest;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ org(*tri, triorg);
+ dest(*tri, tridest);
+ /* Mark vertices if possible. */
+ if (vertexmark(triorg) == 0) {
+ setvertexmark(triorg, subsegmark);
+ }
+ if (vertexmark(tridest) == 0) {
+ setvertexmark(tridest, subsegmark);
+ }
+ /* Check if there's already a subsegment here. */
+ tspivot(*tri, newsubseg);
+ if (newsubseg.ss == m->dummysub) {
+ /* Make new subsegment and initialize its vertices. */
+ makesubseg(m, &newsubseg);
+ setsorg(newsubseg, tridest);
+ setsdest(newsubseg, triorg);
+ setsegorg(newsubseg, tridest);
+ setsegdest(newsubseg, triorg);
+ /* Bond new subsegment to the two triangles it is sandwiched between. */
+ /* Note that the facing triangle `oppotri' might be equal to */
+ /* `dummytri' (outer space), but the new subsegment is bonded to it */
+ /* all the same. */
+ tsbond(*tri, newsubseg);
+ sym(*tri, oppotri);
+ ssymself(newsubseg);
+ tsbond(oppotri, newsubseg);
+ setmark(newsubseg, subsegmark);
+ if (b->verbose > 2) {
+ printf(" Inserting new ");
+ printsubseg(m, b, &newsubseg);
+ }
+ } else {
+ if (mark(newsubseg) == 0) {
+ setmark(newsubseg, subsegmark);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* Terminology */
+/* */
+/* A "local transformation" replaces a small set of triangles with another */
+/* set of triangles. This may or may not involve inserting or deleting a */
+/* vertex. */
+/* */
+/* The term "casing" is used to describe the set of triangles that are */
+/* attached to the triangles being transformed, but are not transformed */
+/* themselves. Think of the casing as a fixed hollow structure inside */
+/* which all the action happens. A "casing" is only defined relative to */
+/* a single transformation; each occurrence of a transformation will */
+/* involve a different casing. */
+/* */
+/*****************************************************************************/
+
+/*****************************************************************************/
+/* */
+/* flip() Transform two triangles to two different triangles by flipping */
+/* an edge counterclockwise within a quadrilateral. */
+/* */
+/* Imagine the original triangles, abc and bad, oriented so that the */
+/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
+/* and the vertex a on the right. The vertex c lies below the edge, and */
+/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
+/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
+/* */
+/* The triangles abc and bad are deleted and replaced by the triangles cdb */
+/* and dca. The triangles that represent abc and bad are NOT deallocated; */
+/* they are reused for dca and cdb, respectively. Hence, any handles that */
+/* may have held the original triangles are still valid, although not */
+/* directed as they were before. */
+/* */
+/* Upon completion of this routine, the `flipedge' handle holds the edge */
+/* dc of triangle dca, and is directed down, from vertex d to vertex c. */
+/* (Hence, the two triangles have rotated counterclockwise.) */
+/* */
+/* WARNING: This transformation is geometrically valid only if the */
+/* quadrilateral adbc is convex. Furthermore, this transformation is */
+/* valid only if there is not a subsegment between the triangles abc and */
+/* bad. This routine does not check either of these preconditions, and */
+/* it is the responsibility of the calling routine to ensure that they are */
+/* met. If they are not, the streets shall be filled with wailing and */
+/* gnashing of teeth. */
+/* */
+/*****************************************************************************/
+
+void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
+{
+ struct otri botleft, botright;
+ struct otri topleft, topright;
+ struct otri top;
+ struct otri botlcasing, botrcasing;
+ struct otri toplcasing, toprcasing;
+ struct osub botlsubseg, botrsubseg;
+ struct osub toplsubseg, toprsubseg;
+ vertex leftvertex, rightvertex, botvertex;
+ vertex farvertex;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ /* Identify the vertices of the quadrilateral. */
+ org(*flipedge, rightvertex);
+ dest(*flipedge, leftvertex);
+ apex(*flipedge, botvertex);
+ sym(*flipedge, top);
+ apex(top, farvertex);
+
+ /* Identify the casing of the quadrilateral. */
+ lprev(top, topleft);
+ sym(topleft, toplcasing);
+ lnext(top, topright);
+ sym(topright, toprcasing);
+ lnext(*flipedge, botleft);
+ sym(botleft, botlcasing);
+ lprev(*flipedge, botright);
+ sym(botright, botrcasing);
+ /* Rotate the quadrilateral one-quarter turn counterclockwise. */
+ bond(topleft, botlcasing);
+ bond(botleft, botrcasing);
+ bond(botright, toprcasing);
+ bond(topright, toplcasing);
+
+ if (m->checksegments) {
+ /* Check for subsegments and rebond them to the quadrilateral. */
+ tspivot(topleft, toplsubseg);
+ tspivot(botleft, botlsubseg);
+ tspivot(botright, botrsubseg);
+ tspivot(topright, toprsubseg);
+ if (toplsubseg.ss == m->dummysub) {
+ tsdissolve(topright);
+ } else {
+ tsbond(topright, toplsubseg);
+ }
+ if (botlsubseg.ss == m->dummysub) {
+ tsdissolve(topleft);
+ } else {
+ tsbond(topleft, botlsubseg);
+ }
+ if (botrsubseg.ss == m->dummysub) {
+ tsdissolve(botleft);
+ } else {
+ tsbond(botleft, botrsubseg);
+ }
+ if (toprsubseg.ss == m->dummysub) {
+ tsdissolve(botright);
+ } else {
+ tsbond(botright, toprsubseg);
+ }
+ }
+
+ /* New vertex assignments for the rotated quadrilateral. */
+ setorg(*flipedge, farvertex);
+ setdest(*flipedge, botvertex);
+ setapex(*flipedge, rightvertex);
+ setorg(top, botvertex);
+ setdest(top, farvertex);
+ setapex(top, leftvertex);
+ if (b->verbose > 2) {
+ printf(" Edge flip results in left ");
+ printtriangle(m, b, &top);
+ printf(" and right ");
+ printtriangle(m, b, flipedge);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* unflip() Transform two triangles to two different triangles by */
+/* flipping an edge clockwise within a quadrilateral. Reverses */
+/* the flip() operation so that the data structures representing */
+/* the triangles are back where they were before the flip(). */
+/* */
+/* Imagine the original triangles, abc and bad, oriented so that the */
+/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
+/* and the vertex a on the right. The vertex c lies below the edge, and */
+/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
+/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
+/* */
+/* The triangles abc and bad are deleted and replaced by the triangles cdb */
+/* and dca. The triangles that represent abc and bad are NOT deallocated; */
+/* they are reused for cdb and dca, respectively. Hence, any handles that */
+/* may have held the original triangles are still valid, although not */
+/* directed as they were before. */
+/* */
+/* Upon completion of this routine, the `flipedge' handle holds the edge */
+/* cd of triangle cdb, and is directed up, from vertex c to vertex d. */
+/* (Hence, the two triangles have rotated clockwise.) */
+/* */
+/* WARNING: This transformation is geometrically valid only if the */
+/* quadrilateral adbc is convex. Furthermore, this transformation is */
+/* valid only if there is not a subsegment between the triangles abc and */
+/* bad. This routine does not check either of these preconditions, and */
+/* it is the responsibility of the calling routine to ensure that they are */
+/* met. If they are not, the streets shall be filled with wailing and */
+/* gnashing of teeth. */
+/* */
+/*****************************************************************************/
+
+void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
+{
+ struct otri botleft, botright;
+ struct otri topleft, topright;
+ struct otri top;
+ struct otri botlcasing, botrcasing;
+ struct otri toplcasing, toprcasing;
+ struct osub botlsubseg, botrsubseg;
+ struct osub toplsubseg, toprsubseg;
+ vertex leftvertex, rightvertex, botvertex;
+ vertex farvertex;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ /* Identify the vertices of the quadrilateral. */
+ org(*flipedge, rightvertex);
+ dest(*flipedge, leftvertex);
+ apex(*flipedge, botvertex);
+ sym(*flipedge, top);
+ apex(top, farvertex);
+
+ /* Identify the casing of the quadrilateral. */
+ lprev(top, topleft);
+ sym(topleft, toplcasing);
+ lnext(top, topright);
+ sym(topright, toprcasing);
+ lnext(*flipedge, botleft);
+ sym(botleft, botlcasing);
+ lprev(*flipedge, botright);
+ sym(botright, botrcasing);
+ /* Rotate the quadrilateral one-quarter turn clockwise. */
+ bond(topleft, toprcasing);
+ bond(botleft, toplcasing);
+ bond(botright, botlcasing);
+ bond(topright, botrcasing);
+
+ if (m->checksegments) {
+ /* Check for subsegments and rebond them to the quadrilateral. */
+ tspivot(topleft, toplsubseg);
+ tspivot(botleft, botlsubseg);
+ tspivot(botright, botrsubseg);
+ tspivot(topright, toprsubseg);
+ if (toplsubseg.ss == m->dummysub) {
+ tsdissolve(botleft);
+ } else {
+ tsbond(botleft, toplsubseg);
+ }
+ if (botlsubseg.ss == m->dummysub) {
+ tsdissolve(botright);
+ } else {
+ tsbond(botright, botlsubseg);
+ }
+ if (botrsubseg.ss == m->dummysub) {
+ tsdissolve(topright);
+ } else {
+ tsbond(topright, botrsubseg);
+ }
+ if (toprsubseg.ss == m->dummysub) {
+ tsdissolve(topleft);
+ } else {
+ tsbond(topleft, toprsubseg);
+ }
+ }
+
+ /* New vertex assignments for the rotated quadrilateral. */
+ setorg(*flipedge, botvertex);
+ setdest(*flipedge, farvertex);
+ setapex(*flipedge, leftvertex);
+ setorg(top, farvertex);
+ setdest(top, botvertex);
+ setapex(top, rightvertex);
+ if (b->verbose > 2) {
+ printf(" Edge unflip results in left ");
+ printtriangle(m, b, flipedge);
+ printf(" and right ");
+ printtriangle(m, b, &top);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* insertvertex() Insert a vertex into a Delaunay triangulation, */
+/* performing flips as necessary to maintain the Delaunay */
+/* property. */
+/* */
+/* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */
+/* the search for the containing triangle begins from `searchtri'. If */
+/* `searchtri.tri' is NULL, a full point location procedure is called. */
+/* If `insertvertex' is found inside a triangle, the triangle is split into */
+/* three; if `insertvertex' lies on an edge, the edge is split in two, */
+/* thereby splitting the two adjacent triangles into four. Edge flips are */
+/* used to restore the Delaunay property. If `insertvertex' lies on an */
+/* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */
+/* returned. On return, `searchtri' is set to a handle whose origin is the */
+/* existing vertex. */
+/* */
+/* Normally, the parameter `splitseg' is set to NULL, implying that no */
+/* subsegment should be split. In this case, if `insertvertex' is found to */
+/* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */
+/* returned. On return, `searchtri' is set to a handle whose primary edge */
+/* is the violated subsegment. */
+/* */
+/* If the calling routine wishes to split a subsegment by inserting a */
+/* vertex in it, the parameter `splitseg' should be that subsegment. In */
+/* this case, `searchtri' MUST be the triangle handle reached by pivoting */
+/* from that subsegment; no point location is done. */
+/* */
+/* `segmentflaws' and `triflaws' are flags that indicate whether or not */
+/* there should be checks for the creation of encroached subsegments or bad */
+/* quality triangles. If a newly inserted vertex encroaches upon */
+/* subsegments, these subsegments are added to the list of subsegments to */
+/* be split if `segmentflaws' is set. If bad triangles are created, these */
+/* are added to the queue if `triflaws' is set. */
+/* */
+/* If a duplicate vertex or violated segment does not prevent the vertex */
+/* from being inserted, the return value will be ENCROACHINGVERTEX if the */
+/* vertex encroaches upon a subsegment (and checking is enabled), or */
+/* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */
+/* handle whose origin is the newly inserted vertex. */
+/* */
+/* insertvertex() does not use flip() for reasons of speed; some */
+/* information can be reused from edge flip to edge flip, like the */
+/* locations of subsegments. */
+/* */
+/*****************************************************************************/
+
+enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
+ vertex newvertex, struct otri *searchtri,
+ struct osub *splitseg,
+ int segmentflaws, int triflaws)
+{
+ struct otri horiz;
+ struct otri top;
+ struct otri botleft, botright;
+ struct otri topleft, topright;
+ struct otri newbotleft, newbotright;
+ struct otri newtopright;
+ struct otri botlcasing, botrcasing;
+ struct otri toplcasing, toprcasing;
+ struct otri testtri;
+ struct osub botlsubseg, botrsubseg;
+ struct osub toplsubseg, toprsubseg;
+ struct osub brokensubseg;
+ struct osub checksubseg;
+ struct osub rightsubseg;
+ struct osub newsubseg;
+ struct badsubseg *encroached;
+ struct flipstacker *newflip;
+ vertex first;
+ vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
+ vertex segmentorg, segmentdest;
+ float attrib;
+ float area;
+ enum insertvertexresult success;
+ enum locateresult intersect;
+ int doflip;
+ int mirrorflag;
+ int enq;
+ int i;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by spivot() and tspivot(). */
+
+ if (b->verbose > 1) {
+ printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
+ }
+
+ if (splitseg == (struct osub *) NULL) {
+ /* Find the location of the vertex to be inserted. Check if a good */
+ /* starting triangle has already been provided by the caller. */
+ if (searchtri->tri == m->dummytri) {
+ /* Find a boundary triangle. */
+ horiz.tri = m->dummytri;
+ horiz.orient = 0;
+ symself(horiz);
+ /* Search for a triangle containing `newvertex'. */
+ intersect = locate(m, b, newvertex, &horiz);
+ } else {
+ /* Start searching from the triangle provided by the caller. */
+ otricopy(*searchtri, horiz);
+ intersect = preciselocate(m, b, newvertex, &horiz, 1);
+ }
+ } else {
+ /* The calling routine provides the subsegment in which */
+ /* the vertex is inserted. */
+ otricopy(*searchtri, horiz);
+ intersect = ONEDGE;
+ }
+
+ if (intersect == ONVERTEX) {
+ /* There's already a vertex there. Return in `searchtri' a triangle */
+ /* whose origin is the existing vertex. */
+ otricopy(horiz, *searchtri);
+ otricopy(horiz, m->recenttri);
+ return DUPLICATEVERTEX;
+ }
+ if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
+ /* The vertex falls on an edge or boundary. */
+ if (m->checksegments && (splitseg == (struct osub *) NULL)) {
+ /* Check whether the vertex falls on a subsegment. */
+ tspivot(horiz, brokensubseg);
+ if (brokensubseg.ss != m->dummysub) {
+ /* The vertex falls on a subsegment, and hence will not be inserted. */
+ if (segmentflaws) {
+ enq = b->nobisect != 2;
+ if (enq && (b->nobisect == 1)) {
+ /* This subsegment may be split only if it is an */
+ /* internal boundary. */
+ sym(horiz, testtri);
+ enq = testtri.tri != m->dummytri;
+ }
+ if (enq) {
+ /* Add the subsegment to the list of encroached subsegments. */
+ encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
+ encroached->encsubseg = sencode(brokensubseg);
+ sorg(brokensubseg, encroached->subsegorg);
+ sdest(brokensubseg, encroached->subsegdest);
+ if (b->verbose > 2) {
+ printf(
+ " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
+ encroached->subsegorg[0], encroached->subsegorg[1],
+ encroached->subsegdest[0], encroached->subsegdest[1]);
+ }
+ }
+ }
+ /* Return a handle whose primary edge contains the vertex, */
+ /* which has not been inserted. */
+ otricopy(horiz, *searchtri);
+ otricopy(horiz, m->recenttri);
+ return VIOLATINGVERTEX;
+ }
+ }
+
+ /* Insert the vertex on an edge, dividing one triangle into two (if */
+ /* the edge lies on a boundary) or two triangles into four. */
+ lprev(horiz, botright);
+ sym(botright, botrcasing);
+ sym(horiz, topright);
+ /* Is there a second triangle? (Or does this edge lie on a boundary?) */
+ mirrorflag = topright.tri != m->dummytri;
+ if (mirrorflag) {
+ lnextself(topright);
+ sym(topright, toprcasing);
+ maketriangle(m, b, &newtopright);
+ } else {
+ /* Splitting a boundary edge increases the number of boundary edges. */
+ m->hullsize++;
+ }
+ maketriangle(m, b, &newbotright);
+
+ /* Set the vertices of changed and new triangles. */
+ org(horiz, rightvertex);
+ dest(horiz, leftvertex);
+ apex(horiz, botvertex);
+ setorg(newbotright, botvertex);
+ setdest(newbotright, rightvertex);
+ setapex(newbotright, newvertex);
+ setorg(horiz, newvertex);
+ for (i = 0; i < m->eextras; i++) {
+ /* Set the element attributes of a new triangle. */
+ setelemattribute(newbotright, i, elemattribute(botright, i));
+ }
+ if (b->vararea) {
+ /* Set the area constraint of a new triangle. */
+ setareabound(newbotright, areabound(botright));
+ }
+ if (mirrorflag) {
+ dest(topright, topvertex);
+ setorg(newtopright, rightvertex);
+ setdest(newtopright, topvertex);
+ setapex(newtopright, newvertex);
+ setorg(topright, newvertex);
+ for (i = 0; i < m->eextras; i++) {
+ /* Set the element attributes of another new triangle. */
+ setelemattribute(newtopright, i, elemattribute(topright, i));
+ }
+ if (b->vararea) {
+ /* Set the area constraint of another new triangle. */
+ setareabound(newtopright, areabound(topright));
+ }
+ }
+
+ /* There may be subsegments that need to be bonded */
+ /* to the new triangle(s). */
+ if (m->checksegments) {
+ tspivot(botright, botrsubseg);
+ if (botrsubseg.ss != m->dummysub) {
+ tsdissolve(botright);
+ tsbond(newbotright, botrsubseg);
+ }
+ if (mirrorflag) {
+ tspivot(topright, toprsubseg);
+ if (toprsubseg.ss != m->dummysub) {
+ tsdissolve(topright);
+ tsbond(newtopright, toprsubseg);
+ }
+ }
+ }
+
+ /* Bond the new triangle(s) to the surrounding triangles. */
+ bond(newbotright, botrcasing);
+ lprevself(newbotright);
+ bond(newbotright, botright);
+ lprevself(newbotright);
+ if (mirrorflag) {
+ bond(newtopright, toprcasing);
+ lnextself(newtopright);
+ bond(newtopright, topright);
+ lnextself(newtopright);
+ bond(newtopright, newbotright);
+ }
+
+ if (splitseg != (struct osub *) NULL) {
+ /* Split the subsegment into two. */
+ setsdest(*splitseg, newvertex);
+ segorg(*splitseg, segmentorg);
+ segdest(*splitseg, segmentdest);
+ ssymself(*splitseg);
+ spivot(*splitseg, rightsubseg);
+ insertsubseg(m, b, &newbotright, mark(*splitseg));
+ tspivot(newbotright, newsubseg);
+ setsegorg(newsubseg, segmentorg);
+ setsegdest(newsubseg, segmentdest);
+ sbond(*splitseg, newsubseg);
+ ssymself(newsubseg);
+ sbond(newsubseg, rightsubseg);
+ ssymself(*splitseg);
+ /* Transfer the subsegment's boundary marker to the vertex */
+ /* if required. */
+ if (vertexmark(newvertex) == 0) {
+ setvertexmark(newvertex, mark(*splitseg));
+ }
+ }
+
+ if (m->checkquality) {
+ poolrestart(&m->flipstackers);
+ m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
+ m->lastflip->flippedtri = encode(horiz);
+ m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
+ }
+ if (b->verbose > 2) {
+ printf(" Updating bottom left ");
+ printtriangle(m, b, &botright);
+ if (mirrorflag) {
+ printf(" Updating top left ");
+ printtriangle(m, b, &topright);
+ printf(" Creating top right ");
+ printtriangle(m, b, &newtopright);
+ }
+ printf(" Creating bottom right ");
+ printtriangle(m, b, &newbotright);
+ }
+
+ /* Position `horiz' on the first edge to check for */
+ /* the Delaunay property. */
+ lnextself(horiz);
+ } else {
+ /* Insert the vertex in a triangle, splitting it into three. */
+ lnext(horiz, botleft);
+ lprev(horiz, botright);
+ sym(botleft, botlcasing);
+ sym(botright, botrcasing);
+ maketriangle(m, b, &newbotleft);
+ maketriangle(m, b, &newbotright);
+
+ /* Set the vertices of changed and new triangles. */
+ org(horiz, rightvertex);
+ dest(horiz, leftvertex);
+ apex(horiz, botvertex);
+ setorg(newbotleft, leftvertex);
+ setdest(newbotleft, botvertex);
+ setapex(newbotleft, newvertex);
+ setorg(newbotright, botvertex);
+ setdest(newbotright, rightvertex);
+ setapex(newbotright, newvertex);
+ setapex(horiz, newvertex);
+ for (i = 0; i < m->eextras; i++) {
+ /* Set the element attributes of the new triangles. */
+ attrib = elemattribute(horiz, i);
+ setelemattribute(newbotleft, i, attrib);
+ setelemattribute(newbotright, i, attrib);
+ }
+ if (b->vararea) {
+ /* Set the area constraint of the new triangles. */
+ area = areabound(horiz);
+ setareabound(newbotleft, area);
+ setareabound(newbotright, area);
+ }
+
+ /* There may be subsegments that need to be bonded */
+ /* to the new triangles. */
+ if (m->checksegments) {
+ tspivot(botleft, botlsubseg);
+ if (botlsubseg.ss != m->dummysub) {
+ tsdissolve(botleft);
+ tsbond(newbotleft, botlsubseg);
+ }
+ tspivot(botright, botrsubseg);
+ if (botrsubseg.ss != m->dummysub) {
+ tsdissolve(botright);
+ tsbond(newbotright, botrsubseg);
+ }
+ }
+
+ /* Bond the new triangles to the surrounding triangles. */
+ bond(newbotleft, botlcasing);
+ bond(newbotright, botrcasing);
+ lnextself(newbotleft);
+ lprevself(newbotright);
+ bond(newbotleft, newbotright);
+ lnextself(newbotleft);
+ bond(botleft, newbotleft);
+ lprevself(newbotright);
+ bond(botright, newbotright);
+
+ if (m->checkquality) {
+ poolrestart(&m->flipstackers);
+ m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
+ m->lastflip->flippedtri = encode(horiz);
+ m->lastflip->prevflip = (struct flipstacker *) NULL;
+ }
+ if (b->verbose > 2) {
+ printf(" Updating top ");
+ printtriangle(m, b, &horiz);
+ printf(" Creating left ");
+ printtriangle(m, b, &newbotleft);
+ printf(" Creating right ");
+ printtriangle(m, b, &newbotright);
+ }
+ }
+
+ /* The insertion is successful by default, unless an encroached */
+ /* subsegment is found. */
+ success = SUCCESSFULVERTEX;
+ /* Circle around the newly inserted vertex, checking each edge opposite */
+ /* it for the Delaunay property. Non-Delaunay edges are flipped. */
+ /* `horiz' is always the edge being checked. `first' marks where to */
+ /* stop circling. */
+ org(horiz, first);
+ rightvertex = first;
+ dest(horiz, leftvertex);
+ /* Circle until finished. */
+ while (1) {
+ /* By default, the edge will be flipped. */
+ doflip = 1;
+
+ if (m->checksegments) {
+ /* Check for a subsegment, which cannot be flipped. */
+ tspivot(horiz, checksubseg);
+ if (checksubseg.ss != m->dummysub) {
+ /* The edge is a subsegment and cannot be flipped. */
+ doflip = 0;
+ }
+ }
+
+ if (doflip) {
+ /* Check if the edge is a boundary edge. */
+ sym(horiz, top);
+ if (top.tri == m->dummytri) {
+ /* The edge is a boundary edge and cannot be flipped. */
+ doflip = 0;
+ } else {
+ /* Find the vertex on the other side of the edge. */
+ apex(top, farvertex);
+ /* In the incremental Delaunay triangulation algorithm, any of */
+ /* `leftvertex', `rightvertex', and `farvertex' could be vertices */
+ /* of the triangular bounding box. These vertices must be */
+ /* treated as if they are infinitely distant, even though their */
+ /* "coordinates" are not. */
+ if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
+ (leftvertex == m->infvertex3)) {
+ /* `leftvertex' is infinitely distant. Check the convexity of */
+ /* the boundary of the triangulation. 'farvertex' might be */
+ /* infinite as well, but trust me, this same condition should */
+ /* be applied. */
+ doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
+ > 0.0;
+ } else if ((rightvertex == m->infvertex1) ||
+ (rightvertex == m->infvertex2) ||
+ (rightvertex == m->infvertex3)) {
+ /* `rightvertex' is infinitely distant. Check the convexity of */
+ /* the boundary of the triangulation. 'farvertex' might be */
+ /* infinite as well, but trust me, this same condition should */
+ /* be applied. */
+ doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
+ > 0.0;
+ } else if ((farvertex == m->infvertex1) ||
+ (farvertex == m->infvertex2) ||
+ (farvertex == m->infvertex3)) {
+ /* `farvertex' is infinitely distant and cannot be inside */
+ /* the circumcircle of the triangle `horiz'. */
+ doflip = 0;
+ } else {
+ /* Test whether the edge is locally Delaunay. */
+ doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
+ farvertex) > 0.0;
+ }
+ if (doflip) {
+ /* We made it! Flip the edge `horiz' by rotating its containing */
+ /* quadrilateral (the two triangles adjacent to `horiz'). */
+ /* Identify the casing of the quadrilateral. */
+ lprev(top, topleft);
+ sym(topleft, toplcasing);
+ lnext(top, topright);
+ sym(topright, toprcasing);
+ lnext(horiz, botleft);
+ sym(botleft, botlcasing);
+ lprev(horiz, botright);
+ sym(botright, botrcasing);
+ /* Rotate the quadrilateral one-quarter turn counterclockwise. */
+ bond(topleft, botlcasing);
+ bond(botleft, botrcasing);
+ bond(botright, toprcasing);
+ bond(topright, toplcasing);
+ if (m->checksegments) {
+ /* Check for subsegments and rebond them to the quadrilateral. */
+ tspivot(topleft, toplsubseg);
+ tspivot(botleft, botlsubseg);
+ tspivot(botright, botrsubseg);
+ tspivot(topright, toprsubseg);
+ if (toplsubseg.ss == m->dummysub) {
+ tsdissolve(topright);
+ } else {
+ tsbond(topright, toplsubseg);
+ }
+ if (botlsubseg.ss == m->dummysub) {
+ tsdissolve(topleft);
+ } else {
+ tsbond(topleft, botlsubseg);
+ }
+ if (botrsubseg.ss == m->dummysub) {
+ tsdissolve(botleft);
+ } else {
+ tsbond(botleft, botrsubseg);
+ }
+ if (toprsubseg.ss == m->dummysub) {
+ tsdissolve(botright);
+ } else {
+ tsbond(botright, toprsubseg);
+ }
+ }
+ /* New vertex assignments for the rotated quadrilateral. */
+ setorg(horiz, farvertex);
+ setdest(horiz, newvertex);
+ setapex(horiz, rightvertex);
+ setorg(top, newvertex);
+ setdest(top, farvertex);
+ setapex(top, leftvertex);
+ for (i = 0; i < m->eextras; i++) {
+ /* Take the average of the two triangles' attributes. */
+ attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
+ setelemattribute(top, i, attrib);
+ setelemattribute(horiz, i, attrib);
+ }
+ if (b->vararea) {
+ if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
+ area = -1.0;
+ } else {
+ /* Take the average of the two triangles' area constraints. */
+ /* This prevents small area constraints from migrating a */
+ /* long, long way from their original location due to flips. */
+ area = 0.5 * (areabound(top) + areabound(horiz));
+ }
+ setareabound(top, area);
+ setareabound(horiz, area);
+ }
+
+ if (m->checkquality) {
+ newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
+ newflip->flippedtri = encode(horiz);
+ newflip->prevflip = m->lastflip;
+ m->lastflip = newflip;
+ }
+ if (b->verbose > 2) {
+ printf(" Edge flip results in left ");
+ lnextself(topleft);
+ printtriangle(m, b, &topleft);
+ printf(" and right ");
+ printtriangle(m, b, &horiz);
+ }
+ /* On the next iterations, consider the two edges that were */
+ /* exposed (this is, are now visible to the newly inserted */
+ /* vertex) by the edge flip. */
+ lprevself(horiz);
+ leftvertex = farvertex;
+ }
+ }
+ }
+ if (!doflip) {
+ /* The handle `horiz' is accepted as locally Delaunay. */
+ /* Look for the next edge around the newly inserted vertex. */
+ lnextself(horiz);
+ sym(horiz, testtri);
+ /* Check for finishing a complete revolution about the new vertex, or */
+ /* falling outside of the triangulation. The latter will happen */
+ /* when a vertex is inserted at a boundary. */
+ if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
+ /* We're done. Return a triangle whose origin is the new vertex. */
+ lnext(horiz, *searchtri);
+ lnext(horiz, m->recenttri);
+ return success;
+ }
+ /* Finish finding the next edge around the newly inserted vertex. */
+ lnext(testtri, horiz);
+ rightvertex = leftvertex;
+ dest(horiz, leftvertex);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
+/* has a certain "nice" shape. This includes the */
+/* polygons that result from deletion of a vertex or */
+/* insertion of a segment. */
+/* */
+/* This is a conceptually difficult routine. The starting assumption is */
+/* that we have a polygon with n sides. n - 1 of these sides are currently */
+/* represented as edges in the mesh. One side, called the "base", need not */
+/* be. */
+/* */
+/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */
+/* triangles that share a common origin. For each of these triangles, the */
+/* edge opposite the origin is one of the sides of the polygon. The */
+/* primary edge of each triangle is the edge directed from the origin to */
+/* the destination; note that this is not the same edge that is a side of */
+/* the polygon. `firstedge' is the primary edge of the first triangle. */
+/* From there, the triangles follow in counterclockwise order about the */
+/* polygon, until `lastedge', the primary edge of the last triangle. */
+/* `firstedge' and `lastedge' are probably connected to other triangles */
+/* beyond the extremes of the fan, but their identity is not important, as */
+/* long as the fan remains connected to them. */
+/* */
+/* Imagine the polygon oriented so that its base is at the bottom. This */
+/* puts `firstedge' on the far right, and `lastedge' on the far left. */
+/* The right vertex of the base is the destination of `firstedge', and the */
+/* left vertex of the base is the apex of `lastedge'. */
+/* */
+/* The challenge now is to find the right sequence of edge flips to */
+/* transform the fan into a Delaunay triangulation of the polygon. Each */
+/* edge flip effectively removes one triangle from the fan, committing it */
+/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */
+/* is set, the final flip will be performed, resulting in a fan of one */
+/* (useless?) triangle. If `doflip' is not set, the final flip is not */
+/* performed, resulting in a fan of two triangles, and an unfinished */
+/* triangular polygon that is not yet filled out with a single triangle. */
+/* On completion of the routine, `lastedge' is the last remaining triangle, */
+/* or the leftmost of the last two. */
+/* */
+/* Although the flips are performed in the order described above, the */
+/* decisions about what flips to perform are made in precisely the reverse */
+/* order. The recursive triangulatepolygon() procedure makes a decision, */
+/* uses up to two recursive calls to triangulate the "subproblems" */
+/* (polygons with fewer edges), and then performs an edge flip. */
+/* */
+/* The "decision" it makes is which vertex of the polygon should be */
+/* connected to the base. This decision is made by testing every possible */
+/* vertex. Once the best vertex is found, the two edges that connect this */
+/* vertex to the base become the bases for two smaller polygons. These */
+/* are triangulated recursively. Unfortunately, this approach can take */
+/* O(n^2) time not only in the worst case, but in many common cases. It's */
+/* rarely a big deal for vertex deletion, where n is rarely larger than */
+/* ten, but it could be a big deal for segment insertion, especially if */
+/* there's a lot of long segments that each cut many triangles. I ought to */
+/* code a faster algorithm some day. */
+/* */
+/* The `edgecount' parameter is the number of sides of the polygon, */
+/* including its base. `triflaws' is a flag that determines whether the */
+/* new triangles should be tested for quality, and enqueued if they are */
+/* bad. */
+/* */
+/*****************************************************************************/
+
+void triangulatepolygon(struct mesh *m, struct behavior *b,
+ struct otri *firstedge, struct otri *lastedge,
+ int edgecount, int doflip, int triflaws)
+{
+ struct otri testtri;
+ struct otri besttri;
+ struct otri tempedge;
+ vertex leftbasevertex, rightbasevertex;
+ vertex testvertex;
+ vertex bestvertex;
+ int bestnumber;
+ int i;
+ triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
+
+ /* Identify the base vertices. */
+ apex(*lastedge, leftbasevertex);
+ dest(*firstedge, rightbasevertex);
+ if (b->verbose > 2) {
+ printf(" Triangulating interior polygon at edge\n");
+ printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
+ leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
+ }
+ /* Find the best vertex to connect the base to. */
+ onext(*firstedge, besttri);
+ dest(besttri, bestvertex);
+ otricopy(besttri, testtri);
+ bestnumber = 1;
+ for (i = 2; i <= edgecount - 2; i++) {
+ onextself(testtri);
+ dest(testtri, testvertex);
+ /* Is this a better vertex? */
+ if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
+ testvertex) > 0.0) {
+ otricopy(testtri, besttri);
+ bestvertex = testvertex;
+ bestnumber = i;
+ }
+ }
+ if (b->verbose > 2) {
+ printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
+ bestvertex[1]);
+ }
+ if (bestnumber > 1) {
+ /* Recursively triangulate the smaller polygon on the right. */
+ oprev(besttri, tempedge);
+ triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
+ triflaws);
+ }
+ if (bestnumber < edgecount - 2) {
+ /* Recursively triangulate the smaller polygon on the left. */
+ sym(besttri, tempedge);
+ triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
+ triflaws);
+ /* Find `besttri' again; it may have been lost to edge flips. */
+ sym(tempedge, besttri);
+ }
+ if (doflip) {
+ /* Do one final edge flip. */
+ flip(m, b, &besttri);
+ }
+ /* Return the base triangle. */
+ otricopy(besttri, *lastedge);
+}
+
+/** **/
+/** **/
+/********* Mesh transformation routines end here *********/
+
+/********* Divide-and-conquer Delaunay triangulation begins here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* The divide-and-conquer bounding box */
+/* */
+/* I originally implemented the divide-and-conquer and incremental Delaunay */
+/* triangulations using the edge-based data structure presented by Guibas */
+/* and Stolfi. Switching to a triangle-based data structure doubled the */
+/* speed. However, I had to think of a few extra tricks to maintain the */
+/* elegance of the original algorithms. */
+/* */
+/* The "bounding box" used by my variant of the divide-and-conquer */
+/* algorithm uses one triangle for each edge of the convex hull of the */
+/* triangulation. These bounding triangles all share a common apical */
+/* vertex, which is represented by NULL and which represents nothing. */
+/* The bounding triangles are linked in a circular fan about this NULL */
+/* vertex, and the edges on the convex hull of the triangulation appear */
+/* opposite the NULL vertex. You might find it easiest to imagine that */
+/* the NULL vertex is a point in 3D space behind the center of the */
+/* triangulation, and that the bounding triangles form a sort of cone. */
+/* */
+/* This bounding box makes it easy to represent degenerate cases. For */
+/* instance, the triangulation of two vertices is a single edge. This edge */
+/* is represented by two bounding box triangles, one on each "side" of the */
+/* edge. These triangles are also linked together in a fan about the NULL */
+/* vertex. */
+/* */
+/* The bounding box also makes it easy to traverse the convex hull, as the */
+/* divide-and-conquer algorithm needs to do. */
+/* */
+/*****************************************************************************/
+
+/*****************************************************************************/
+/* */
+/* vertexsort() Sort an array of vertices by x-coordinate, using the */
+/* y-coordinate as a secondary key. */
+/* */
+/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */
+/* the usual quicksort mistakes. */
+/* */
+/*****************************************************************************/
+
+void vertexsort(vertex *sortarray, int arraysize)
+{
+ int left, right;
+ int pivot;
+ float pivotx, pivoty;
+ vertex temp;
+
+ if (arraysize == 2) {
+ /* Recursive base case. */
+ if ((sortarray[0][0] > sortarray[1][0]) ||
+ ((sortarray[0][0] == sortarray[1][0]) &&
+ (sortarray[0][1] > sortarray[1][1]))) {
+ temp = sortarray[1];
+ sortarray[1] = sortarray[0];
+ sortarray[0] = temp;
+ }
+ return;
+ }
+ /* Choose a random pivot to split the array. */
+ pivot = (int) randomnation((unsigned int) arraysize);
+ pivotx = sortarray[pivot][0];
+ pivoty = sortarray[pivot][1];
+ /* Split the array. */
+ left = -1;
+ right = arraysize;
+ while (left < right) {
+ /* Search for a vertex whose x-coordinate is too large for the left. */
+ do {
+ left++;
+ } while ((left <= right) && ((sortarray[left][0] < pivotx) ||
+ ((sortarray[left][0] == pivotx) &&
+ (sortarray[left][1] < pivoty))));
+ /* Search for a vertex whose x-coordinate is too small for the right. */
+ do {
+ right--;
+ } while ((left <= right) && ((sortarray[right][0] > pivotx) ||
+ ((sortarray[right][0] == pivotx) &&
+ (sortarray[right][1] > pivoty))));
+ if (left < right) {
+ /* Swap the left and right vertices. */
+ temp = sortarray[left];
+ sortarray[left] = sortarray[right];
+ sortarray[right] = temp;
+ }
+ }
+ if (left > 1) {
+ /* Recursively sort the left subset. */
+ vertexsort(sortarray, left);
+ }
+ if (right < arraysize - 2) {
+ /* Recursively sort the right subset. */
+ vertexsort(&sortarray[right + 1], arraysize - right - 1);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* vertexmedian() An order statistic algorithm, almost. Shuffles an */
+/* array of vertices so that the first `median' vertices */
+/* occur lexicographically before the remaining vertices. */
+/* */
+/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
+/* if axis == 1. Very similar to the vertexsort() procedure, but runs in */
+/* randomized linear time. */
+/* */
+/*****************************************************************************/
+
+void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
+{
+ int left, right;
+ int pivot;
+ float pivot1, pivot2;
+ vertex temp;
+
+ if (arraysize == 2) {
+ /* Recursive base case. */
+ if ((sortarray[0][axis] > sortarray[1][axis]) ||
+ ((sortarray[0][axis] == sortarray[1][axis]) &&
+ (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
+ temp = sortarray[1];
+ sortarray[1] = sortarray[0];
+ sortarray[0] = temp;
+ }
+ return;
+ }
+ /* Choose a random pivot to split the array. */
+ pivot = (int) randomnation((unsigned int) arraysize);
+ pivot1 = sortarray[pivot][axis];
+ pivot2 = sortarray[pivot][1 - axis];
+ /* Split the array. */
+ left = -1;
+ right = arraysize;
+ while (left < right) {
+ /* Search for a vertex whose x-coordinate is too large for the left. */
+ do {
+ left++;
+ } while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
+ ((sortarray[left][axis] == pivot1) &&
+ (sortarray[left][1 - axis] < pivot2))));
+ /* Search for a vertex whose x-coordinate is too small for the right. */
+ do {
+ right--;
+ } while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
+ ((sortarray[right][axis] == pivot1) &&
+ (sortarray[right][1 - axis] > pivot2))));
+ if (left < right) {
+ /* Swap the left and right vertices. */
+ temp = sortarray[left];
+ sortarray[left] = sortarray[right];
+ sortarray[right] = temp;
+ }
+ }
+ /* Unlike in vertexsort(), at most one of the following */
+ /* conditionals is true. */
+ if (left > median) {
+ /* Recursively shuffle the left subset. */
+ vertexmedian(sortarray, left, median, axis);
+ }
+ if (right < median - 1) {
+ /* Recursively shuffle the right subset. */
+ vertexmedian(&sortarray[right + 1], arraysize - right - 1,
+ median - right - 1, axis);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* alternateaxes() Sorts the vertices as appropriate for the divide-and- */
+/* conquer algorithm with alternating cuts. */
+/* */
+/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */
+/* For the base case, subsets containing only two or three vertices are */
+/* always sorted by x-coordinate. */
+/* */
+/*****************************************************************************/
+
+void alternateaxes(vertex *sortarray, int arraysize, int axis)
+{
+ int divider;
+
+ divider = arraysize >> 1;
+ if (arraysize <= 3) {
+ /* Recursive base case: subsets of two or three vertices will be */
+ /* handled specially, and should always be sorted by x-coordinate. */
+ axis = 0;
+ }
+ /* Partition with a horizontal or vertical cut. */
+ vertexmedian(sortarray, arraysize, divider, axis);
+ /* Recursively partition the subsets with a cross cut. */
+ if (arraysize - divider >= 2) {
+ if (divider >= 2) {
+ alternateaxes(sortarray, divider, 1 - axis);
+ }
+ alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* mergehulls() Merge two adjacent Delaunay triangulations into a */
+/* single Delaunay triangulation. */
+/* */
+/* This is similar to the algorithm given by Guibas and Stolfi, but uses */
+/* a triangle-based, rather than edge-based, data structure. */
+/* */
+/* The algorithm walks up the gap between the two triangulations, knitting */
+/* them together. As they are merged, some of their bounding triangles */
+/* are converted into real triangles of the triangulation. The procedure */
+/* pulls each hull's bounding triangles apart, then knits them together */
+/* like the teeth of two gears. The Delaunay property determines, at each */
+/* step, whether the next "tooth" is a bounding triangle of the left hull */
+/* or the right. When a bounding triangle becomes real, its apex is */
+/* changed from NULL to a real vertex. */
+/* */
+/* Only two new triangles need to be allocated. These become new bounding */
+/* triangles at the top and bottom of the seam. They are used to connect */
+/* the remaining bounding triangles (those that have not been converted */
+/* into real triangles) into a single fan. */
+/* */
+/* On entry, `farleft' and `innerleft' are bounding triangles of the left */
+/* triangulation. The origin of `farleft' is the leftmost vertex, and */
+/* the destination of `innerleft' is the rightmost vertex of the */
+/* triangulation. Similarly, `innerright' and `farright' are bounding */
+/* triangles of the right triangulation. The origin of `innerright' and */
+/* destination of `farright' are the leftmost and rightmost vertices. */
+/* */
+/* On completion, the origin of `farleft' is the leftmost vertex of the */
+/* merged triangulation, and the destination of `farright' is the rightmost */
+/* vertex. */
+/* */
+/*****************************************************************************/
+
+void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
+ struct otri *innerleft, struct otri *innerright,
+ struct otri *farright, int axis)
+{
+ struct otri leftcand, rightcand;
+ struct otri baseedge;
+ struct otri nextedge;
+ struct otri sidecasing, topcasing, outercasing;
+ struct otri checkedge;
+ vertex innerleftdest;
+ vertex innerrightorg;
+ vertex innerleftapex, innerrightapex;
+ vertex farleftpt, farrightpt;
+ vertex farleftapex, farrightapex;
+ vertex lowerleft, lowerright;
+ vertex upperleft, upperright;
+ vertex nextapex;
+ vertex checkvertex;
+ int changemade;
+ int badedge;
+ int leftfinished, rightfinished;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ dest(*innerleft, innerleftdest);
+ apex(*innerleft, innerleftapex);
+ org(*innerright, innerrightorg);
+ apex(*innerright, innerrightapex);
+ /* Special treatment for horizontal cuts. */
+ if (b->dwyer && (axis == 1)) {
+ org(*farleft, farleftpt);
+ apex(*farleft, farleftapex);
+ dest(*farright, farrightpt);
+ apex(*farright, farrightapex);
+ /* The pointers to the extremal vertices are shifted to point to the */
+ /* topmost and bottommost vertex of each hull, rather than the */
+ /* leftmost and rightmost vertices. */
+ while (farleftapex[1] < farleftpt[1]) {
+ lnextself(*farleft);
+ symself(*farleft);
+ farleftpt = farleftapex;
+ apex(*farleft, farleftapex);
+ }
+ sym(*innerleft, checkedge);
+ apex(checkedge, checkvertex);
+ while (checkvertex[1] > innerleftdest[1]) {
+ lnext(checkedge, *innerleft);
+ innerleftapex = innerleftdest;
+ innerleftdest = checkvertex;
+ sym(*innerleft, checkedge);
+ apex(checkedge, checkvertex);
+ }
+ while (innerrightapex[1] < innerrightorg[1]) {
+ lnextself(*innerright);
+ symself(*innerright);
+ innerrightorg = innerrightapex;
+ apex(*innerright, innerrightapex);
+ }
+ sym(*farright, checkedge);
+ apex(checkedge, checkvertex);
+ while (checkvertex[1] > farrightpt[1]) {
+ lnext(checkedge, *farright);
+ farrightapex = farrightpt;
+ farrightpt = checkvertex;
+ sym(*farright, checkedge);
+ apex(checkedge, checkvertex);
+ }
+ }
+ /* Find a line tangent to and below both hulls. */
+ do {
+ changemade = 0;
+ /* Make innerleftdest the "bottommost" vertex of the left hull. */
+ if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
+ 0.0) {
+ lprevself(*innerleft);
+ symself(*innerleft);
+ innerleftdest = innerleftapex;
+ apex(*innerleft, innerleftapex);
+ changemade = 1;
+ }
+ /* Make innerrightorg the "bottommost" vertex of the right hull. */
+ if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
+ 0.0) {
+ lnextself(*innerright);
+ symself(*innerright);
+ innerrightorg = innerrightapex;
+ apex(*innerright, innerrightapex);
+ changemade = 1;
+ }
+ } while (changemade);
+ /* Find the two candidates to be the next "gear tooth." */
+ sym(*innerleft, leftcand);
+ sym(*innerright, rightcand);
+ /* Create the bottom new bounding triangle. */
+ maketriangle(m, b, &baseedge);
+ /* Connect it to the bounding boxes of the left and right triangulations. */
+ bond(baseedge, *innerleft);
+ lnextself(baseedge);
+ bond(baseedge, *innerright);
+ lnextself(baseedge);
+ setorg(baseedge, innerrightorg);
+ setdest(baseedge, innerleftdest);
+ /* Apex is intentionally left NULL. */
+ if (b->verbose > 2) {
+ printf(" Creating base bounding ");
+ printtriangle(m, b, &baseedge);
+ }
+ /* Fix the extreme triangles if necessary. */
+ org(*farleft, farleftpt);
+ if (innerleftdest == farleftpt) {
+ lnext(baseedge, *farleft);
+ }
+ dest(*farright, farrightpt);
+ if (innerrightorg == farrightpt) {
+ lprev(baseedge, *farright);
+ }
+ /* The vertices of the current knitting edge. */
+ lowerleft = innerleftdest;
+ lowerright = innerrightorg;
+ /* The candidate vertices for knitting. */
+ apex(leftcand, upperleft);
+ apex(rightcand, upperright);
+ /* Walk up the gap between the two triangulations, knitting them together. */
+ while (1) {
+ /* Have we reached the top? (This isn't quite the right question, */
+ /* because even though the left triangulation might seem finished now, */
+ /* moving up on the right triangulation might reveal a new vertex of */
+ /* the left triangulation. And vice-versa.) */
+ leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
+ 0.0;
+ rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
+ <= 0.0;
+ if (leftfinished && rightfinished) {
+ /* Create the top new bounding triangle. */
+ maketriangle(m, b, &nextedge);
+ setorg(nextedge, lowerleft);
+ setdest(nextedge, lowerright);
+ /* Apex is intentionally left NULL. */
+ /* Connect it to the bounding boxes of the two triangulations. */
+ bond(nextedge, baseedge);
+ lnextself(nextedge);
+ bond(nextedge, rightcand);
+ lnextself(nextedge);
+ bond(nextedge, leftcand);
+ if (b->verbose > 2) {
+ printf(" Creating top bounding ");
+ printtriangle(m, b, &nextedge);
+ }
+ /* Special treatment for horizontal cuts. */
+ if (b->dwyer && (axis == 1)) {
+ org(*farleft, farleftpt);
+ apex(*farleft, farleftapex);
+ dest(*farright, farrightpt);
+ apex(*farright, farrightapex);
+ sym(*farleft, checkedge);
+ apex(checkedge, checkvertex);
+ /* The pointers to the extremal vertices are restored to the */
+ /* leftmost and rightmost vertices (rather than topmost and */
+ /* bottommost). */
+ while (checkvertex[0] < farleftpt[0]) {
+ lprev(checkedge, *farleft);
+ farleftapex = farleftpt;
+ farleftpt = checkvertex;
+ sym(*farleft, checkedge);
+ apex(checkedge, checkvertex);
+ }
+ while (farrightapex[0] > farrightpt[0]) {
+ lprevself(*farright);
+ symself(*farright);
+ farrightpt = farrightapex;
+ apex(*farright, farrightapex);
+ }
+ }
+ return;
+ }
+ /* Consider eliminating edges from the left triangulation. */
+ if (!leftfinished) {
+ /* What vertex would be exposed if an edge were deleted? */
+ lprev(leftcand, nextedge);
+ symself(nextedge);
+ apex(nextedge, nextapex);
+ /* If nextapex is NULL, then no vertex would be exposed; the */
+ /* triangulation would have been eaten right through. */
+ if (nextapex != (vertex) NULL) {
+ /* Check whether the edge is Delaunay. */
+ badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
+ 0.0;
+ while (badedge) {
+ /* Eliminate the edge with an edge flip. As a result, the */
+ /* left triangulation will have one more boundary triangle. */
+ lnextself(nextedge);
+ sym(nextedge, topcasing);
+ lnextself(nextedge);
+ sym(nextedge, sidecasing);
+ bond(nextedge, topcasing);
+ bond(leftcand, sidecasing);
+ lnextself(leftcand);
+ sym(leftcand, outercasing);
+ lprevself(nextedge);
+ bond(nextedge, outercasing);
+ /* Correct the vertices to reflect the edge flip. */
+ setorg(leftcand, lowerleft);
+ setdest(leftcand, NULL);
+ setapex(leftcand, nextapex);
+ setorg(nextedge, NULL);
+ setdest(nextedge, upperleft);
+ setapex(nextedge, nextapex);
+ /* Consider the newly exposed vertex. */
+ upperleft = nextapex;
+ /* What vertex would be exposed if another edge were deleted? */
+ otricopy(sidecasing, nextedge);
+ apex(nextedge, nextapex);
+ if (nextapex != (vertex) NULL) {
+ /* Check whether the edge is Delaunay. */
+ badedge = incircle(m, b, lowerleft, lowerright, upperleft,
+ nextapex) > 0.0;
+ } else {
+ /* Avoid eating right through the triangulation. */
+ badedge = 0;
+ }
+ }
+ }
+ }
+ /* Consider eliminating edges from the right triangulation. */
+ if (!rightfinished) {
+ /* What vertex would be exposed if an edge were deleted? */
+ lnext(rightcand, nextedge);
+ symself(nextedge);
+ apex(nextedge, nextapex);
+ /* If nextapex is NULL, then no vertex would be exposed; the */
+ /* triangulation would have been eaten right through. */
+ if (nextapex != (vertex) NULL) {
+ /* Check whether the edge is Delaunay. */
+ badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
+ 0.0;
+ while (badedge) {
+ /* Eliminate the edge with an edge flip. As a result, the */
+ /* right triangulation will have one more boundary triangle. */
+ lprevself(nextedge);
+ sym(nextedge, topcasing);
+ lprevself(nextedge);
+ sym(nextedge, sidecasing);
+ bond(nextedge, topcasing);
+ bond(rightcand, sidecasing);
+ lprevself(rightcand);
+ sym(rightcand, outercasing);
+ lnextself(nextedge);
+ bond(nextedge, outercasing);
+ /* Correct the vertices to reflect the edge flip. */
+ setorg(rightcand, NULL);
+ setdest(rightcand, lowerright);
+ setapex(rightcand, nextapex);
+ setorg(nextedge, upperright);
+ setdest(nextedge, NULL);
+ setapex(nextedge, nextapex);
+ /* Consider the newly exposed vertex. */
+ upperright = nextapex;
+ /* What vertex would be exposed if another edge were deleted? */
+ otricopy(sidecasing, nextedge);
+ apex(nextedge, nextapex);
+ if (nextapex != (vertex) NULL) {
+ /* Check whether the edge is Delaunay. */
+ badedge = incircle(m, b, lowerleft, lowerright, upperright,
+ nextapex) > 0.0;
+ } else {
+ /* Avoid eating right through the triangulation. */
+ badedge = 0;
+ }
+ }
+ }
+ }
+ if (leftfinished || (!rightfinished &&
+ (incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
+ 0.0))) {
+ /* Knit the triangulations, adding an edge from `lowerleft' */
+ /* to `upperright'. */
+ bond(baseedge, rightcand);
+ lprev(rightcand, baseedge);
+ setdest(baseedge, lowerleft);
+ lowerright = upperright;
+ sym(baseedge, rightcand);
+ apex(rightcand, upperright);
+ } else {
+ /* Knit the triangulations, adding an edge from `upperleft' */
+ /* to `lowerright'. */
+ bond(baseedge, leftcand);
+ lnext(leftcand, baseedge);
+ setorg(baseedge, lowerright);
+ lowerleft = upperleft;
+ sym(baseedge, leftcand);
+ apex(leftcand, upperleft);
+ }
+ if (b->verbose > 2) {
+ printf(" Connecting ");
+ printtriangle(m, b, &baseedge);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* divconqrecurse() Recursively form a Delaunay triangulation by the */
+/* divide-and-conquer method. */
+/* */
+/* Recursively breaks down the problem into smaller pieces, which are */
+/* knitted together by mergehulls(). The base cases (problems of two or */
+/* three vertices) are handled specially here. */
+/* */
+/* On completion, `farleft' and `farright' are bounding triangles such that */
+/* the origin of `farleft' is the leftmost vertex (breaking ties by */
+/* choosing the highest leftmost vertex), and the destination of */
+/* `farright' is the rightmost vertex (breaking ties by choosing the */
+/* lowest rightmost vertex). */
+/* */
+/*****************************************************************************/
+
+void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
+ int vertices, int axis,
+ struct otri *farleft, struct otri *farright)
+{
+ struct otri midtri, tri1, tri2, tri3;
+ struct otri innerleft, innerright;
+ float area;
+ int divider;
+
+ if (b->verbose > 2) {
+ printf(" Triangulating %d vertices.\n", vertices);
+ }
+ if (vertices == 2) {
+ /* The triangulation of two vertices is an edge. An edge is */
+ /* represented by two bounding triangles. */
+ maketriangle(m, b, farleft);
+ setorg(*farleft, sortarray[0]);
+ setdest(*farleft, sortarray[1]);
+ /* The apex is intentionally left NULL. */
+ maketriangle(m, b, farright);
+ setorg(*farright, sortarray[1]);
+ setdest(*farright, sortarray[0]);
+ /* The apex is intentionally left NULL. */
+ bond(*farleft, *farright);
+ lprevself(*farleft);
+ lnextself(*farright);
+ bond(*farleft, *farright);
+ lprevself(*farleft);
+ lnextself(*farright);
+ bond(*farleft, *farright);
+ if (b->verbose > 2) {
+ printf(" Creating ");
+ printtriangle(m, b, farleft);
+ printf(" Creating ");
+ printtriangle(m, b, farright);
+ }
+ /* Ensure that the origin of `farleft' is sortarray[0]. */
+ lprev(*farright, *farleft);
+ return;
+ } else if (vertices == 3) {
+ /* The triangulation of three vertices is either a triangle (with */
+ /* three bounding triangles) or two edges (with four bounding */
+ /* triangles). In either case, four triangles are created. */
+ maketriangle(m, b, &midtri);
+ maketriangle(m, b, &tri1);
+ maketriangle(m, b, &tri2);
+ maketriangle(m, b, &tri3);
+ area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
+ if (area == 0.0) {
+ /* Three collinear vertices; the triangulation is two edges. */
+ setorg(midtri, sortarray[0]);
+ setdest(midtri, sortarray[1]);
+ setorg(tri1, sortarray[1]);
+ setdest(tri1, sortarray[0]);
+ setorg(tri2, sortarray[2]);
+ setdest(tri2, sortarray[1]);
+ setorg(tri3, sortarray[1]);
+ setdest(tri3, sortarray[2]);
+ /* All apices are intentionally left NULL. */
+ bond(midtri, tri1);
+ bond(tri2, tri3);
+ lnextself(midtri);
+ lprevself(tri1);
+ lnextself(tri2);
+ lprevself(tri3);
+ bond(midtri, tri3);
+ bond(tri1, tri2);
+ lnextself(midtri);
+ lprevself(tri1);
+ lnextself(tri2);
+ lprevself(tri3);
+ bond(midtri, tri1);
+ bond(tri2, tri3);
+ /* Ensure that the origin of `farleft' is sortarray[0]. */
+ otricopy(tri1, *farleft);
+ /* Ensure that the destination of `farright' is sortarray[2]. */
+ otricopy(tri2, *farright);
+ } else {
+ /* The three vertices are not collinear; the triangulation is one */
+ /* triangle, namely `midtri'. */
+ setorg(midtri, sortarray[0]);
+ setdest(tri1, sortarray[0]);
+ setorg(tri3, sortarray[0]);
+ /* Apices of tri1, tri2, and tri3 are left NULL. */
+ if (area > 0.0) {
+ /* The vertices are in counterclockwise order. */
+ setdest(midtri, sortarray[1]);
+ setorg(tri1, sortarray[1]);
+ setdest(tri2, sortarray[1]);
+ setapex(midtri, sortarray[2]);
+ setorg(tri2, sortarray[2]);
+ setdest(tri3, sortarray[2]);
+ } else {
+ /* The vertices are in clockwise order. */
+ setdest(midtri, sortarray[2]);
+ setorg(tri1, sortarray[2]);
+ setdest(tri2, sortarray[2]);
+ setapex(midtri, sortarray[1]);
+ setorg(tri2, sortarray[1]);
+ setdest(tri3, sortarray[1]);
+ }
+ /* The topology does not depend on how the vertices are ordered. */
+ bond(midtri, tri1);
+ lnextself(midtri);
+ bond(midtri, tri2);
+ lnextself(midtri);
+ bond(midtri, tri3);
+ lprevself(tri1);
+ lnextself(tri2);
+ bond(tri1, tri2);
+ lprevself(tri1);
+ lprevself(tri3);
+ bond(tri1, tri3);
+ lnextself(tri2);
+ lprevself(tri3);
+ bond(tri2, tri3);
+ /* Ensure that the origin of `farleft' is sortarray[0]. */
+ otricopy(tri1, *farleft);
+ /* Ensure that the destination of `farright' is sortarray[2]. */
+ if (area > 0.0) {
+ otricopy(tri2, *farright);
+ } else {
+ lnext(*farleft, *farright);
+ }
+ }
+ if (b->verbose > 2) {
+ printf(" Creating ");
+ printtriangle(m, b, &midtri);
+ printf(" Creating ");
+ printtriangle(m, b, &tri1);
+ printf(" Creating ");
+ printtriangle(m, b, &tri2);
+ printf(" Creating ");
+ printtriangle(m, b, &tri3);
+ }
+ return;
+ } else {
+ /* Split the vertices in half. */
+ divider = vertices >> 1;
+ /* Recursively triangulate each half. */
+ divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
+ divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
+ &innerright, farright);
+ if (b->verbose > 1) {
+ printf(" Joining triangulations with %d and %d vertices.\n", divider,
+ vertices - divider);
+ }
+ /* Merge the two triangulations into one. */
+ mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
+ }
+}
+
+long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
+{
+ struct otri searchedge;
+ struct otri dissolveedge;
+ struct otri deadtriangle;
+ vertex markorg;
+ long hullsize;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (b->verbose) {
+ printf(" Removing ghost triangles.\n");
+ }
+ /* Find an edge on the convex hull to start point location from. */
+ lprev(*startghost, searchedge);
+ symself(searchedge);
+ m->dummytri[0] = encode(searchedge);
+ /* Remove the bounding box and count the convex hull edges. */
+ otricopy(*startghost, dissolveedge);
+ hullsize = 0;
+ do {
+ hullsize++;
+ lnext(dissolveedge, deadtriangle);
+ lprevself(dissolveedge);
+ symself(dissolveedge);
+ /* If no PSLG is involved, set the boundary markers of all the vertices */
+ /* on the convex hull. If a PSLG is used, this step is done later. */
+ if (!b->poly) {
+ /* Watch out for the case where all the input vertices are collinear. */
+ if (dissolveedge.tri != m->dummytri) {
+ org(dissolveedge, markorg);
+ if (vertexmark(markorg) == 0) {
+ setvertexmark(markorg, 1);
+ }
+ }
+ }
+ /* Remove a bounding triangle from a convex hull triangle. */
+ dissolve(dissolveedge);
+ /* Find the next bounding triangle. */
+ sym(deadtriangle, dissolveedge);
+ /* Delete the bounding triangle. */
+ triangledealloc(m, deadtriangle.tri);
+ } while (!otriequal(dissolveedge, *startghost));
+ return hullsize;
+}
+
+/*****************************************************************************/
+/* */
+/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
+/* conquer method. */
+/* */
+/* Sorts the vertices, calls a recursive procedure to triangulate them, and */
+/* removes the bounding box, setting boundary markers as appropriate. */
+/* */
+/*****************************************************************************/
+
+long divconqdelaunay(struct mesh *m, struct behavior *b)
+{
+ vertex *sortarray;
+ struct otri hullleft, hullright;
+ int divider;
+ int i, j;
+
+ if (b->verbose) {
+ printf(" Sorting vertices.\n");
+ }
+
+ /* Allocate an array of pointers to vertices for sorting. */
+ sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
+ traversalinit(&m->vertices);
+ for (i = 0; i < m->invertices; i++) {
+ sortarray[i] = vertextraverse(m);
+ }
+ /* Sort the vertices. */
+ vertexsort(sortarray, m->invertices);
+ /* Discard duplicate vertices, which can really mess up the algorithm. */
+ i = 0;
+ for (j = 1; j < m->invertices; j++) {
+ if ((sortarray[i][0] == sortarray[j][0])
+ && (sortarray[i][1] == sortarray[j][1])) {
+ if (!b->quiet) {
+ printf(
+"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
+ sortarray[j][0], sortarray[j][1]);
+ }
+ setvertextype(sortarray[j], UNDEADVERTEX);
+ m->undeads++;
+ } else {
+ i++;
+ sortarray[i] = sortarray[j];
+ }
+ }
+ i++;
+ if (b->dwyer) {
+ /* Re-sort the array of vertices to accommodate alternating cuts. */
+ divider = i >> 1;
+ if (i - divider >= 2) {
+ if (divider >= 2) {
+ alternateaxes(sortarray, divider, 1);
+ }
+ alternateaxes(&sortarray[divider], i - divider, 1);
+ }
+ }
+
+ if (b->verbose) {
+ printf(" Forming triangulation.\n");
+ }
+
+ /* Form the Delaunay triangulation. */
+ divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
+ trifree((int *) sortarray);
+
+ return removeghosts(m, b, &hullleft);
+}
+
+/** **/
+/** **/
+/********* Divide-and-conquer Delaunay triangulation ends here *********/
+
+/********* General mesh construction routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* delaunay() Form a Delaunay triangulation. */
+/* */
+/*****************************************************************************/
+
+long delaunay(struct mesh *m, struct behavior *b)
+{
+ long hulledges;
+
+ m->eextras = 0;
+ initializetrisubpools(m, b);
+
+ if (!b->quiet) {
+ printf(
+ "Constructing Delaunay triangulation by divide-and-conquer method.\n");
+ }
+ hulledges = divconqdelaunay(m, b);
+
+ if (m->triangles.items == 0) {
+ /* The input vertices were all collinear, so there are no triangles. */
+ return 0l;
+ } else {
+ return hulledges;
+ }
+}
+
+/** **/
+/** **/
+/********* General mesh construction routines end here *********/
+
+/********* Segment insertion begins here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* finddirection() Find the first triangle on the path from one point */
+/* to another. */
+/* */
+/* Finds the triangle that intersects a line segment drawn from the */
+/* origin of `searchtri' to the point `searchpoint', and returns the result */
+/* in `searchtri'. The origin of `searchtri' does not change, even though */
+/* the triangle returned may differ from the one passed in. This routine */
+/* is used to find the direction to move in to get from one point to */
+/* another. */
+/* */
+/* The return value notes whether the destination or apex of the found */
+/* triangle is collinear with the two points in question. */
+/* */
+/*****************************************************************************/
+
+enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
+ struct otri *searchtri,
+ vertex searchpoint)
+{
+ struct otri checktri;
+ vertex startvertex;
+ vertex leftvertex, rightvertex;
+ float leftccw, rightccw;
+ int leftflag, rightflag;
+ triangle ptr; /* Temporary variable used by onext() and oprev(). */
+
+ org(*searchtri, startvertex);
+ dest(*searchtri, rightvertex);
+ apex(*searchtri, leftvertex);
+ /* Is `searchpoint' to the left? */
+ leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
+ leftflag = leftccw > 0.0;
+ /* Is `searchpoint' to the right? */
+ rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
+ rightflag = rightccw > 0.0;
+ if (leftflag && rightflag) {
+ /* `searchtri' faces directly away from `searchpoint'. We could go left */
+ /* or right. Ask whether it's a triangle or a boundary on the left. */
+ onext(*searchtri, checktri);
+ if (checktri.tri == m->dummytri) {
+ leftflag = 0;
+ } else {
+ rightflag = 0;
+ }
+ }
+ while (leftflag) {
+ /* Turn left until satisfied. */
+ onextself(*searchtri);
+ if (searchtri->tri == m->dummytri) {
+ printf("Internal error in finddirection(): Unable to find a\n");
+ printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
+ startvertex[1]);
+ printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
+ internalerror();
+ }
+ apex(*searchtri, leftvertex);
+ rightccw = leftccw;
+ leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
+ leftflag = leftccw > 0.0;
+ }
+ while (rightflag) {
+ /* Turn right until satisfied. */
+ oprevself(*searchtri);
+ if (searchtri->tri == m->dummytri) {
+ printf("Internal error in finddirection(): Unable to find a\n");
+ printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
+ startvertex[1]);
+ printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
+ internalerror();
+ }
+ dest(*searchtri, rightvertex);
+ leftccw = rightccw;
+ rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
+ rightflag = rightccw > 0.0;
+ }
+ if (leftccw == 0.0) {
+ return LEFTCOLLINEAR;
+ } else if (rightccw == 0.0) {
+ return RIGHTCOLLINEAR;
+ } else {
+ return WITHIN;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* segmentintersection() Find the intersection of an existing segment */
+/* and a segment that is being inserted. Insert */
+/* a vertex at the intersection, splitting an */
+/* existing subsegment. */
+/* */
+/* The segment being inserted connects the apex of splittri to endpoint2. */
+/* splitsubseg is the subsegment being split, and MUST adjoin splittri. */
+/* Hence, endpoints of the subsegment being split are the origin and */
+/* destination of splittri. */
+/* */
+/* On completion, splittri is a handle having the newly inserted */
+/* intersection point as its origin, and endpoint1 as its destination. */
+/* */
+/*****************************************************************************/
+
+void segmentintersection(struct mesh *m, struct behavior *b,
+ struct otri *splittri, struct osub *splitsubseg,
+ vertex endpoint2)
+{
+ struct osub opposubseg;
+ vertex endpoint1;
+ vertex torg, tdest;
+ vertex leftvertex, rightvertex;
+ vertex newvertex;
+ enum insertvertexresult success;
+ enum finddirectionresult collinear;
+ float ex, ey;
+ float tx, ty;
+ float etx, ety;
+ float split, denom;
+ int i;
+ triangle ptr; /* Temporary variable used by onext(). */
+ subseg sptr; /* Temporary variable used by snext(). */
+
+ /* Find the other three segment endpoints. */
+ apex(*splittri, endpoint1);
+ org(*splittri, torg);
+ dest(*splittri, tdest);
+ /* Segment intersection formulae; see the Antonio reference. */
+ tx = tdest[0] - torg[0];
+ ty = tdest[1] - torg[1];
+ ex = endpoint2[0] - endpoint1[0];
+ ey = endpoint2[1] - endpoint1[1];
+ etx = torg[0] - endpoint2[0];
+ ety = torg[1] - endpoint2[1];
+ denom = ty * ex - tx * ey;
+ if (denom == 0.0) {
+ printf("Internal error in segmentintersection():");
+ printf(" Attempt to find intersection of parallel segments.\n");
+ internalerror();
+ }
+ split = (ey * etx - ex * ety) / denom;
+ /* Create the new vertex. */
+ newvertex = (vertex) poolalloc(&m->vertices);
+ /* Interpolate its coordinate and attributes. */
+ for (i = 0; i < 2 + m->nextras; i++) {
+ newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
+ }
+ setvertexmark(newvertex, mark(*splitsubseg));
+ setvertextype(newvertex, INPUTVERTEX);
+ if (b->verbose > 1) {
+ printf(
+ " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
+ torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
+ }
+ /* Insert the intersection vertex. This should always succeed. */
+ success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
+ if (success != SUCCESSFULVERTEX) {
+ printf("Internal error in segmentintersection():\n");
+ printf(" Failure to split a segment.\n");
+ internalerror();
+ }
+ /* Record a triangle whose origin is the new vertex. */
+ setvertex2tri(newvertex, encode(*splittri));
+ if (m->steinerleft > 0) {
+ m->steinerleft--;
+ }
+
+ /* Divide the segment into two, and correct the segment endpoints. */
+ ssymself(*splitsubseg);
+ spivot(*splitsubseg, opposubseg);
+ sdissolve(*splitsubseg);
+ sdissolve(opposubseg);
+ do {
+ setsegorg(*splitsubseg, newvertex);
+ snextself(*splitsubseg);
+ } while (splitsubseg->ss != m->dummysub);
+ do {
+ setsegorg(opposubseg, newvertex);
+ snextself(opposubseg);
+ } while (opposubseg.ss != m->dummysub);
+
+ /* Inserting the vertex may have caused edge flips. We wish to rediscover */
+ /* the edge connecting endpoint1 to the new intersection vertex. */
+ collinear = finddirection(m, b, splittri, endpoint1);
+ dest(*splittri, rightvertex);
+ apex(*splittri, leftvertex);
+ if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
+ onextself(*splittri);
+ } else if ((rightvertex[0] != endpoint1[0]) ||
+ (rightvertex[1] != endpoint1[1])) {
+ printf("Internal error in segmentintersection():\n");
+ printf(" Topological inconsistency after splitting a segment.\n");
+ internalerror();
+ }
+ /* `splittri' should have destination endpoint1. */
+}
+
+/*****************************************************************************/
+/* */
+/* scoutsegment() Scout the first triangle on the path from one endpoint */
+/* to another, and check for completion (reaching the */
+/* second endpoint), a collinear vertex, or the */
+/* intersection of two segments. */
+/* */
+/* Returns one if the entire segment is successfully inserted, and zero if */
+/* the job must be finished by conformingedge() or constrainededge(). */
+/* */
+/* If the first triangle on the path has the second endpoint as its */
+/* destination or apex, a subsegment is inserted and the job is done. */
+/* */
+/* If the first triangle on the path has a destination or apex that lies on */
+/* the segment, a subsegment is inserted connecting the first endpoint to */
+/* the collinear vertex, and the search is continued from the collinear */
+/* vertex. */
+/* */
+/* If the first triangle on the path has a subsegment opposite its origin, */
+/* then there is a segment that intersects the segment being inserted. */
+/* Their intersection vertex is inserted, splitting the subsegment. */
+/* */
+/*****************************************************************************/
+
+int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
+ vertex endpoint2, int newmark)
+{
+ struct otri crosstri;
+ struct osub crosssubseg;
+ vertex leftvertex, rightvertex;
+ enum finddirectionresult collinear;
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ collinear = finddirection(m, b, searchtri, endpoint2);
+ dest(*searchtri, rightvertex);
+ apex(*searchtri, leftvertex);
+ if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
+ ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
+ /* The segment is already an edge in the mesh. */
+ if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
+ lprevself(*searchtri);
+ }
+ /* Insert a subsegment, if there isn't already one there. */
+ insertsubseg(m, b, searchtri, newmark);
+ return 1;
+ } else if (collinear == LEFTCOLLINEAR) {
+ /* We've collided with a vertex between the segment's endpoints. */
+ /* Make the collinear vertex be the triangle's origin. */
+ lprevself(*searchtri);
+ insertsubseg(m, b, searchtri, newmark);
+ /* Insert the remainder of the segment. */
+ return scoutsegment(m, b, searchtri, endpoint2, newmark);
+ } else if (collinear == RIGHTCOLLINEAR) {
+ /* We've collided with a vertex between the segment's endpoints. */
+ insertsubseg(m, b, searchtri, newmark);
+ /* Make the collinear vertex be the triangle's origin. */
+ lnextself(*searchtri);
+ /* Insert the remainder of the segment. */
+ return scoutsegment(m, b, searchtri, endpoint2, newmark);
+ } else {
+ lnext(*searchtri, crosstri);
+ tspivot(crosstri, crosssubseg);
+ /* Check for a crossing segment. */
+ if (crosssubseg.ss == m->dummysub) {
+ return 0;
+ } else {
+ /* Insert a vertex at the intersection. */
+ segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
+ otricopy(crosstri, *searchtri);
+ insertsubseg(m, b, searchtri, newmark);
+ /* Insert the remainder of the segment. */
+ return scoutsegment(m, b, searchtri, endpoint2, newmark);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
+/* recursively from an existing vertex. Pay special */
+/* attention to stacking inverted triangles. */
+/* */
+/* This is a support routine for inserting segments into a constrained */
+/* Delaunay triangulation. */
+/* */
+/* The origin of fixuptri is treated as if it has just been inserted, and */
+/* the local Delaunay condition needs to be enforced. It is only enforced */
+/* in one sector, however, that being the angular range defined by */
+/* fixuptri. */
+/* */
+/* This routine also needs to make decisions regarding the "stacking" of */
+/* triangles. (Read the description of constrainededge() below before */
+/* reading on here, so you understand the algorithm.) If the position of */
+/* the new vertex (the origin of fixuptri) indicates that the vertex before */
+/* it on the polygon is a reflex vertex, then "stack" the triangle by */
+/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */
+/* triangles are identified.) */
+/* */
+/* Otherwise, check whether the vertex before that was a reflex vertex. */
+/* If so, perform an edge flip, thereby eliminating an inverted triangle */
+/* (popping it off the stack). The edge flip may result in the creation */
+/* of a new inverted triangle, depending on whether or not the new vertex */
+/* is visible to the vertex three edges behind on the polygon. */
+/* */
+/* If neither of the two vertices behind the new vertex are reflex */
+/* vertices, fixuptri and fartri, the triangle opposite it, are not */
+/* inverted; hence, ensure that the edge between them is locally Delaunay. */
+/* */
+/* `leftside' indicates whether or not fixuptri is to the left of the */
+/* segment being inserted. (Imagine that the segment is pointing up from */
+/* endpoint1 to endpoint2.) */
+/* */
+/*****************************************************************************/
+
+void delaunayfixup(struct mesh *m, struct behavior *b,
+ struct otri *fixuptri, int leftside)
+{
+ struct otri neartri;
+ struct otri fartri;
+ struct osub faredge;
+ vertex nearvertex, leftvertex, rightvertex, farvertex;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ lnext(*fixuptri, neartri);
+ sym(neartri, fartri);
+ /* Check if the edge opposite the origin of fixuptri can be flipped. */
+ if (fartri.tri == m->dummytri) {
+ return;
+ }
+ tspivot(neartri, faredge);
+ if (faredge.ss != m->dummysub) {
+ return;
+ }
+ /* Find all the relevant vertices. */
+ apex(neartri, nearvertex);
+ org(neartri, leftvertex);
+ dest(neartri, rightvertex);
+ apex(fartri, farvertex);
+ /* Check whether the previous polygon vertex is a reflex vertex. */
+ if (leftside) {
+ if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
+ /* leftvertex is a reflex vertex too. Nothing can */
+ /* be done until a convex section is found. */
+ return;
+ }
+ } else {
+ if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
+ /* rightvertex is a reflex vertex too. Nothing can */
+ /* be done until a convex section is found. */
+ return;
+ }
+ }
+ if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
+ /* fartri is not an inverted triangle, and farvertex is not a reflex */
+ /* vertex. As there are no reflex vertices, fixuptri isn't an */
+ /* inverted triangle, either. Hence, test the edge between the */
+ /* triangles to ensure it is locally Delaunay. */
+ if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
+ 0.0) {
+ return;
+ }
+ /* Not locally Delaunay; go on to an edge flip. */
+ } /* else fartri is inverted; remove it from the stack by flipping. */
+ flip(m, b, &neartri);
+ lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */
+ /* Recursively process the two triangles that result from the flip. */
+ delaunayfixup(m, b, fixuptri, leftside);
+ delaunayfixup(m, b, &fartri, leftside);
+}
+
+/*****************************************************************************/
+/* */
+/* constrainededge() Force a segment into a constrained Delaunay */
+/* triangulation by deleting the triangles it */
+/* intersects, and triangulating the polygons that */
+/* form on each side of it. */
+/* */
+/* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */
+/* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */
+/* boundary marker of the segment. */
+/* */
+/* To insert a segment, every triangle whose interior intersects the */
+/* segment is deleted. The union of these deleted triangles is a polygon */
+/* (which is not necessarily monotone, but is close enough), which is */
+/* divided into two polygons by the new segment. This routine's task is */
+/* to generate the Delaunay triangulation of these two polygons. */
+/* */
+/* You might think of this routine's behavior as a two-step process. The */
+/* first step is to walk from endpoint1 to endpoint2, flipping each edge */
+/* encountered. This step creates a fan of edges connected to endpoint1, */
+/* including the desired edge to endpoint2. The second step enforces the */
+/* Delaunay condition on each side of the segment in an incremental manner: */
+/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */
+/* independently on each side of the segment), each vertex is "enforced" */
+/* as if it had just been inserted, but affecting only the previous */
+/* vertices. The result is the same as if the vertices had been inserted */
+/* in the order they appear on the polygon, so the result is Delaunay. */
+/* */
+/* In truth, constrainededge() interleaves these two steps. The procedure */
+/* walks from endpoint1 to endpoint2, and each time an edge is encountered */
+/* and flipped, the newly exposed vertex (at the far end of the flipped */
+/* edge) is "enforced" upon the previously flipped edges, usually affecting */
+/* only one side of the polygon (depending upon which side of the segment */
+/* the vertex falls on). */
+/* */
+/* The algorithm is complicated by the need to handle polygons that are not */
+/* convex. Although the polygon is not necessarily monotone, it can be */
+/* triangulated in a manner similar to the stack-based algorithms for */
+/* monotone polygons. For each reflex vertex (local concavity) of the */
+/* polygon, there will be an inverted triangle formed by one of the edge */
+/* flips. (An inverted triangle is one with negative area - that is, its */
+/* vertices are arranged in clockwise order - and is best thought of as a */
+/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */
+/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */
+/* later. */
+/* */
+/* A reflex vertex is popped from the stack when a vertex is inserted that */
+/* is visible to the reflex vertex. (However, if the vertex behind the */
+/* reflex vertex is not visible to the reflex vertex, a new inverted */
+/* triangle will take its place on the stack.) These details are handled */
+/* by the delaunayfixup() routine above. */
+/* */
+/*****************************************************************************/
+
+void constrainededge(struct mesh *m, struct behavior *b,
+ struct otri *starttri, vertex endpoint2, int newmark)
+{
+ struct otri fixuptri, fixuptri2;
+ struct osub crosssubseg;
+ vertex endpoint1;
+ vertex farvertex;
+ float area;
+ int collision;
+ int done;
+ triangle ptr; /* Temporary variable used by sym() and oprev(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ org(*starttri, endpoint1);
+ lnext(*starttri, fixuptri);
+ flip(m, b, &fixuptri);
+ /* `collision' indicates whether we have found a vertex directly */
+ /* between endpoint1 and endpoint2. */
+ collision = 0;
+ done = 0;
+ do {
+ org(fixuptri, farvertex);
+ /* `farvertex' is the extreme point of the polygon we are "digging" */
+ /* to get from endpoint1 to endpoint2. */
+ if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
+ oprev(fixuptri, fixuptri2);
+ /* Enforce the Delaunay condition around endpoint2. */
+ delaunayfixup(m, b, &fixuptri, 0);
+ delaunayfixup(m, b, &fixuptri2, 1);
+ done = 1;
+ } else {
+ /* Check whether farvertex is to the left or right of the segment */
+ /* being inserted, to decide which edge of fixuptri to dig */
+ /* through next. */
+ area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
+ if (area == 0.0) {
+ /* We've collided with a vertex between endpoint1 and endpoint2. */
+ collision = 1;
+ oprev(fixuptri, fixuptri2);
+ /* Enforce the Delaunay condition around farvertex. */
+ delaunayfixup(m, b, &fixuptri, 0);
+ delaunayfixup(m, b, &fixuptri2, 1);
+ done = 1;
+ } else {
+ if (area > 0.0) { /* farvertex is to the left of the segment. */
+ oprev(fixuptri, fixuptri2);
+ /* Enforce the Delaunay condition around farvertex, on the */
+ /* left side of the segment only. */
+ delaunayfixup(m, b, &fixuptri2, 1);
+ /* Flip the edge that crosses the segment. After the edge is */
+ /* flipped, one of its endpoints is the fan vertex, and the */
+ /* destination of fixuptri is the fan vertex. */
+ lprevself(fixuptri);
+ } else { /* farvertex is to the right of the segment. */
+ delaunayfixup(m, b, &fixuptri, 0);
+ /* Flip the edge that crosses the segment. After the edge is */
+ /* flipped, one of its endpoints is the fan vertex, and the */
+ /* destination of fixuptri is the fan vertex. */
+ oprevself(fixuptri);
+ }
+ /* Check for two intersecting segments. */
+ tspivot(fixuptri, crosssubseg);
+ if (crosssubseg.ss == m->dummysub) {
+ flip(m, b, &fixuptri); /* May create inverted triangle at left. */
+ } else {
+ /* We've collided with a segment between endpoint1 and endpoint2. */
+ collision = 1;
+ /* Insert a vertex at the intersection. */
+ segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
+ done = 1;
+ }
+ }
+ }
+ } while (!done);
+ /* Insert a subsegment to make the segment permanent. */
+ insertsubseg(m, b, &fixuptri, newmark);
+ /* If there was a collision with an interceding vertex, install another */
+ /* segment connecting that vertex with endpoint2. */
+ if (collision) {
+ /* Insert the remainder of the segment. */
+ if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
+ constrainededge(m, b, &fixuptri, endpoint2, newmark);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* insertsegment() Insert a PSLG segment into a triangulation. */
+/* */
+/*****************************************************************************/
+
+void insertsegment(struct mesh *m, struct behavior *b,
+ vertex endpoint1, vertex endpoint2, int newmark)
+{
+ struct otri searchtri1, searchtri2;
+ triangle encodedtri;
+ vertex checkvertex;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (b->verbose > 1) {
+ printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
+ endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
+ }
+
+ /* Find a triangle whose origin is the segment's first endpoint. */
+ checkvertex = (vertex) NULL;
+ encodedtri = vertex2tri(endpoint1);
+ if (encodedtri != (triangle) NULL) {
+ decode(encodedtri, searchtri1);
+ org(searchtri1, checkvertex);
+ }
+ if (checkvertex != endpoint1) {
+ /* Find a boundary triangle to search from. */
+ searchtri1.tri = m->dummytri;
+ searchtri1.orient = 0;
+ symself(searchtri1);
+ /* Search for the segment's first endpoint by point location. */
+ if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
+ printf(
+ "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
+ printf(" (%.12g, %.12g) in triangulation.\n",
+ endpoint1[0], endpoint1[1]);
+ internalerror();
+ }
+ }
+ /* Remember this triangle to improve subsequent point location. */
+ otricopy(searchtri1, m->recenttri);
+ /* Scout the beginnings of a path from the first endpoint */
+ /* toward the second. */
+ if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
+ /* The segment was easily inserted. */
+ return;
+ }
+ /* The first endpoint may have changed if a collision with an intervening */
+ /* vertex on the segment occurred. */
+ org(searchtri1, endpoint1);
+
+ /* Find a triangle whose origin is the segment's second endpoint. */
+ checkvertex = (vertex) NULL;
+ encodedtri = vertex2tri(endpoint2);
+ if (encodedtri != (triangle) NULL) {
+ decode(encodedtri, searchtri2);
+ org(searchtri2, checkvertex);
+ }
+ if (checkvertex != endpoint2) {
+ /* Find a boundary triangle to search from. */
+ searchtri2.tri = m->dummytri;
+ searchtri2.orient = 0;
+ symself(searchtri2);
+ /* Search for the segment's second endpoint by point location. */
+ if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
+ printf(
+ "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
+ printf(" (%.12g, %.12g) in triangulation.\n",
+ endpoint2[0], endpoint2[1]);
+ internalerror();
+ }
+ }
+ /* Remember this triangle to improve subsequent point location. */
+ otricopy(searchtri2, m->recenttri);
+ /* Scout the beginnings of a path from the second endpoint */
+ /* toward the first. */
+ if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
+ /* The segment was easily inserted. */
+ return;
+ }
+ /* The second endpoint may have changed if a collision with an intervening */
+ /* vertex on the segment occurred. */
+ org(searchtri2, endpoint2);
+
+ /* Insert the segment directly into the triangulation. */
+ constrainededge(m, b, &searchtri1, endpoint2, newmark);
+}
+
+/*****************************************************************************/
+/* */
+/* markhull() Cover the convex hull of a triangulation with subsegments. */
+/* */
+/*****************************************************************************/
+
+void markhull(struct mesh *m, struct behavior *b)
+{
+ struct otri hulltri;
+ struct otri nexttri;
+ struct otri starttri;
+ triangle ptr; /* Temporary variable used by sym() and oprev(). */
+
+ /* Find a triangle handle on the hull. */
+ hulltri.tri = m->dummytri;
+ hulltri.orient = 0;
+ symself(hulltri);
+ /* Remember where we started so we know when to stop. */
+ otricopy(hulltri, starttri);
+ /* Go once counterclockwise around the convex hull. */
+ do {
+ /* Create a subsegment if there isn't already one here. */
+ insertsubseg(m, b, &hulltri, 1);
+ /* To find the next hull edge, go clockwise around the next vertex. */
+ lnextself(hulltri);
+ oprev(hulltri, nexttri);
+ while (nexttri.tri != m->dummytri) {
+ otricopy(nexttri, hulltri);
+ oprev(hulltri, nexttri);
+ }
+ } while (!otriequal(hulltri, starttri));
+}
+
+/*****************************************************************************/
+/* */
+/* formskeleton() Create the segments of a triangulation, including PSLG */
+/* segments and edges on the convex hull. */
+/* */
+/* The PSLG segments are read from a .poly file. The return value is the */
+/* number of segments in the file. */
+/* */
+/*****************************************************************************/
+
+void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
+ int *segmentmarkerlist, int numberofsegments)
+{
+ char polyfilename[6];
+ int index;
+ vertex endpoint1, endpoint2;
+ int segmentmarkers;
+ int end1, end2;
+ int boundmarker;
+ int i;
+
+ if (b->poly) {
+ if (!b->quiet) {
+ printf("Recovering segments in Delaunay triangulation.\n");
+ }
+ strcpy(polyfilename, "input");
+ m->insegments = numberofsegments;
+ segmentmarkers = segmentmarkerlist != (int *) NULL;
+ index = 0;
+ /* If the input vertices are collinear, there is no triangulation, */
+ /* so don't try to insert segments. */
+ if (m->triangles.items == 0) {
+ return;
+ }
+
+ /* If segments are to be inserted, compute a mapping */
+ /* from vertices to triangles. */
+ if (m->insegments > 0) {
+ makevertexmap(m, b);
+ if (b->verbose) {
+ printf(" Recovering PSLG segments.\n");
+ }
+ }
+
+ boundmarker = 0;
+ /* Read and insert the segments. */
+ for (i = 0; i < m->insegments; i++) {
+ end1 = segmentlist[index++];
+ end2 = segmentlist[index++];
+ if (segmentmarkers) {
+ boundmarker = segmentmarkerlist[i];
+ }
+ if ((end1 < b->firstnumber) ||
+ (end1 >= b->firstnumber + m->invertices)) {
+ if (!b->quiet) {
+ printf("Warning: Invalid first endpoint of segment %d in %s.\n",
+ b->firstnumber + i, polyfilename);
+ }
+ } else if ((end2 < b->firstnumber) ||
+ (end2 >= b->firstnumber + m->invertices)) {
+ if (!b->quiet) {
+ printf("Warning: Invalid second endpoint of segment %d in %s.\n",
+ b->firstnumber + i, polyfilename);
+ }
+ } else {
+ /* Find the vertices numbered `end1' and `end2'. */
+ endpoint1 = getvertex(m, b, end1);
+ endpoint2 = getvertex(m, b, end2);
+ if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
+ if (!b->quiet) {
+ printf("Warning: Endpoints of segment %d are coincident in %s.\n",
+ b->firstnumber + i, polyfilename);
+ }
+ } else {
+ insertsegment(m, b, endpoint1, endpoint2, boundmarker);
+ }
+ }
+ }
+ } else {
+ m->insegments = 0;
+ }
+ if (b->convex || !b->poly) {
+ /* Enclose the convex hull with subsegments. */
+ if (b->verbose) {
+ printf(" Enclosing convex hull with segments.\n");
+ }
+ markhull(m, b);
+ }
+}
+
+/** **/
+/** **/
+/********* Segment insertion ends here *********/
+
+/********* Carving out holes and concavities begins here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* infecthull() Virally infect all of the triangles of the convex hull */
+/* that are not protected by subsegments. Where there are */
+/* subsegments, set boundary markers as appropriate. */
+/* */
+/*****************************************************************************/
+
+void infecthull(struct mesh *m, struct behavior *b)
+{
+ struct otri hulltri;
+ struct otri nexttri;
+ struct otri starttri;
+ struct osub hullsubseg;
+ triangle **deadtriangle;
+ vertex horg, hdest;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (b->verbose) {
+ printf(" Marking concavities (external triangles) for elimination.\n");
+ }
+ /* Find a triangle handle on the hull. */
+ hulltri.tri = m->dummytri;
+ hulltri.orient = 0;
+ symself(hulltri);
+ /* Remember where we started so we know when to stop. */
+ otricopy(hulltri, starttri);
+ /* Go once counterclockwise around the convex hull. */
+ do {
+ /* Ignore triangles that are already infected. */
+ if (!infected(hulltri)) {
+ /* Is the triangle protected by a subsegment? */
+ tspivot(hulltri, hullsubseg);
+ if (hullsubseg.ss == m->dummysub) {
+ /* The triangle is not protected; infect it. */
+ if (!infected(hulltri)) {
+ infect(hulltri);
+ deadtriangle = (triangle **) poolalloc(&m->viri);
+ *deadtriangle = hulltri.tri;
+ }
+ } else {
+ /* The triangle is protected; set boundary markers if appropriate. */
+ if (mark(hullsubseg) == 0) {
+ setmark(hullsubseg, 1);
+ org(hulltri, horg);
+ dest(hulltri, hdest);
+ if (vertexmark(horg) == 0) {
+ setvertexmark(horg, 1);
+ }
+ if (vertexmark(hdest) == 0) {
+ setvertexmark(hdest, 1);
+ }
+ }
+ }
+ }
+ /* To find the next hull edge, go clockwise around the next vertex. */
+ lnextself(hulltri);
+ oprev(hulltri, nexttri);
+ while (nexttri.tri != m->dummytri) {
+ otricopy(nexttri, hulltri);
+ oprev(hulltri, nexttri);
+ }
+ } while (!otriequal(hulltri, starttri));
+}
+
+/*****************************************************************************/
+/* */
+/* plague() Spread the virus from all infected triangles to any neighbors */
+/* not protected by subsegments. Delete all infected triangles. */
+/* */
+/* This is the procedure that actually creates holes and concavities. */
+/* */
+/* This procedure operates in two phases. The first phase identifies all */
+/* the triangles that will die, and marks them as infected. They are */
+/* marked to ensure that each triangle is added to the virus pool only */
+/* once, so the procedure will terminate. */
+/* */
+/* The second phase actually eliminates the infected triangles. It also */
+/* eliminates orphaned vertices. */
+/* */
+/*****************************************************************************/
+
+void plague(struct mesh *m, struct behavior *b)
+{
+ struct otri testtri;
+ struct otri neighbor;
+ triangle **virusloop;
+ triangle **deadtriangle;
+ struct osub neighborsubseg;
+ vertex testvertex;
+ vertex norg, ndest;
+ vertex deadorg, deaddest, deadapex;
+ int killorg;
+ triangle ptr; /* Temporary variable used by sym() and onext(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (b->verbose) {
+ printf(" Marking neighbors of marked triangles.\n");
+ }
+ /* Loop through all the infected triangles, spreading the virus to */
+ /* their neighbors, then to their neighbors' neighbors. */
+ traversalinit(&m->viri);
+ virusloop = (triangle **) traverse(&m->viri);
+ while (virusloop != (triangle **) NULL) {
+ testtri.tri = *virusloop;
+ /* A triangle is marked as infected by messing with one of its pointers */
+ /* to subsegments, setting it to an illegal value. Hence, we have to */
+ /* temporarily uninfect this triangle so that we can examine its */
+ /* adjacent subsegments. */
+ uninfect(testtri);
+ if (b->verbose > 2) {
+ /* Assign the triangle an orientation for convenience in */
+ /* checking its vertices. */
+ testtri.orient = 0;
+ org(testtri, deadorg);
+ dest(testtri, deaddest);
+ apex(testtri, deadapex);
+ printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ deadorg[0], deadorg[1], deaddest[0], deaddest[1],
+ deadapex[0], deadapex[1]);
+ }
+ /* Check each of the triangle's three neighbors. */
+ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
+ /* Find the neighbor. */
+ sym(testtri, neighbor);
+ /* Check for a subsegment between the triangle and its neighbor. */
+ tspivot(testtri, neighborsubseg);
+ /* Check if the neighbor is nonexistent or already infected. */
+ if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
+ if (neighborsubseg.ss != m->dummysub) {
+ /* There is a subsegment separating the triangle from its */
+ /* neighbor, but both triangles are dying, so the subsegment */
+ /* dies too. */
+ subsegdealloc(m, neighborsubseg.ss);
+ if (neighbor.tri != m->dummytri) {
+ /* Make sure the subsegment doesn't get deallocated again */
+ /* later when the infected neighbor is visited. */
+ uninfect(neighbor);
+ tsdissolve(neighbor);
+ infect(neighbor);
+ }
+ }
+ } else { /* The neighbor exists and is not infected. */
+ if (neighborsubseg.ss == m->dummysub) {
+ /* There is no subsegment protecting the neighbor, so */
+ /* the neighbor becomes infected. */
+ if (b->verbose > 2) {
+ org(neighbor, deadorg);
+ dest(neighbor, deaddest);
+ apex(neighbor, deadapex);
+ printf(
+ " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ deadorg[0], deadorg[1], deaddest[0], deaddest[1],
+ deadapex[0], deadapex[1]);
+ }
+ infect(neighbor);
+ /* Ensure that the neighbor's neighbors will be infected. */
+ deadtriangle = (triangle **) poolalloc(&m->viri);
+ *deadtriangle = neighbor.tri;
+ } else { /* The neighbor is protected by a subsegment. */
+ /* Remove this triangle from the subsegment. */
+ stdissolve(neighborsubseg);
+ /* The subsegment becomes a boundary. Set markers accordingly. */
+ if (mark(neighborsubseg) == 0) {
+ setmark(neighborsubseg, 1);
+ }
+ org(neighbor, norg);
+ dest(neighbor, ndest);
+ if (vertexmark(norg) == 0) {
+ setvertexmark(norg, 1);
+ }
+ if (vertexmark(ndest) == 0) {
+ setvertexmark(ndest, 1);
+ }
+ }
+ }
+ }
+ /* Remark the triangle as infected, so it doesn't get added to the */
+ /* virus pool again. */
+ infect(testtri);
+ virusloop = (triangle **) traverse(&m->viri);
+ }
+
+ if (b->verbose) {
+ printf(" Deleting marked triangles.\n");
+ }
+
+ traversalinit(&m->viri);
+ virusloop = (triangle **) traverse(&m->viri);
+ while (virusloop != (triangle **) NULL) {
+ testtri.tri = *virusloop;
+
+ /* Check each of the three corners of the triangle for elimination. */
+ /* This is done by walking around each vertex, checking if it is */
+ /* still connected to at least one live triangle. */
+ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
+ org(testtri, testvertex);
+ /* Check if the vertex has already been tested. */
+ if (testvertex != (vertex) NULL) {
+ killorg = 1;
+ /* Mark the corner of the triangle as having been tested. */
+ setorg(testtri, NULL);
+ /* Walk counterclockwise about the vertex. */
+ onext(testtri, neighbor);
+ /* Stop upon reaching a boundary or the starting triangle. */
+ while ((neighbor.tri != m->dummytri) &&
+ (!otriequal(neighbor, testtri))) {
+ if (infected(neighbor)) {
+ /* Mark the corner of this triangle as having been tested. */
+ setorg(neighbor, NULL);
+ } else {
+ /* A live triangle. The vertex survives. */
+ killorg = 0;
+ }
+ /* Walk counterclockwise about the vertex. */
+ onextself(neighbor);
+ }
+ /* If we reached a boundary, we must walk clockwise as well. */
+ if (neighbor.tri == m->dummytri) {
+ /* Walk clockwise about the vertex. */
+ oprev(testtri, neighbor);
+ /* Stop upon reaching a boundary. */
+ while (neighbor.tri != m->dummytri) {
+ if (infected(neighbor)) {
+ /* Mark the corner of this triangle as having been tested. */
+ setorg(neighbor, NULL);
+ } else {
+ /* A live triangle. The vertex survives. */
+ killorg = 0;
+ }
+ /* Walk clockwise about the vertex. */
+ oprevself(neighbor);
+ }
+ }
+ if (killorg) {
+ if (b->verbose > 1) {
+ printf(" Deleting vertex (%.12g, %.12g)\n",
+ testvertex[0], testvertex[1]);
+ }
+ setvertextype(testvertex, UNDEADVERTEX);
+ m->undeads++;
+ }
+ }
+ }
+
+ /* Record changes in the number of boundary edges, and disconnect */
+ /* dead triangles from their neighbors. */
+ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
+ sym(testtri, neighbor);
+ if (neighbor.tri == m->dummytri) {
+ /* There is no neighboring triangle on this edge, so this edge */
+ /* is a boundary edge. This triangle is being deleted, so this */
+ /* boundary edge is deleted. */
+ m->hullsize--;
+ } else {
+ /* Disconnect the triangle from its neighbor. */
+ dissolve(neighbor);
+ /* There is a neighboring triangle on this edge, so this edge */
+ /* becomes a boundary edge when this triangle is deleted. */
+ m->hullsize++;
+ }
+ }
+ /* Return the dead triangle to the pool of triangles. */
+ triangledealloc(m, testtri.tri);
+ virusloop = (triangle **) traverse(&m->viri);
+ }
+ /* Empty the virus pool. */
+ poolrestart(&m->viri);
+}
+
+/*****************************************************************************/
+/* */
+/* regionplague() Spread regional attributes and/or area constraints */
+/* (from a .poly file) throughout the mesh. */
+/* */
+/* This procedure operates in two phases. The first phase spreads an */
+/* attribute and/or an area constraint through a (segment-bounded) region. */
+/* The triangles are marked to ensure that each triangle is added to the */
+/* virus pool only once, so the procedure will terminate. */
+/* */
+/* The second phase uninfects all infected triangles, returning them to */
+/* normal. */
+/* */
+/*****************************************************************************/
+
+void regionplague(struct mesh *m, struct behavior *b,
+ float attribute, float area)
+{
+ struct otri testtri;
+ struct otri neighbor;
+ triangle **virusloop;
+ triangle **regiontri;
+ struct osub neighborsubseg;
+ vertex regionorg, regiondest, regionapex;
+ triangle ptr; /* Temporary variable used by sym() and onext(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (b->verbose > 1) {
+ printf(" Marking neighbors of marked triangles.\n");
+ }
+ /* Loop through all the infected triangles, spreading the attribute */
+ /* and/or area constraint to their neighbors, then to their neighbors' */
+ /* neighbors. */
+ traversalinit(&m->viri);
+ virusloop = (triangle **) traverse(&m->viri);
+ while (virusloop != (triangle **) NULL) {
+ testtri.tri = *virusloop;
+ /* A triangle is marked as infected by messing with one of its pointers */
+ /* to subsegments, setting it to an illegal value. Hence, we have to */
+ /* temporarily uninfect this triangle so that we can examine its */
+ /* adjacent subsegments. */
+ uninfect(testtri);
+ if (b->regionattrib) {
+ /* Set an attribute. */
+ setelemattribute(testtri, m->eextras, attribute);
+ }
+ if (b->vararea) {
+ /* Set an area constraint. */
+ setareabound(testtri, area);
+ }
+ if (b->verbose > 2) {
+ /* Assign the triangle an orientation for convenience in */
+ /* checking its vertices. */
+ testtri.orient = 0;
+ org(testtri, regionorg);
+ dest(testtri, regiondest);
+ apex(testtri, regionapex);
+ printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ regionorg[0], regionorg[1], regiondest[0], regiondest[1],
+ regionapex[0], regionapex[1]);
+ }
+ /* Check each of the triangle's three neighbors. */
+ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
+ /* Find the neighbor. */
+ sym(testtri, neighbor);
+ /* Check for a subsegment between the triangle and its neighbor. */
+ tspivot(testtri, neighborsubseg);
+ /* Make sure the neighbor exists, is not already infected, and */
+ /* isn't protected by a subsegment. */
+ if ((neighbor.tri != m->dummytri) && !infected(neighbor)
+ && (neighborsubseg.ss == m->dummysub)) {
+ if (b->verbose > 2) {
+ org(neighbor, regionorg);
+ dest(neighbor, regiondest);
+ apex(neighbor, regionapex);
+ printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ regionorg[0], regionorg[1], regiondest[0], regiondest[1],
+ regionapex[0], regionapex[1]);
+ }
+ /* Infect the neighbor. */
+ infect(neighbor);
+ /* Ensure that the neighbor's neighbors will be infected. */
+ regiontri = (triangle **) poolalloc(&m->viri);
+ *regiontri = neighbor.tri;
+ }
+ }
+ /* Remark the triangle as infected, so it doesn't get added to the */
+ /* virus pool again. */
+ infect(testtri);
+ virusloop = (triangle **) traverse(&m->viri);
+ }
+
+ /* Uninfect all triangles. */
+ if (b->verbose > 1) {
+ printf(" Unmarking marked triangles.\n");
+ }
+ traversalinit(&m->viri);
+ virusloop = (triangle **) traverse(&m->viri);
+ while (virusloop != (triangle **) NULL) {
+ testtri.tri = *virusloop;
+ uninfect(testtri);
+ virusloop = (triangle **) traverse(&m->viri);
+ }
+ /* Empty the virus pool. */
+ poolrestart(&m->viri);
+}
+
+/*****************************************************************************/
+/* */
+/* carveholes() Find the holes and infect them. Find the area */
+/* constraints and infect them. Infect the convex hull. */
+/* Spread the infection and kill triangles. Spread the */
+/* area constraints. */
+/* */
+/* This routine mainly calls other routines to carry out all these */
+/* functions. */
+/* */
+/*****************************************************************************/
+
+void carveholes(struct mesh *m, struct behavior *b, float *holelist, int holes,
+ float *regionlist, int regions)
+{
+ struct otri searchtri;
+ struct otri triangleloop;
+ struct otri *regiontris;
+ triangle **holetri;
+ triangle **regiontri;
+ vertex searchorg, searchdest;
+ enum locateresult intersect;
+ int i;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (!(b->quiet || (b->noholes && b->convex))) {
+ printf("Removing unwanted triangles.\n");
+ if (b->verbose && (holes > 0)) {
+ printf(" Marking holes for elimination.\n");
+ }
+ }
+
+ if (regions > 0) {
+ /* Allocate storage for the triangles in which region points fall. */
+ regiontris = (struct otri *) trimalloc(regions *
+ (int) sizeof(struct otri));
+ } else {
+ regiontris = (struct otri *) NULL;
+ }
+
+ if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
+ /* Initialize a pool of viri to be used for holes, concavities, */
+ /* regional attributes, and/or regional area constraints. */
+ poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
+ }
+
+ if (!b->convex) {
+ /* Mark as infected any unprotected triangles on the boundary. */
+ /* This is one way by which concavities are created. */
+ infecthull(m, b);
+ }
+
+ if ((holes > 0) && !b->noholes) {
+ /* Infect each triangle in which a hole lies. */
+ for (i = 0; i < 2 * holes; i += 2) {
+ /* Ignore holes that aren't within the bounds of the mesh. */
+ if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
+ && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
+ /* Start searching from some triangle on the outer boundary. */
+ searchtri.tri = m->dummytri;
+ searchtri.orient = 0;
+ symself(searchtri);
+ /* Ensure that the hole is to the left of this boundary edge; */
+ /* otherwise, locate() will falsely report that the hole */
+ /* falls within the starting triangle. */
+ org(searchtri, searchorg);
+ dest(searchtri, searchdest);
+ if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
+ 0.0) {
+ /* Find a triangle that contains the hole. */
+ intersect = locate(m, b, &holelist[i], &searchtri);
+ if ((intersect != OUTSIDE) && (!infected(searchtri))) {
+ /* Infect the triangle. This is done by marking the triangle */
+ /* as infected and including the triangle in the virus pool. */
+ infect(searchtri);
+ holetri = (triangle **) poolalloc(&m->viri);
+ *holetri = searchtri.tri;
+ }
+ }
+ }
+ }
+ }
+
+ /* Now, we have to find all the regions BEFORE we carve the holes, because */
+ /* locate() won't work when the triangulation is no longer convex. */
+ /* (Incidentally, this is the reason why regional attributes and area */
+ /* constraints can't be used when refining a preexisting mesh, which */
+ /* might not be convex; they can only be used with a freshly */
+ /* triangulated PSLG.) */
+ if (regions > 0) {
+ /* Find the starting triangle for each region. */
+ for (i = 0; i < regions; i++) {
+ regiontris[i].tri = m->dummytri;
+ /* Ignore region points that aren't within the bounds of the mesh. */
+ if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
+ (regionlist[4 * i + 1] >= m->ymin) &&
+ (regionlist[4 * i + 1] <= m->ymax)) {
+ /* Start searching from some triangle on the outer boundary. */
+ searchtri.tri = m->dummytri;
+ searchtri.orient = 0;
+ symself(searchtri);
+ /* Ensure that the region point is to the left of this boundary */
+ /* edge; otherwise, locate() will falsely report that the */
+ /* region point falls within the starting triangle. */
+ org(searchtri, searchorg);
+ dest(searchtri, searchdest);
+ if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) >
+ 0.0) {
+ /* Find a triangle that contains the region point. */
+ intersect = locate(m, b, ®ionlist[4 * i], &searchtri);
+ if ((intersect != OUTSIDE) && (!infected(searchtri))) {
+ /* Record the triangle for processing after the */
+ /* holes have been carved. */
+ otricopy(searchtri, regiontris[i]);
+ }
+ }
+ }
+ }
+ }
+
+ if (m->viri.items > 0) {
+ /* Carve the holes and concavities. */
+ plague(m, b);
+ }
+ /* The virus pool should be empty now. */
+
+ if (regions > 0) {
+ if (!b->quiet) {
+ if (b->regionattrib) {
+ if (b->vararea) {
+ printf("Spreading regional attributes and area constraints.\n");
+ } else {
+ printf("Spreading regional attributes.\n");
+ }
+ } else {
+ printf("Spreading regional area constraints.\n");
+ }
+ }
+ if (b->regionattrib && !b->refine) {
+ /* Assign every triangle a regional attribute of zero. */
+ traversalinit(&m->triangles);
+ triangleloop.orient = 0;
+ triangleloop.tri = triangletraverse(m);
+ while (triangleloop.tri != (triangle *) NULL) {
+ setelemattribute(triangleloop, m->eextras, 0.0);
+ triangleloop.tri = triangletraverse(m);
+ }
+ }
+ for (i = 0; i < regions; i++) {
+ if (regiontris[i].tri != m->dummytri) {
+ /* Make sure the triangle under consideration still exists. */
+ /* It may have been eaten by the virus. */
+ if (!deadtri(regiontris[i].tri)) {
+ /* Put one triangle in the virus pool. */
+ infect(regiontris[i]);
+ regiontri = (triangle **) poolalloc(&m->viri);
+ *regiontri = regiontris[i].tri;
+ /* Apply one region's attribute and/or area constraint. */
+ regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]);
+ /* The virus pool should be empty now. */
+ }
+ }
+ }
+ if (b->regionattrib && !b->refine) {
+ /* Note the fact that each triangle has an additional attribute. */
+ m->eextras++;
+ }
+ }
+
+ /* Free up memory. */
+ if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
+ pooldeinit(&m->viri);
+ }
+ if (regions > 0) {
+ trifree((int *) regiontris);
+ }
+}
+
+/** **/
+/** **/
+/********* Carving out holes and concavities ends here *********/
+
+/*****************************************************************************/
+/* */
+/* highorder() Create extra nodes for quadratic subparametric elements. */
+/* */
+/*****************************************************************************/
+
+void highorder(struct mesh *m, struct behavior *b)
+{
+ struct otri triangleloop, trisym;
+ struct osub checkmark;
+ vertex newvertex;
+ vertex torg, tdest;
+ int i;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (!b->quiet) {
+ printf("Adding vertices for second-order triangles.\n");
+ }
+ /* The following line ensures that dead items in the pool of nodes */
+ /* cannot be allocated for the extra nodes associated with high */
+ /* order elements. This ensures that the primary nodes (at the */
+ /* corners of elements) will occur earlier in the output files, and */
+ /* have lower indices, than the extra nodes. */
+ m->vertices.deaditemstack = (int *) NULL;
+
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ /* To loop over the set of edges, loop over all triangles, and look at */
+ /* the three edges of each triangle. If there isn't another triangle */
+ /* adjacent to the edge, operate on the edge. If there is another */
+ /* adjacent triangle, operate on the edge only if the current triangle */
+ /* has a smaller pointer than its neighbor. This way, each edge is */
+ /* considered only once. */
+ while (triangleloop.tri != (triangle *) NULL) {
+ for (triangleloop.orient = 0; triangleloop.orient < 3;
+ triangleloop.orient++) {
+ sym(triangleloop, trisym);
+ if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
+ org(triangleloop, torg);
+ dest(triangleloop, tdest);
+ /* Create a new node in the middle of the edge. Interpolate */
+ /* its attributes. */
+ newvertex = (vertex) poolalloc(&m->vertices);
+ for (i = 0; i < 2 + m->nextras; i++) {
+ newvertex[i] = 0.5 * (torg[i] + tdest[i]);
+ }
+ /* Set the new node's marker to zero or one, depending on */
+ /* whether it lies on a boundary. */
+ setvertexmark(newvertex, trisym.tri == m->dummytri);
+ setvertextype(newvertex,
+ trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
+ if (b->usesegments) {
+ tspivot(triangleloop, checkmark);
+ /* If this edge is a segment, transfer the marker to the new node. */
+ if (checkmark.ss != m->dummysub) {
+ setvertexmark(newvertex, mark(checkmark));
+ setvertextype(newvertex, SEGMENTVERTEX);
+ }
+ }
+ if (b->verbose > 1) {
+ printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
+ }
+ /* Record the new node in the (one or two) adjacent elements. */
+ triangleloop.tri[m->highorderindex + triangleloop.orient] =
+ (triangle) newvertex;
+ if (trisym.tri != m->dummytri) {
+ trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex;
+ }
+ }
+ }
+ triangleloop.tri = triangletraverse(m);
+ }
+}
+
+/********* File I/O routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* transfernodes() Read the vertices from memory. */
+/* */
+/*****************************************************************************/
+
+void transfernodes(struct mesh *m, struct behavior *b, float *pointlist,
+ float *pointattriblist, int *pointmarkerlist,
+ int numberofpoints, int numberofpointattribs)
+{
+ vertex vertexloop;
+ float x, y;
+ int i, j;
+ int coordindex;
+ int attribindex;
+
+ m->invertices = numberofpoints;
+ m->mesh_dim = 2;
+ m->nextras = numberofpointattribs;
+ m->readnodefile = 0;
+ if (m->invertices < 3) {
+ printf("Error: Input must have at least three input vertices.\n");
+ triexit(1);
+ }
+ if (m->nextras == 0) {
+ b->weighted = 0;
+ }
+
+ initializevertexpool(m, b);
+
+ /* Read the vertices. */
+ coordindex = 0;
+ attribindex = 0;
+ for (i = 0; i < m->invertices; i++) {
+ vertexloop = (vertex) poolalloc(&m->vertices);
+ /* Read the vertex coordinates. */
+ x = vertexloop[0] = pointlist[coordindex++];
+ y = vertexloop[1] = pointlist[coordindex++];
+ /* Read the vertex attributes. */
+ for (j = 0; j < numberofpointattribs; j++) {
+ vertexloop[2 + j] = pointattriblist[attribindex++];
+ }
+ if (pointmarkerlist != (int *) NULL) {
+ /* Read a vertex marker. */
+ setvertexmark(vertexloop, pointmarkerlist[i]);
+ } else {
+ /* If no markers are specified, they default to zero. */
+ setvertexmark(vertexloop, 0);
+ }
+ setvertextype(vertexloop, INPUTVERTEX);
+ /* Determine the smallest and largest x and y coordinates. */
+ if (i == 0) {
+ m->xmin = m->xmax = x;
+ m->ymin = m->ymax = y;
+ } else {
+ m->xmin = (x < m->xmin) ? x : m->xmin;
+ m->xmax = (x > m->xmax) ? x : m->xmax;
+ m->ymin = (y < m->ymin) ? y : m->ymin;
+ m->ymax = (y > m->ymax) ? y : m->ymax;
+ }
+ }
+
+ /* Nonexistent x value used as a flag to mark circle events in sweepline */
+ /* Delaunay algorithm. */
+ m->xminextreme = 10 * m->xmin - 9 * m->xmax;
+}
+
+/*****************************************************************************/
+/* */
+/* writenodes() Number the vertices and write them to a .node file. */
+/* */
+/* To save memory, the vertex numbers are written over the boundary markers */
+/* after the vertices are written to a file. */
+/* */
+/*****************************************************************************/
+
+void writenodes(struct mesh *m, struct behavior *b, float **pointlist,
+ float **pointattriblist, int **pointmarkerlist)
+{
+ float *plist;
+ float *palist;
+ int *pmlist;
+ int coordindex;
+ int attribindex;
+ vertex vertexloop;
+ long outvertices;
+ int vertexnumber;
+ int i;
+
+ if (b->jettison) {
+ outvertices = m->vertices.items - m->undeads;
+ } else {
+ outvertices = m->vertices.items;
+ }
+
+ if (!b->quiet) {
+ printf("Writing vertices.\n");
+ }
+ /* Allocate memory for output vertices if necessary. */
+ if (*pointlist == (float *) NULL) {
+ *pointlist = (float *) trimalloc((int) (outvertices * 2 * sizeof(float)));
+ }
+ /* Allocate memory for output vertex attributes if necessary. */
+ if ((m->nextras > 0) && (*pointattriblist == (float *) NULL)) {
+ *pointattriblist = (float *) trimalloc((int) (outvertices * m->nextras *
+ sizeof(float)));
+ }
+ /* Allocate memory for output vertex markers if necessary. */
+ if (!b->nobound && (*pointmarkerlist == (int *) NULL)) {
+ *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int)));
+ }
+ plist = *pointlist;
+ palist = *pointattriblist;
+ pmlist = *pointmarkerlist;
+ coordindex = 0;
+ attribindex = 0;
+ traversalinit(&m->vertices);
+ vertexnumber = b->firstnumber;
+ vertexloop = vertextraverse(m);
+ while (vertexloop != (vertex) NULL) {
+ if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
+ /* X and y coordinates. */
+ plist[coordindex++] = vertexloop[0];
+ plist[coordindex++] = vertexloop[1];
+ /* Vertex attributes. */
+ for (i = 0; i < m->nextras; i++) {
+ palist[attribindex++] = vertexloop[2 + i];
+ }
+ if (!b->nobound) {
+ /* Copy the boundary marker. */
+ pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
+ }
+ setvertexmark(vertexloop, vertexnumber);
+ vertexnumber++;
+ }
+ vertexloop = vertextraverse(m);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* numbernodes() Number the vertices. */
+/* */
+/* Each vertex is assigned a marker equal to its number. */
+/* */
+/* Used when writenodes() is not called because no .node file is written. */
+/* */
+/*****************************************************************************/
+
+void numbernodes(struct mesh *m, struct behavior *b)
+{
+ vertex vertexloop;
+ int vertexnumber;
+
+ traversalinit(&m->vertices);
+ vertexnumber = b->firstnumber;
+ vertexloop = vertextraverse(m);
+ while (vertexloop != (vertex) NULL) {
+ setvertexmark(vertexloop, vertexnumber);
+ if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
+ vertexnumber++;
+ }
+ vertexloop = vertextraverse(m);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* writeelements() Write the triangles to an .ele file. */
+/* */
+/*****************************************************************************/
+
+void writeelements(struct mesh *m, struct behavior *b,
+ int **trianglelist, float **triangleattriblist)
+{
+ int *tlist;
+ float *talist;
+ int vertexindex;
+ int attribindex;
+ struct otri triangleloop;
+ vertex p1, p2, p3;
+ vertex mid1, mid2, mid3;
+ long elementnumber;
+ int i;
+
+ if (!b->quiet) {
+ printf("Writing triangles.\n");
+ }
+ /* Allocate memory for output triangles if necessary. */
+ if (*trianglelist == (int *) NULL) {
+ *trianglelist = (int *) trimalloc((int) (m->triangles.items *
+ ((b->order + 1) * (b->order + 2) /
+ 2) * sizeof(int)));
+ }
+ /* Allocate memory for output triangle attributes if necessary. */
+ if ((m->eextras > 0) && (*triangleattriblist == (float *) NULL)) {
+ *triangleattriblist = (float *) trimalloc((int) (m->triangles.items *
+ m->eextras *
+ sizeof(float)));
+ }
+ tlist = *trianglelist;
+ talist = *triangleattriblist;
+ vertexindex = 0;
+ attribindex = 0;
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ triangleloop.orient = 0;
+ elementnumber = b->firstnumber;
+ while (triangleloop.tri != (triangle *) NULL) {
+ org(triangleloop, p1);
+ dest(triangleloop, p2);
+ apex(triangleloop, p3);
+ if (b->order == 1) {
+ tlist[vertexindex++] = vertexmark(p1);
+ tlist[vertexindex++] = vertexmark(p2);
+ tlist[vertexindex++] = vertexmark(p3);
+ } else {
+ mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
+ mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
+ mid3 = (vertex) triangleloop.tri[m->highorderindex];
+ tlist[vertexindex++] = vertexmark(p1);
+ tlist[vertexindex++] = vertexmark(p2);
+ tlist[vertexindex++] = vertexmark(p3);
+ tlist[vertexindex++] = vertexmark(mid1);
+ tlist[vertexindex++] = vertexmark(mid2);
+ tlist[vertexindex++] = vertexmark(mid3);
+ }
+
+ for (i = 0; i < m->eextras; i++) {
+ talist[attribindex++] = elemattribute(triangleloop, i);
+ }
+ triangleloop.tri = triangletraverse(m);
+ elementnumber++;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* writepoly() Write the segments and holes to a .poly file. */
+/* */
+/*****************************************************************************/
+
+void writepoly(struct mesh *m, struct behavior *b,
+ int **segmentlist, int **segmentmarkerlist)
+{
+ int *slist;
+ int *smlist;
+ int index;
+ struct osub subsegloop;
+ vertex endpoint1, endpoint2;
+ long subsegnumber;
+
+ if (!b->quiet) {
+ printf("Writing segments.\n");
+ }
+ /* Allocate memory for output segments if necessary. */
+ if (*segmentlist == (int *) NULL) {
+ *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 *
+ sizeof(int)));
+ }
+ /* Allocate memory for output segment markers if necessary. */
+ if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) {
+ *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items *
+ sizeof(int)));
+ }
+ slist = *segmentlist;
+ smlist = *segmentmarkerlist;
+ index = 0;
+
+ traversalinit(&m->subsegs);
+ subsegloop.ss = subsegtraverse(m);
+ subsegloop.ssorient = 0;
+ subsegnumber = b->firstnumber;
+ while (subsegloop.ss != (subseg *) NULL) {
+ sorg(subsegloop, endpoint1);
+ sdest(subsegloop, endpoint2);
+ /* Copy indices of the segment's two endpoints. */
+ slist[index++] = vertexmark(endpoint1);
+ slist[index++] = vertexmark(endpoint2);
+ if (!b->nobound) {
+ /* Copy the boundary marker. */
+ smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
+ }
+ subsegloop.ss = subsegtraverse(m);
+ subsegnumber++;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* writeedges() Write the edges to an .edge file. */
+/* */
+/*****************************************************************************/
+
+void writeedges(struct mesh *m, struct behavior *b,
+ int **edgelist, int **edgemarkerlist)
+{
+ int *elist;
+ int *emlist;
+ int index;
+ struct otri triangleloop, trisym;
+ struct osub checkmark;
+ vertex p1, p2;
+ long edgenumber;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (!b->quiet) {
+ printf("Writing edges.\n");
+ }
+ /* Allocate memory for edges if necessary. */
+ if (*edgelist == (int *) NULL) {
+ *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
+ }
+ /* Allocate memory for edge markers if necessary. */
+ if (!b->nobound && (*edgemarkerlist == (int *) NULL)) {
+ *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int)));
+ }
+ elist = *edgelist;
+ emlist = *edgemarkerlist;
+ index = 0;
+
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ edgenumber = b->firstnumber;
+ /* To loop over the set of edges, loop over all triangles, and look at */
+ /* the three edges of each triangle. If there isn't another triangle */
+ /* adjacent to the edge, operate on the edge. If there is another */
+ /* adjacent triangle, operate on the edge only if the current triangle */
+ /* has a smaller pointer than its neighbor. This way, each edge is */
+ /* considered only once. */
+ while (triangleloop.tri != (triangle *) NULL) {
+ for (triangleloop.orient = 0; triangleloop.orient < 3;
+ triangleloop.orient++) {
+ sym(triangleloop, trisym);
+ if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
+ org(triangleloop, p1);
+ dest(triangleloop, p2);
+ elist[index++] = vertexmark(p1);
+ elist[index++] = vertexmark(p2);
+ if (b->nobound) {
+ } else {
+ /* Edge number, indices of two endpoints, and a boundary marker. */
+ /* If there's no subsegment, the boundary marker is zero. */
+ if (b->usesegments) {
+ tspivot(triangleloop, checkmark);
+ if (checkmark.ss == m->dummysub) {
+ emlist[edgenumber - b->firstnumber] = 0;
+ } else {
+ emlist[edgenumber - b->firstnumber] = mark(checkmark);
+ }
+ } else {
+ emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
+ }
+ }
+ edgenumber++;
+ }
+ }
+ triangleloop.tri = triangletraverse(m);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */
+/* file. */
+/* */
+/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
+/* Hence, the Voronoi vertices are listed by traversing the Delaunay */
+/* triangles, and the Voronoi edges are listed by traversing the Delaunay */
+/* edges. */
+/* */
+/* WARNING: In order to assign numbers to the Voronoi vertices, this */
+/* procedure messes up the subsegments or the extra nodes of every */
+/* element. Hence, you should call this procedure last. */
+/* */
+/*****************************************************************************/
+
+void writevoronoi(struct mesh *m, struct behavior *b, float **vpointlist,
+ float **vpointattriblist, int **vpointmarkerlist,
+ int **vedgelist, int **vedgemarkerlist, float **vnormlist)
+{
+ float *plist;
+ float *palist;
+ int *elist;
+ float *normlist;
+ int coordindex;
+ int attribindex;
+ struct otri triangleloop, trisym;
+ vertex torg, tdest, tapex;
+ float circumcenter[2];
+ float xi, eta;
+ long vnodenumber, vedgenumber;
+ int p1, p2;
+ int i;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (!b->quiet) {
+ printf("Writing Voronoi vertices.\n");
+ }
+ /* Allocate memory for Voronoi vertices if necessary. */
+ if (*vpointlist == (float *) NULL) {
+ *vpointlist = (float *) trimalloc((int) (m->triangles.items * 2 *
+ sizeof(float)));
+ }
+ /* Allocate memory for Voronoi vertex attributes if necessary. */
+ if (*vpointattriblist == (float *) NULL) {
+ *vpointattriblist = (float *) trimalloc((int) (m->triangles.items *
+ m->nextras * sizeof(float)));
+ }
+ *vpointmarkerlist = (int *) NULL;
+ plist = *vpointlist;
+ palist = *vpointattriblist;
+ coordindex = 0;
+ attribindex = 0;
+
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ triangleloop.orient = 0;
+ vnodenumber = b->firstnumber;
+ while (triangleloop.tri != (triangle *) NULL) {
+ org(triangleloop, torg);
+ dest(triangleloop, tdest);
+ apex(triangleloop, tapex);
+ findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);
+
+ /* X and y coordinates. */
+ plist[coordindex++] = circumcenter[0];
+ plist[coordindex++] = circumcenter[1];
+ for (i = 2; i < 2 + m->nextras; i++) {
+ /* Interpolate the vertex attributes at the circumcenter. */
+ palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
+ + eta * (tapex[i] - torg[i]);
+ }
+
+ * (int *) (triangleloop.tri + 6) = (int) vnodenumber;
+ triangleloop.tri = triangletraverse(m);
+ vnodenumber++;
+ }
+
+ if (!b->quiet) {
+ printf("Writing Voronoi edges.\n");
+ }
+ /* Allocate memory for output Voronoi edges if necessary. */
+ if (*vedgelist == (int *) NULL) {
+ *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
+ }
+ *vedgemarkerlist = (int *) NULL;
+ /* Allocate memory for output Voronoi norms if necessary. */
+ if (*vnormlist == (float *) NULL) {
+ *vnormlist = (float *) trimalloc((int) (m->edges * 2 * sizeof(float)));
+ }
+ elist = *vedgelist;
+ normlist = *vnormlist;
+ coordindex = 0;
+
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ vedgenumber = b->firstnumber;
+ /* To loop over the set of edges, loop over all triangles, and look at */
+ /* the three edges of each triangle. If there isn't another triangle */
+ /* adjacent to the edge, operate on the edge. If there is another */
+ /* adjacent triangle, operate on the edge only if the current triangle */
+ /* has a smaller pointer than its neighbor. This way, each edge is */
+ /* considered only once. */
+ while (triangleloop.tri != (triangle *) NULL) {
+ for (triangleloop.orient = 0; triangleloop.orient < 3;
+ triangleloop.orient++) {
+ sym(triangleloop, trisym);
+ if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
+ /* Find the number of this triangle (and Voronoi vertex). */
+ p1 = * (int *) (triangleloop.tri + 6);
+ if (trisym.tri == m->dummytri) {
+ org(triangleloop, torg);
+ dest(triangleloop, tdest);
+ /* Copy an infinite ray. Index of one endpoint, and -1. */
+ elist[coordindex] = p1;
+ normlist[coordindex++] = tdest[1] - torg[1];
+ elist[coordindex] = -1;
+ normlist[coordindex++] = torg[0] - tdest[0];
+ } else {
+ /* Find the number of the adjacent triangle (and Voronoi vertex). */
+ p2 = * (int *) (trisym.tri + 6);
+ /* Finite edge. Write indices of two endpoints. */
+ elist[coordindex] = p1;
+ normlist[coordindex++] = 0.0;
+ elist[coordindex] = p2;
+ normlist[coordindex++] = 0.0;
+ }
+ vedgenumber++;
+ }
+ }
+ triangleloop.tri = triangletraverse(m);
+ }
+}
+
+
+void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
+{
+ int *nlist;
+ int index;
+ struct otri triangleloop, trisym;
+ long elementnumber;
+ int neighbor1, neighbor2, neighbor3;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (!b->quiet) {
+ printf("Writing neighbors.\n");
+ }
+ /* Allocate memory for neighbors if necessary. */
+ if (*neighborlist == (int *) NULL) {
+ *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 *
+ sizeof(int)));
+ }
+ nlist = *neighborlist;
+ index = 0;
+
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ triangleloop.orient = 0;
+ elementnumber = b->firstnumber;
+ while (triangleloop.tri != (triangle *) NULL) {
+ * (int *) (triangleloop.tri + 6) = (int) elementnumber;
+ triangleloop.tri = triangletraverse(m);
+ elementnumber++;
+ }
+ * (int *) (m->dummytri + 6) = -1;
+
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ elementnumber = b->firstnumber;
+ while (triangleloop.tri != (triangle *) NULL) {
+ triangleloop.orient = 1;
+ sym(triangleloop, trisym);
+ neighbor1 = * (int *) (trisym.tri + 6);
+ triangleloop.orient = 2;
+ sym(triangleloop, trisym);
+ neighbor2 = * (int *) (trisym.tri + 6);
+ triangleloop.orient = 0;
+ sym(triangleloop, trisym);
+ neighbor3 = * (int *) (trisym.tri + 6);
+ nlist[index++] = neighbor1;
+ nlist[index++] = neighbor2;
+ nlist[index++] = neighbor3;
+
+ triangleloop.tri = triangletraverse(m);
+ elementnumber++;
+ }
+}
+
+/** **/
+/** **/
+/********* File I/O routines end here *********/
+
+/*****************************************************************************/
+/* */
+/* quality_statistics() Print statistics about the quality of the mesh. */
+/* */
+/*****************************************************************************/
+
+void quality_statistics(struct mesh *m, struct behavior *b)
+{
+ struct otri triangleloop;
+ vertex p[3];
+ float cossquaretable[8];
+ float ratiotable[16];
+ float dx[3], dy[3];
+ float edgelength[3];
+ float dotproduct;
+ float cossquare;
+ float triarea;
+ float shortest, longest;
+ float trilongest2;
+ float smallestarea, biggestarea;
+ float triminaltitude2;
+ float minaltitude;
+ float triaspect2;
+ float worstaspect;
+ float smallestangle, biggestangle;
+ float radconst, degconst;
+ int angletable[18];
+ int aspecttable[16];
+ int aspectindex;
+ int tendegree;
+ int acutebiggest;
+ int i, ii, j, k;
+
+ printf("Mesh quality statistics:\n\n");
+ radconst = PI / 18.0;
+ degconst = 180.0 / PI;
+ for (i = 0; i < 8; i++) {
+ cossquaretable[i] = cos(radconst * (float) (i + 1));
+ cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
+ }
+ for (i = 0; i < 18; i++) {
+ angletable[i] = 0;
+ }
+
+ ratiotable[0] = 1.5; ratiotable[1] = 2.0;
+ ratiotable[2] = 2.5; ratiotable[3] = 3.0;
+ ratiotable[4] = 4.0; ratiotable[5] = 6.0;
+ ratiotable[6] = 10.0; ratiotable[7] = 15.0;
+ ratiotable[8] = 25.0; ratiotable[9] = 50.0;
+ ratiotable[10] = 100.0; ratiotable[11] = 300.0;
+ ratiotable[12] = 1000.0; ratiotable[13] = 10000.0;
+ ratiotable[14] = 100000.0; ratiotable[15] = 0.0;
+ for (i = 0; i < 16; i++) {
+ aspecttable[i] = 0;
+ }
+
+ worstaspect = 0.0;
+ minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
+ minaltitude = minaltitude * minaltitude;
+ shortest = minaltitude;
+ longest = 0.0;
+ smallestarea = minaltitude;
+ biggestarea = 0.0;
+ worstaspect = 0.0;
+ smallestangle = 0.0;
+ biggestangle = 2.0;
+ acutebiggest = 1;
+
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ triangleloop.orient = 0;
+ while (triangleloop.tri != (triangle *) NULL) {
+ org(triangleloop, p[0]);
+ dest(triangleloop, p[1]);
+ apex(triangleloop, p[2]);
+ trilongest2 = 0.0;
+
+ for (i = 0; i < 3; i++) {
+ j = plus1mod3[i];
+ k = minus1mod3[i];
+ dx[i] = p[j][0] - p[k][0];
+ dy[i] = p[j][1] - p[k][1];
+ edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
+ if (edgelength[i] > trilongest2) {
+ trilongest2 = edgelength[i];
+ }
+ if (edgelength[i] > longest) {
+ longest = edgelength[i];
+ }
+ if (edgelength[i] < shortest) {
+ shortest = edgelength[i];
+ }
+ }
+
+ triarea = counterclockwise(m, b, p[0], p[1], p[2]);
+ if (triarea < smallestarea) {
+ smallestarea = triarea;
+ }
+ if (triarea > biggestarea) {
+ biggestarea = triarea;
+ }
+ triminaltitude2 = triarea * triarea / trilongest2;
+ if (triminaltitude2 < minaltitude) {
+ minaltitude = triminaltitude2;
+ }
+ triaspect2 = trilongest2 / triminaltitude2;
+ if (triaspect2 > worstaspect) {
+ worstaspect = triaspect2;
+ }
+ aspectindex = 0;
+ while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
+ && (aspectindex < 15)) {
+ aspectindex++;
+ }
+ aspecttable[aspectindex]++;
+
+ for (i = 0; i < 3; i++) {
+ j = plus1mod3[i];
+ k = minus1mod3[i];
+ dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
+ cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
+ tendegree = 8;
+ for (ii = 7; ii >= 0; ii--) {
+ if (cossquare > cossquaretable[ii]) {
+ tendegree = ii;
+ }
+ }
+ if (dotproduct <= 0.0) {
+ angletable[tendegree]++;
+ if (cossquare > smallestangle) {
+ smallestangle = cossquare;
+ }
+ if (acutebiggest && (cossquare < biggestangle)) {
+ biggestangle = cossquare;
+ }
+ } else {
+ angletable[17 - tendegree]++;
+ if (acutebiggest || (cossquare > biggestangle)) {
+ biggestangle = cossquare;
+ acutebiggest = 0;
+ }
+ }
+ }
+ triangleloop.tri = triangletraverse(m);
+ }
+
+ shortest = sqrt(shortest);
+ longest = sqrt(longest);
+ minaltitude = sqrt(minaltitude);
+ worstaspect = sqrt(worstaspect);
+ smallestarea *= 0.5;
+ biggestarea *= 0.5;
+ if (smallestangle >= 1.0) {
+ smallestangle = 0.0;
+ } else {
+ smallestangle = degconst * acos(sqrt(smallestangle));
+ }
+ if (biggestangle >= 1.0) {
+ biggestangle = 180.0;
+ } else {
+ if (acutebiggest) {
+ biggestangle = degconst * acos(sqrt(biggestangle));
+ } else {
+ biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
+ }
+ }
+
+ printf(" Smallest area: %16.5g | Largest area: %16.5g\n",
+ smallestarea, biggestarea);
+ printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n",
+ shortest, longest);
+ printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n",
+ minaltitude, worstaspect);
+
+ printf(" Triangle aspect ratio histogram:\n");
+ printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
+ ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
+ aspecttable[8]);
+ for (i = 1; i < 7; i++) {
+ printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
+ ratiotable[i - 1], ratiotable[i], aspecttable[i],
+ ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
+ }
+ printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n",
+ ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
+ aspecttable[15]);
+ printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n");
+
+ printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n",
+ smallestangle, biggestangle);
+
+ printf(" Angle histogram:\n");
+ for (i = 0; i < 9; i++) {
+ printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
+ i * 10, i * 10 + 10, angletable[i],
+ i * 10 + 90, i * 10 + 100, angletable[i + 9]);
+ }
+ printf("\n");
+}
+
+/*****************************************************************************/
+/* */
+/* statistics() Print all sorts of cool facts. */
+/* */
+/*****************************************************************************/
+
+void statistics(struct mesh *m, struct behavior *b)
+{
+ printf("\nStatistics:\n\n");
+ printf(" Input vertices: %d\n", m->invertices);
+ if (b->refine) {
+ printf(" Input triangles: %d\n", m->inelements);
+ }
+ if (b->poly) {
+ printf(" Input segments: %d\n", m->insegments);
+ if (!b->refine) {
+ printf(" Input holes: %d\n", m->holes);
+ }
+ }
+
+ printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads);
+ printf(" Mesh triangles: %ld\n", m->triangles.items);
+ printf(" Mesh edges: %ld\n", m->edges);
+ printf(" Mesh exterior boundary edges: %ld\n", m->hullsize);
+ if (b->poly || b->refine) {
+ printf(" Mesh interior boundary edges: %ld\n",
+ m->subsegs.items - m->hullsize);
+ printf(" Mesh subsegments (constrained edges): %ld\n",
+ m->subsegs.items);
+ }
+ printf("\n");
+
+ if (b->verbose) {
+ quality_statistics(m, b);
+ printf("Memory allocation statistics:\n\n");
+ printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems);
+ printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems);
+ if (m->subsegs.maxitems > 0) {
+ printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
+ }
+ if (m->viri.maxitems > 0) {
+ printf(" Maximum number of viri: %ld\n", m->viri.maxitems);
+ }
+ if (m->badsubsegs.maxitems > 0) {
+ printf(" Maximum number of encroached subsegments: %ld\n",
+ m->badsubsegs.maxitems);
+ }
+ if (m->badtriangles.maxitems > 0) {
+ printf(" Maximum number of bad triangles: %ld\n",
+ m->badtriangles.maxitems);
+ }
+ if (m->flipstackers.maxitems > 0) {
+ printf(" Maximum number of stacked triangle flips: %ld\n",
+ m->flipstackers.maxitems);
+ }
+ if (m->splaynodes.maxitems > 0) {
+ printf(" Maximum number of splay tree nodes: %ld\n",
+ m->splaynodes.maxitems);
+ }
+ printf(" Approximate heap memory use (bytes): %ld\n\n",
+ m->vertices.maxitems * m->vertices.itembytes +
+ m->triangles.maxitems * m->triangles.itembytes +
+ m->subsegs.maxitems * m->subsegs.itembytes +
+ m->viri.maxitems * m->viri.itembytes +
+ m->badsubsegs.maxitems * m->badsubsegs.itembytes +
+ m->badtriangles.maxitems * m->badtriangles.itembytes +
+ m->flipstackers.maxitems * m->flipstackers.itembytes +
+ m->splaynodes.maxitems * m->splaynodes.itembytes);
+
+ printf("Algorithmic statistics:\n\n");
+ if (!b->weighted) {
+ printf(" Number of incircle tests: %ld\n", m->incirclecount);
+ } else {
+ printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount);
+ }
+ printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount);
+ if (m->hyperbolacount > 0) {
+ printf(" Number of right-of-hyperbola tests: %ld\n",
+ m->hyperbolacount);
+ }
+ if (m->circletopcount > 0) {
+ printf(" Number of circle top computations: %ld\n",
+ m->circletopcount);
+ }
+ if (m->circumcentercount > 0) {
+ printf(" Number of triangle circumcenter computations: %ld\n",
+ m->circumcentercount);
+ }
+ printf("\n");
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* main() or triangulate() Gosh, do everything. */
+/* */
+/* The sequence is roughly as follows. Many of these steps can be skipped, */
+/* depending on the command line switches. */
+/* */
+/* - Initialize constants and parse the command line. */
+/* - Read the vertices from a file and either */
+/* - triangulate them (no -r), or */
+/* - read an old mesh from files and reconstruct it (-r). */
+/* - Insert the PSLG segments (-p), and possibly segments on the convex */
+/* hull (-c). */
+/* - Read the holes (-p), regional attributes (-pA), and regional area */
+/* constraints (-pa). Carve the holes and concavities, and spread the */
+/* regional attributes and area constraints. */
+/* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */
+/* Also enforce the conforming Delaunay property (-q and -a). */
+/* - Compute the number of edges in the resulting mesh. */
+/* - Promote the mesh's linear triangles to higher order elements (-o). */
+/* - Write the output files and print the statistics. */
+/* - Check the consistency and Delaunay property of the mesh (-C). */
+/* */
+/*****************************************************************************/
+
+void triangulate(char *triswitches, struct triangulateio *in,
+ struct triangulateio *out, struct triangulateio *vorout)
+{
+ struct mesh m;
+ struct behavior b;
+ float *holearray; /* Array of holes. */
+ float *regionarray; /* Array of regional attributes and area constraints. */
+
+ triangleinit(&m);
+ parsecommandline(1, &triswitches, &b);
+ m.steinerleft = b.steiner;
+
+ transfernodes(&m, &b, in->pointlist, in->pointattributelist,
+ in->pointmarkerlist, in->numberofpoints,
+ in->numberofpointattributes);
+
+ m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
+ /* Ensure that no vertex can be mistaken for a triangular bounding */
+ /* box vertex in insertvertex(). */
+ m.infvertex1 = (vertex) NULL;
+ m.infvertex2 = (vertex) NULL;
+ m.infvertex3 = (vertex) NULL;
+
+ if (b.usesegments) {
+ m.checksegments = 1; /* Segments will be introduced next. */
+ if (!b.refine) {
+ /* Insert PSLG segments and/or convex hull segments. */
+ formskeleton(&m, &b, in->segmentlist,
+ in->segmentmarkerlist, in->numberofsegments);
+ }
+ }
+
+ if (b.poly && (m.triangles.items > 0)) {
+ holearray = in->holelist;
+ m.holes = in->numberofholes;
+ regionarray = in->regionlist;
+ m.regions = in->numberofregions;
+ if (!b.refine) {
+ /* Carve out holes and concavities. */
+ carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
+ }
+ } else {
+ /* Without a PSLG, there can be no holes or regional attributes */
+ /* or area constraints. The following are set to zero to avoid */
+ /* an accidental free() later. */
+ m.holes = 0;
+ m.regions = 0;
+ }
+
+ /* Calculate the number of edges. */
+ m.edges = (3l * m.triangles.items + m.hullsize) / 2l;
+
+ if (b.order > 1) {
+ highorder(&m, &b); /* Promote elements to higher polynomial order. */
+ }
+ if (!b.quiet) {
+ printf("\n");
+ }
+
+ if (b.jettison) {
+ out->numberofpoints = m.vertices.items - m.undeads;
+ } else {
+ out->numberofpoints = m.vertices.items;
+ }
+ out->numberofpointattributes = m.nextras;
+ out->numberoftriangles = m.triangles.items;
+ out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
+ out->numberoftriangleattributes = m.eextras;
+ out->numberofedges = m.edges;
+ if (b.usesegments) {
+ out->numberofsegments = m.subsegs.items;
+ } else {
+ out->numberofsegments = m.hullsize;
+ }
+ if (vorout != (struct triangulateio *) NULL) {
+ vorout->numberofpoints = m.triangles.items;
+ vorout->numberofpointattributes = m.nextras;
+ vorout->numberofedges = m.edges;
+ }
+ /* If not using iteration numbers, don't write a .node file if one was */
+ /* read, because the original one would be overwritten! */
+ if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
+ if (!b.quiet) {
+ printf("NOT writing vertices.\n");
+ }
+ numbernodes(&m, &b); /* We must remember to number the vertices. */
+ } else {
+ /* writenodes() numbers the vertices too. */
+ writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
+ &out->pointmarkerlist);
+ }
+ if (b.noelewritten) {
+ if (!b.quiet) {
+ printf("NOT writing triangles.\n");
+ }
+ } else {
+ writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
+ }
+ /* The -c switch (convex switch) causes a PSLG to be written */
+ /* even if none was read. */
+ if (b.poly || b.convex) {
+ /* If not using iteration numbers, don't overwrite the .poly file. */
+ if (b.nopolywritten || b.noiterationnum) {
+ if (!b.quiet) {
+ printf("NOT writing segments.\n");
+ }
+ } else {
+ writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
+ out->numberofholes = m.holes;
+ out->numberofregions = m.regions;
+ if (b.poly) {
+ out->holelist = in->holelist;
+ out->regionlist = in->regionlist;
+ } else {
+ out->holelist = (float *) NULL;
+ out->regionlist = (float *) NULL;
+ }
+ }
+ }
+ if (b.edgesout) {
+ writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
+ }
+ if (b.voronoi) {
+ writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
+ &vorout->pointmarkerlist, &vorout->edgelist,
+ &vorout->edgemarkerlist, &vorout->normlist);
+ }
+ if (b.neighbors) {
+ writeneighbors(&m, &b, &out->neighborlist);
+ }
+
+ if (!b.quiet) {
+ statistics(&m, &b);
+ }
+
+ triangledeinit(&m, &b);
+}
diff --git a/cv-node/lib/elas/triangle.h b/cv-node/lib/elas/triangle.h
new file mode 100644
index 0000000000000000000000000000000000000000..654dd5c5ff289299b1cf644ea71689470b319449
--- /dev/null
+++ b/cv-node/lib/elas/triangle.h
@@ -0,0 +1,285 @@
+/*****************************************************************************/
+/* */
+/* (triangle.h) */
+/* */
+/* Include file for programs that call Triangle. */
+/* */
+/* Accompanies Triangle Version 1.6 */
+/* July 28, 2005 */
+/* */
+/* Copyright 1996, 2005 */
+/* Jonathan Richard Shewchuk */
+/* 2360 Woolsey #H */
+/* Berkeley, California 94705-1927 */
+/* jrs@cs.berkeley.edu */
+/* */
+/* Modified by Andreas Geiger, 2011 */
+/*****************************************************************************/
+
+/*****************************************************************************/
+/* */
+/* How to call Triangle from another program */
+/* */
+/* */
+/* If you haven't read Triangle's instructions (run "triangle -h" to read */
+/* them), you won't understand what follows. */
+/* */
+/* Triangle must be compiled into an object file (triangle.o) with the */
+/* TRILIBRARY symbol defined (generally by using the -DTRILIBRARY compiler */
+/* switch). The makefile included with Triangle will do this for you if */
+/* you run "make trilibrary". The resulting object file can be called via */
+/* the procedure triangulate(). */
+/* */
+/* If the size of the object file is important to you, you may wish to */
+/* generate a reduced version of triangle.o. The REDUCED symbol gets rid */
+/* of all features that are primarily of research interest. Specifically, */
+/* the -DREDUCED switch eliminates Triangle's -i, -F, -s, and -C switches. */
+/* The CDT_ONLY symbol gets rid of all meshing algorithms above and beyond */
+/* constrained Delaunay triangulation. Specifically, the -DCDT_ONLY switch */
+/* eliminates Triangle's -r, -q, -a, -u, -D, -Y, -S, and -s switches. */
+/* */
+/* IMPORTANT: These definitions (TRILIBRARY, REDUCED, CDT_ONLY) must be */
+/* made in the makefile or in triangle.c itself. Putting these definitions */
+/* in this file (triangle.h) will not create the desired effect. */
+/* */
+/* */
+/* The calling convention for triangulate() follows. */
+/* */
+/* void triangulate(triswitches, in, out, vorout) */
+/* char *triswitches; */
+/* struct triangulateio *in; */
+/* struct triangulateio *out; */
+/* struct triangulateio *vorout; */
+/* */
+/* `triswitches' is a string containing the command line switches you wish */
+/* to invoke. No initial dash is required. Some suggestions: */
+/* */
+/* - You'll probably find it convenient to use the `z' switch so that */
+/* points (and other items) are numbered from zero. This simplifies */
+/* indexing, because the first item of any type always starts at index */
+/* [0] of the corresponding array, whether that item's number is zero or */
+/* one. */
+/* - You'll probably want to use the `Q' (quiet) switch in your final code, */
+/* but you can take advantage of Triangle's printed output (including the */
+/* `V' switch) while debugging. */
+/* - If you are not using the `q', `a', `u', `D', `j', or `s' switches, */
+/* then the output points will be identical to the input points, except */
+/* possibly for the boundary markers. If you don't need the boundary */
+/* markers, you should use the `N' (no nodes output) switch to save */
+/* memory. (If you do need boundary markers, but need to save memory, a */
+/* good nasty trick is to set out->pointlist equal to in->pointlist */
+/* before calling triangulate(), so that Triangle overwrites the input */
+/* points with identical copies.) */
+/* - The `I' (no iteration numbers) and `g' (.off file output) switches */
+/* have no effect when Triangle is compiled with TRILIBRARY defined. */
+/* */
+/* `in', `out', and `vorout' are descriptions of the input, the output, */
+/* and the Voronoi output. If the `v' (Voronoi output) switch is not used, */
+/* `vorout' may be NULL. `in' and `out' may never be NULL. */
+/* */
+/* Certain fields of the input and output structures must be initialized, */
+/* as described below. */
+/* */
+/*****************************************************************************/
+
+/*****************************************************************************/
+/* */
+/* The `triangulateio' structure. */
+/* */
+/* Used to pass data into and out of the triangulate() procedure. */
+/* */
+/* */
+/* Arrays are used to store points, triangles, markers, and so forth. In */
+/* all cases, the first item in any array is stored starting at index [0]. */
+/* However, that item is item number `1' unless the `z' switch is used, in */
+/* which case it is item number `0'. Hence, you may find it easier to */
+/* index points (and triangles in the neighbor list) if you use the `z' */
+/* switch. Unless, of course, you're calling Triangle from a Fortran */
+/* program. */
+/* */
+/* Description of fields (except the `numberof' fields, which are obvious): */
+/* */
+/* `pointlist': An array of point coordinates. The first point's x */
+/* coordinate is at index [0] and its y coordinate at index [1], followed */
+/* by the coordinates of the remaining points. Each point occupies two */
+/* REALs. */
+/* `pointattributelist': An array of point attributes. Each point's */
+/* attributes occupy `numberofpointattributes' REALs. */
+/* `pointmarkerlist': An array of point markers; one int per point. */
+/* */
+/* `trianglelist': An array of triangle corners. The first triangle's */
+/* first corner is at index [0], followed by its other two corners in */
+/* counterclockwise order, followed by any other nodes if the triangle */
+/* represents a nonlinear element. Each triangle occupies */
+/* `numberofcorners' ints. */
+/* `triangleattributelist': An array of triangle attributes. Each */
+/* triangle's attributes occupy `numberoftriangleattributes' REALs. */
+/* `trianglearealist': An array of triangle area constraints; one REAL per */
+/* triangle. Input only. */
+/* `neighborlist': An array of triangle neighbors; three ints per */
+/* triangle. Output only. */
+/* */
+/* `segmentlist': An array of segment endpoints. The first segment's */
+/* endpoints are at indices [0] and [1], followed by the remaining */
+/* segments. Two ints per segment. */
+/* `segmentmarkerlist': An array of segment markers; one int per segment. */
+/* */
+/* `holelist': An array of holes. The first hole's x and y coordinates */
+/* are at indices [0] and [1], followed by the remaining holes. Two */
+/* REALs per hole. Input only, although the pointer is copied to the */
+/* output structure for your convenience. */
+/* */
+/* `regionlist': An array of regional attributes and area constraints. */
+/* The first constraint's x and y coordinates are at indices [0] and [1], */
+/* followed by the regional attribute at index [2], followed by the */
+/* maximum area at index [3], followed by the remaining area constraints. */
+/* Four REALs per area constraint. Note that each regional attribute is */
+/* used only if you select the `A' switch, and each area constraint is */
+/* used only if you select the `a' switch (with no number following), but */
+/* omitting one of these switches does not change the memory layout. */
+/* Input only, although the pointer is copied to the output structure for */
+/* your convenience. */
+/* */
+/* `edgelist': An array of edge endpoints. The first edge's endpoints are */
+/* at indices [0] and [1], followed by the remaining edges. Two ints per */
+/* edge. Output only. */
+/* `edgemarkerlist': An array of edge markers; one int per edge. Output */
+/* only. */
+/* `normlist': An array of normal vectors, used for infinite rays in */
+/* Voronoi diagrams. The first normal vector's x and y magnitudes are */
+/* at indices [0] and [1], followed by the remaining vectors. For each */
+/* finite edge in a Voronoi diagram, the normal vector written is the */
+/* zero vector. Two REALs per edge. Output only. */
+/* */
+/* */
+/* Any input fields that Triangle will examine must be initialized. */
+/* Furthermore, for each output array that Triangle will write to, you */
+/* must either provide space by setting the appropriate pointer to point */
+/* to the space you want the data written to, or you must initialize the */
+/* pointer to NULL, which tells Triangle to allocate space for the results. */
+/* The latter option is preferable, because Triangle always knows exactly */
+/* how much space to allocate. The former option is provided mainly for */
+/* people who need to call Triangle from Fortran code, though it also makes */
+/* possible some nasty space-saving tricks, like writing the output to the */
+/* same arrays as the input. */
+/* */
+/* Triangle will not free() any input or output arrays, including those it */
+/* allocates itself; that's up to you. You should free arrays allocated by */
+/* Triangle by calling the trifree() procedure defined below. (By default, */
+/* trifree() just calls the standard free() library procedure, but */
+/* applications that call triangulate() may replace trimalloc() and */
+/* trifree() in triangle.c to use specialized memory allocators.) */
+/* */
+/* Here's a guide to help you decide which fields you must initialize */
+/* before you call triangulate(). */
+/* */
+/* `in': */
+/* */
+/* - `pointlist' must always point to a list of points; `numberofpoints' */
+/* and `numberofpointattributes' must be properly set. */
+/* `pointmarkerlist' must either be set to NULL (in which case all */
+/* markers default to zero), or must point to a list of markers. If */
+/* `numberofpointattributes' is not zero, `pointattributelist' must */
+/* point to a list of point attributes. */
+/* - If the `r' switch is used, `trianglelist' must point to a list of */
+/* triangles, and `numberoftriangles', `numberofcorners', and */
+/* `numberoftriangleattributes' must be properly set. If */
+/* `numberoftriangleattributes' is not zero, `triangleattributelist' */
+/* must point to a list of triangle attributes. If the `a' switch is */
+/* used (with no number following), `trianglearealist' must point to a */
+/* list of triangle area constraints. `neighborlist' may be ignored. */
+/* - If the `p' switch is used, `segmentlist' must point to a list of */
+/* segments, `numberofsegments' must be properly set, and */
+/* `segmentmarkerlist' must either be set to NULL (in which case all */
+/* markers default to zero), or must point to a list of markers. */
+/* - If the `p' switch is used without the `r' switch, then */
+/* `numberofholes' and `numberofregions' must be properly set. If */
+/* `numberofholes' is not zero, `holelist' must point to a list of */
+/* holes. If `numberofregions' is not zero, `regionlist' must point to */
+/* a list of region constraints. */
+/* - If the `p' switch is used, `holelist', `numberofholes', */
+/* `regionlist', and `numberofregions' is copied to `out'. (You can */
+/* nonetheless get away with not initializing them if the `r' switch is */
+/* used.) */
+/* - `edgelist', `edgemarkerlist', `normlist', and `numberofedges' may be */
+/* ignored. */
+/* */
+/* `out': */
+/* */
+/* - `pointlist' must be initialized (NULL or pointing to memory) unless */
+/* the `N' switch is used. `pointmarkerlist' must be initialized */
+/* unless the `N' or `B' switch is used. If `N' is not used and */
+/* `in->numberofpointattributes' is not zero, `pointattributelist' must */
+/* be initialized. */
+/* - `trianglelist' must be initialized unless the `E' switch is used. */
+/* `neighborlist' must be initialized if the `n' switch is used. If */
+/* the `E' switch is not used and (`in->numberofelementattributes' is */
+/* not zero or the `A' switch is used), `elementattributelist' must be */
+/* initialized. `trianglearealist' may be ignored. */
+/* - `segmentlist' must be initialized if the `p' or `c' switch is used, */
+/* and the `P' switch is not used. `segmentmarkerlist' must also be */
+/* initialized under these circumstances unless the `B' switch is used. */
+/* - `edgelist' must be initialized if the `e' switch is used. */
+/* `edgemarkerlist' must be initialized if the `e' switch is used and */
+/* the `B' switch is not. */
+/* - `holelist', `regionlist', `normlist', and all scalars may be ignored.*/
+/* */
+/* `vorout' (only needed if `v' switch is used): */
+/* */
+/* - `pointlist' must be initialized. If `in->numberofpointattributes' */
+/* is not zero, `pointattributelist' must be initialized. */
+/* `pointmarkerlist' may be ignored. */
+/* - `edgelist' and `normlist' must both be initialized. */
+/* `edgemarkerlist' may be ignored. */
+/* - Everything else may be ignored. */
+/* */
+/* After a call to triangulate(), the valid fields of `out' and `vorout' */
+/* will depend, in an obvious way, on the choice of switches used. Note */
+/* that when the `p' switch is used, the pointers `holelist' and */
+/* `regionlist' are copied from `in' to `out', but no new space is */
+/* allocated; be careful that you don't free() the same array twice. On */
+/* the other hand, Triangle will never copy the `pointlist' pointer (or any */
+/* others); new space is allocated for `out->pointlist', or if the `N' */
+/* switch is used, `out->pointlist' remains uninitialized. */
+/* */
+/* All of the meaningful `numberof' fields will be properly set; for */
+/* instance, `numberofedges' will represent the number of edges in the */
+/* triangulation whether or not the edges were written. If segments are */
+/* not used, `numberofsegments' will indicate the number of boundary edges. */
+/* */
+/*****************************************************************************/
+
+struct triangulateio {
+ float *pointlist; /* In / out */
+ float *pointattributelist; /* In / out */
+ int *pointmarkerlist; /* In / out */
+ int numberofpoints; /* In / out */
+ int numberofpointattributes; /* In / out */
+
+ int *trianglelist; /* In / out */
+ float *triangleattributelist; /* In / out */
+ float *trianglearealist; /* In only */
+ int *neighborlist; /* Out only */
+ int numberoftriangles; /* In / out */
+ int numberofcorners; /* In / out */
+ int numberoftriangleattributes; /* In / out */
+
+ int *segmentlist; /* In / out */
+ int *segmentmarkerlist; /* In / out */
+ int numberofsegments; /* In / out */
+
+ float *holelist; /* In / pointer to array copied out */
+ int numberofholes; /* In / copied out */
+
+ float *regionlist; /* In / pointer to array copied out */
+ int numberofregions; /* In / copied out */
+
+ int *edgelist; /* Out only */
+ int *edgemarkerlist; /* Not used with Voronoi diagram; out only */
+ float *normlist; /* Used only with Voronoi diagram; out only */
+ int numberofedges; /* Out only */
+};
+
+void triangulate(char *,triangulateio *,triangulateio *,triangulateio *);
+void trifree(int *memptr);
+