1551 lines
41 KiB
C++
1551 lines
41 KiB
C++
//Copyright (C) 2011 by Ivan Fratric
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//
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//Permission is hereby granted, free of charge, to any person obtaining a copy
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//of this software and associated documentation files (the "Software"), to deal
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//in the Software without restriction, including without limitation the rights
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//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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//copies of the Software, and to permit persons to whom the Software is
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//furnished to do so, subject to the following conditions:
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//
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//The above copyright notice and this permission notice shall be included in
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//all copies or substantial portions of the Software.
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//
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//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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//THE SOFTWARE.
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#include <stdio.h>
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#include <string.h>
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#include <math.h>
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#include "triangulator.h"
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#define TRIANGULATOR_VERTEXTYPE_REGULAR 0
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#define TRIANGULATOR_VERTEXTYPE_START 1
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#define TRIANGULATOR_VERTEXTYPE_END 2
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#define TRIANGULATOR_VERTEXTYPE_SPLIT 3
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#define TRIANGULATOR_VERTEXTYPE_MERGE 4
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TriangulatorPoly::TriangulatorPoly() {
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hole = false;
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numpoints = 0;
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points = NULL;
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}
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TriangulatorPoly::~TriangulatorPoly() {
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if(points) delete [] points;
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}
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void TriangulatorPoly::Clear() {
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if(points) delete [] points;
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hole = false;
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numpoints = 0;
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points = NULL;
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}
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void TriangulatorPoly::Init(long numpoints) {
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Clear();
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this->numpoints = numpoints;
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points = new Vector2[numpoints];
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}
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void TriangulatorPoly::Triangle(Vector2 &p1, Vector2 &p2, Vector2 &p3) {
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Init(3);
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points[0] = p1;
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points[1] = p2;
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points[2] = p3;
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}
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TriangulatorPoly::TriangulatorPoly(const TriangulatorPoly &src) {
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hole = src.hole;
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numpoints = src.numpoints;
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points = new Vector2[numpoints];
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memcpy(points, src.points, numpoints*sizeof(Vector2));
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}
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TriangulatorPoly& TriangulatorPoly::operator=(const TriangulatorPoly &src) {
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Clear();
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hole = src.hole;
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numpoints = src.numpoints;
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points = new Vector2[numpoints];
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memcpy(points, src.points, numpoints*sizeof(Vector2));
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return *this;
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}
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int TriangulatorPoly::GetOrientation() {
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long i1,i2;
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real_t area = 0;
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for(i1=0; i1<numpoints; i1++) {
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i2 = i1+1;
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if(i2 == numpoints) i2 = 0;
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area += points[i1].x * points[i2].y - points[i1].y * points[i2].x;
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}
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if(area>0) return TRIANGULATOR_CCW;
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if(area<0) return TRIANGULATOR_CW;
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return 0;
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}
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void TriangulatorPoly::SetOrientation(int orientation) {
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int polyorientation = GetOrientation();
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if(polyorientation&&(polyorientation!=orientation)) {
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Invert();
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}
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}
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void TriangulatorPoly::Invert() {
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long i;
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Vector2 *invpoints;
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invpoints = new Vector2[numpoints];
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for(i=0;i<numpoints;i++) {
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invpoints[i] = points[numpoints-i-1];
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}
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delete [] points;
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points = invpoints;
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}
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Vector2 TriangulatorPartition::Normalize(const Vector2 &p) {
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Vector2 r;
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real_t n = sqrt(p.x*p.x + p.y*p.y);
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if(n!=0) {
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r = p/n;
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} else {
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r.x = 0;
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r.y = 0;
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}
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return r;
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}
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real_t TriangulatorPartition::Distance(const Vector2 &p1, const Vector2 &p2) {
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real_t dx,dy;
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dx = p2.x - p1.x;
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dy = p2.y - p1.y;
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return(sqrt(dx*dx + dy*dy));
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}
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//checks if two lines intersect
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int TriangulatorPartition::Intersects(Vector2 &p11, Vector2 &p12, Vector2 &p21, Vector2 &p22) {
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if((p11.x == p21.x)&&(p11.y == p21.y)) return 0;
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if((p11.x == p22.x)&&(p11.y == p22.y)) return 0;
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if((p12.x == p21.x)&&(p12.y == p21.y)) return 0;
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if((p12.x == p22.x)&&(p12.y == p22.y)) return 0;
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Vector2 v1ort,v2ort,v;
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real_t dot11,dot12,dot21,dot22;
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v1ort.x = p12.y-p11.y;
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v1ort.y = p11.x-p12.x;
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v2ort.x = p22.y-p21.y;
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v2ort.y = p21.x-p22.x;
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v = p21-p11;
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dot21 = v.x*v1ort.x + v.y*v1ort.y;
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v = p22-p11;
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dot22 = v.x*v1ort.x + v.y*v1ort.y;
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v = p11-p21;
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dot11 = v.x*v2ort.x + v.y*v2ort.y;
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v = p12-p21;
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dot12 = v.x*v2ort.x + v.y*v2ort.y;
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if(dot11*dot12>0) return 0;
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if(dot21*dot22>0) return 0;
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return 1;
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}
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//removes holes from inpolys by merging them with non-holes
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int TriangulatorPartition::RemoveHoles(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *outpolys) {
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List<TriangulatorPoly> polys;
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List<TriangulatorPoly>::Element *holeiter,*polyiter,*iter,*iter2;
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long i,i2,holepointindex,polypointindex;
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Vector2 holepoint,polypoint,bestpolypoint;
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Vector2 linep1,linep2;
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Vector2 v1,v2;
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TriangulatorPoly newpoly;
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bool hasholes;
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bool pointvisible;
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bool pointfound;
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//check for trivial case (no holes)
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hasholes = false;
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for(iter = inpolys->front(); iter; iter=iter->next()) {
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if(iter->get().IsHole()) {
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hasholes = true;
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break;
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}
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}
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if(!hasholes) {
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for(iter = inpolys->front(); iter; iter=iter->next()) {
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outpolys->push_back(iter->get());
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}
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return 1;
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}
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polys = *inpolys;
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while(1) {
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//find the hole point with the largest x
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hasholes = false;
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for(iter = polys.front(); iter; iter=iter->next()) {
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if(!iter->get().IsHole()) continue;
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if(!hasholes) {
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hasholes = true;
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holeiter = iter;
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holepointindex = 0;
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}
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for(i=0; i < iter->get().GetNumPoints(); i++) {
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if(iter->get().GetPoint(i).x > holeiter->get().GetPoint(holepointindex).x) {
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holeiter = iter;
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holepointindex = i;
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}
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}
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}
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if(!hasholes) break;
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holepoint = holeiter->get().GetPoint(holepointindex);
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pointfound = false;
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for(iter = polys.front(); iter; iter=iter->next()) {
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if(iter->get().IsHole()) continue;
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for(i=0; i < iter->get().GetNumPoints(); i++) {
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if(iter->get().GetPoint(i).x <= holepoint.x) continue;
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if(!InCone(iter->get().GetPoint((i+iter->get().GetNumPoints()-1)%(iter->get().GetNumPoints())),
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iter->get().GetPoint(i),
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iter->get().GetPoint((i+1)%(iter->get().GetNumPoints())),
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holepoint))
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continue;
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polypoint = iter->get().GetPoint(i);
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if(pointfound) {
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v1 = Normalize(polypoint-holepoint);
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v2 = Normalize(bestpolypoint-holepoint);
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if(v2.x > v1.x) continue;
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}
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pointvisible = true;
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for(iter2 = polys.front(); iter2; iter2=iter2->next()) {
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if(iter2->get().IsHole()) continue;
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for(i2=0; i2 < iter2->get().GetNumPoints(); i2++) {
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linep1 = iter2->get().GetPoint(i2);
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linep2 = iter2->get().GetPoint((i2+1)%(iter2->get().GetNumPoints()));
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if(Intersects(holepoint,polypoint,linep1,linep2)) {
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pointvisible = false;
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break;
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}
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}
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if(!pointvisible) break;
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}
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if(pointvisible) {
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pointfound = true;
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bestpolypoint = polypoint;
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polyiter = iter;
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polypointindex = i;
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}
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}
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}
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if(!pointfound) return 0;
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newpoly.Init(holeiter->get().GetNumPoints() + polyiter->get().GetNumPoints() + 2);
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i2 = 0;
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for(i=0;i<=polypointindex;i++) {
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newpoly[i2] = polyiter->get().GetPoint(i);
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i2++;
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}
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for(i=0;i<=holeiter->get().GetNumPoints();i++) {
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newpoly[i2] = holeiter->get().GetPoint((i+holepointindex)%holeiter->get().GetNumPoints());
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i2++;
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}
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for(i=polypointindex;i<polyiter->get().GetNumPoints();i++) {
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newpoly[i2] = polyiter->get().GetPoint(i);
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i2++;
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}
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polys.erase(holeiter);
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polys.erase(polyiter);
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polys.push_back(newpoly);
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}
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for(iter = polys.front(); iter; iter=iter->next()) {
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outpolys->push_back(iter->get());
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}
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return 1;
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}
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bool TriangulatorPartition::IsConvex(Vector2& p1, Vector2& p2, Vector2& p3) {
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real_t tmp;
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tmp = (p3.y-p1.y)*(p2.x-p1.x)-(p3.x-p1.x)*(p2.y-p1.y);
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if(tmp>0) return 1;
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else return 0;
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}
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bool TriangulatorPartition::IsReflex(Vector2& p1, Vector2& p2, Vector2& p3) {
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real_t tmp;
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tmp = (p3.y-p1.y)*(p2.x-p1.x)-(p3.x-p1.x)*(p2.y-p1.y);
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if(tmp<0) return 1;
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else return 0;
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}
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bool TriangulatorPartition::IsInside(Vector2& p1, Vector2& p2, Vector2& p3, Vector2 &p) {
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if(IsConvex(p1,p,p2)) return false;
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if(IsConvex(p2,p,p3)) return false;
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if(IsConvex(p3,p,p1)) return false;
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return true;
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}
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bool TriangulatorPartition::InCone(Vector2 &p1, Vector2 &p2, Vector2 &p3, Vector2 &p) {
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bool convex;
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convex = IsConvex(p1,p2,p3);
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if(convex) {
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if(!IsConvex(p1,p2,p)) return false;
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if(!IsConvex(p2,p3,p)) return false;
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return true;
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} else {
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if(IsConvex(p1,p2,p)) return true;
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if(IsConvex(p2,p3,p)) return true;
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return false;
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}
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}
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bool TriangulatorPartition::InCone(PartitionVertex *v, Vector2 &p) {
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Vector2 p1,p2,p3;
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p1 = v->previous->p;
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p2 = v->p;
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p3 = v->next->p;
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return InCone(p1,p2,p3,p);
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}
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void TriangulatorPartition::UpdateVertexReflexity(PartitionVertex *v) {
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PartitionVertex *v1,*v3;
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v1 = v->previous;
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v3 = v->next;
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v->isConvex = !IsReflex(v1->p,v->p,v3->p);
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}
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void TriangulatorPartition::UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices) {
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long i;
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PartitionVertex *v1,*v3;
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Vector2 vec1,vec3;
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v1 = v->previous;
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v3 = v->next;
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v->isConvex = IsConvex(v1->p,v->p,v3->p);
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vec1 = Normalize(v1->p - v->p);
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vec3 = Normalize(v3->p - v->p);
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v->angle = vec1.x*vec3.x + vec1.y*vec3.y;
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if(v->isConvex) {
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v->isEar = true;
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for(i=0;i<numvertices;i++) {
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if((vertices[i].p.x==v->p.x)&&(vertices[i].p.y==v->p.y)) continue;
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if((vertices[i].p.x==v1->p.x)&&(vertices[i].p.y==v1->p.y)) continue;
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if((vertices[i].p.x==v3->p.x)&&(vertices[i].p.y==v3->p.y)) continue;
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if(IsInside(v1->p,v->p,v3->p,vertices[i].p)) {
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v->isEar = false;
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break;
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}
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}
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} else {
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v->isEar = false;
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}
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}
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//triangulation by ear removal
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int TriangulatorPartition::Triangulate_EC(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) {
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long numvertices;
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PartitionVertex *vertices;
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PartitionVertex *ear;
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TriangulatorPoly triangle;
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long i,j;
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bool earfound;
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if(poly->GetNumPoints() < 3) return 0;
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if(poly->GetNumPoints() == 3) {
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triangles->push_back(*poly);
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return 1;
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}
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numvertices = poly->GetNumPoints();
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vertices = new PartitionVertex[numvertices];
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for(i=0;i<numvertices;i++) {
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vertices[i].isActive = true;
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vertices[i].p = poly->GetPoint(i);
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if(i==(numvertices-1)) vertices[i].next=&(vertices[0]);
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else vertices[i].next=&(vertices[i+1]);
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if(i==0) vertices[i].previous = &(vertices[numvertices-1]);
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else vertices[i].previous = &(vertices[i-1]);
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}
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for(i=0;i<numvertices;i++) {
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UpdateVertex(&vertices[i],vertices,numvertices);
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}
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for(i=0;i<numvertices-3;i++) {
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earfound = false;
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//find the most extruded ear
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for(j=0;j<numvertices;j++) {
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if(!vertices[j].isActive) continue;
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if(!vertices[j].isEar) continue;
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if(!earfound) {
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earfound = true;
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ear = &(vertices[j]);
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} else {
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if(vertices[j].angle > ear->angle) {
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ear = &(vertices[j]);
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}
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}
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}
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if(!earfound) {
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delete [] vertices;
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return 0;
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}
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triangle.Triangle(ear->previous->p,ear->p,ear->next->p);
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triangles->push_back(triangle);
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ear->isActive = false;
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ear->previous->next = ear->next;
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ear->next->previous = ear->previous;
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if(i==numvertices-4) break;
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UpdateVertex(ear->previous,vertices,numvertices);
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UpdateVertex(ear->next,vertices,numvertices);
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}
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for(i=0;i<numvertices;i++) {
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if(vertices[i].isActive) {
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triangle.Triangle(vertices[i].previous->p,vertices[i].p,vertices[i].next->p);
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triangles->push_back(triangle);
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break;
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}
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}
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delete [] vertices;
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return 1;
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}
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int TriangulatorPartition::Triangulate_EC(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles) {
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List<TriangulatorPoly> outpolys;
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List<TriangulatorPoly>::Element*iter;
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if(!RemoveHoles(inpolys,&outpolys)) return 0;
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for(iter=outpolys.front();iter;iter=iter->next()) {
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if(!Triangulate_EC(&(iter->get()),triangles)) return 0;
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}
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return 1;
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}
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int TriangulatorPartition::ConvexPartition_HM(TriangulatorPoly *poly, List<TriangulatorPoly> *parts) {
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List<TriangulatorPoly> triangles;
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List<TriangulatorPoly>::Element *iter1,*iter2;
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TriangulatorPoly *poly1,*poly2;
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TriangulatorPoly newpoly;
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Vector2 d1,d2,p1,p2,p3;
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long i11,i12,i21,i22,i13,i23,j,k;
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bool isdiagonal;
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long numreflex;
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//check if the poly is already convex
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numreflex = 0;
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for(i11=0;i11<poly->GetNumPoints();i11++) {
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if(i11==0) i12 = poly->GetNumPoints()-1;
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else i12=i11-1;
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if(i11==(poly->GetNumPoints()-1)) i13=0;
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else i13=i11+1;
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if(IsReflex(poly->GetPoint(i12),poly->GetPoint(i11),poly->GetPoint(i13))) {
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numreflex = 1;
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break;
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}
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}
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if(numreflex == 0) {
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parts->push_back(*poly);
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return 1;
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}
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if(!Triangulate_EC(poly,&triangles)) return 0;
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for(iter1 = triangles.front(); iter1 ; iter1=iter1->next()) {
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poly1 = &(iter1->get());
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for(i11=0;i11<poly1->GetNumPoints();i11++) {
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d1 = poly1->GetPoint(i11);
|
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i12 = (i11+1)%(poly1->GetNumPoints());
|
||
d2 = poly1->GetPoint(i12);
|
||
|
||
isdiagonal = false;
|
||
for(iter2 = iter1; iter2 ; iter2=iter2->next()) {
|
||
if(iter1 == iter2) continue;
|
||
poly2 = &(iter2->get());
|
||
|
||
for(i21=0;i21<poly2->GetNumPoints();i21++) {
|
||
if((d2.x != poly2->GetPoint(i21).x)||(d2.y != poly2->GetPoint(i21).y)) continue;
|
||
i22 = (i21+1)%(poly2->GetNumPoints());
|
||
if((d1.x != poly2->GetPoint(i22).x)||(d1.y != poly2->GetPoint(i22).y)) continue;
|
||
isdiagonal = true;
|
||
break;
|
||
}
|
||
if(isdiagonal) break;
|
||
}
|
||
|
||
if(!isdiagonal) continue;
|
||
|
||
p2 = poly1->GetPoint(i11);
|
||
if(i11 == 0) i13 = poly1->GetNumPoints()-1;
|
||
else i13 = i11-1;
|
||
p1 = poly1->GetPoint(i13);
|
||
if(i22 == (poly2->GetNumPoints()-1)) i23 = 0;
|
||
else i23 = i22+1;
|
||
p3 = poly2->GetPoint(i23);
|
||
|
||
if(!IsConvex(p1,p2,p3)) continue;
|
||
|
||
p2 = poly1->GetPoint(i12);
|
||
if(i12 == (poly1->GetNumPoints()-1)) i13 = 0;
|
||
else i13 = i12+1;
|
||
p3 = poly1->GetPoint(i13);
|
||
if(i21 == 0) i23 = poly2->GetNumPoints()-1;
|
||
else i23 = i21-1;
|
||
p1 = poly2->GetPoint(i23);
|
||
|
||
if(!IsConvex(p1,p2,p3)) continue;
|
||
|
||
newpoly.Init(poly1->GetNumPoints()+poly2->GetNumPoints()-2);
|
||
k = 0;
|
||
for(j=i12;j!=i11;j=(j+1)%(poly1->GetNumPoints())) {
|
||
newpoly[k] = poly1->GetPoint(j);
|
||
k++;
|
||
}
|
||
for(j=i22;j!=i21;j=(j+1)%(poly2->GetNumPoints())) {
|
||
newpoly[k] = poly2->GetPoint(j);
|
||
k++;
|
||
}
|
||
|
||
triangles.erase(iter2);
|
||
iter1->get() = newpoly;
|
||
poly1 = &(iter1->get());
|
||
i11 = -1;
|
||
|
||
continue;
|
||
}
|
||
}
|
||
|
||
for(iter1 = triangles.front(); iter1 ; iter1=iter1->next()) {
|
||
parts->push_back(iter1->get());
|
||
}
|
||
|
||
return 1;
|
||
}
|
||
|
||
int TriangulatorPartition::ConvexPartition_HM(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *parts) {
|
||
List<TriangulatorPoly> outpolys;
|
||
List<TriangulatorPoly>::Element* iter;
|
||
|
||
if(!RemoveHoles(inpolys,&outpolys)) return 0;
|
||
for(iter=outpolys.front();iter;iter=iter->next()) {
|
||
if(!ConvexPartition_HM(&(iter->get()),parts)) return 0;
|
||
}
|
||
return 1;
|
||
}
|
||
|
||
//minimum-weight polygon triangulation by dynamic programming
|
||
//O(n^3) time complexity
|
||
//O(n^2) space complexity
|
||
int TriangulatorPartition::Triangulate_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) {
|
||
long i,j,k,gap,n;
|
||
DPState **dpstates;
|
||
Vector2 p1,p2,p3,p4;
|
||
long bestvertex;
|
||
real_t weight,minweight,d1,d2;
|
||
Diagonal diagonal,newdiagonal;
|
||
List<Diagonal> diagonals;
|
||
TriangulatorPoly triangle;
|
||
int ret = 1;
|
||
|
||
n = poly->GetNumPoints();
|
||
dpstates = new DPState *[n];
|
||
for(i=1;i<n;i++) {
|
||
dpstates[i] = new DPState[i];
|
||
}
|
||
|
||
//init states and visibility
|
||
for(i=0;i<(n-1);i++) {
|
||
p1 = poly->GetPoint(i);
|
||
for(j=i+1;j<n;j++) {
|
||
dpstates[j][i].visible = true;
|
||
dpstates[j][i].weight = 0;
|
||
dpstates[j][i].bestvertex = -1;
|
||
if(j!=(i+1)) {
|
||
p2 = poly->GetPoint(j);
|
||
|
||
//visibility check
|
||
if(i==0) p3 = poly->GetPoint(n-1);
|
||
else p3 = poly->GetPoint(i-1);
|
||
if(i==(n-1)) p4 = poly->GetPoint(0);
|
||
else p4 = poly->GetPoint(i+1);
|
||
if(!InCone(p3,p1,p4,p2)) {
|
||
dpstates[j][i].visible = false;
|
||
continue;
|
||
}
|
||
|
||
if(j==0) p3 = poly->GetPoint(n-1);
|
||
else p3 = poly->GetPoint(j-1);
|
||
if(j==(n-1)) p4 = poly->GetPoint(0);
|
||
else p4 = poly->GetPoint(j+1);
|
||
if(!InCone(p3,p2,p4,p1)) {
|
||
dpstates[j][i].visible = false;
|
||
continue;
|
||
}
|
||
|
||
for(k=0;k<n;k++) {
|
||
p3 = poly->GetPoint(k);
|
||
if(k==(n-1)) p4 = poly->GetPoint(0);
|
||
else p4 = poly->GetPoint(k+1);
|
||
if(Intersects(p1,p2,p3,p4)) {
|
||
dpstates[j][i].visible = false;
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
dpstates[n-1][0].visible = true;
|
||
dpstates[n-1][0].weight = 0;
|
||
dpstates[n-1][0].bestvertex = -1;
|
||
|
||
for(gap = 2; gap<n; gap++) {
|
||
for(i=0; i<(n-gap); i++) {
|
||
j = i+gap;
|
||
if(!dpstates[j][i].visible) continue;
|
||
bestvertex = -1;
|
||
for(k=(i+1);k<j;k++) {
|
||
if(!dpstates[k][i].visible) continue;
|
||
if(!dpstates[j][k].visible) continue;
|
||
|
||
if(k<=(i+1)) d1=0;
|
||
else d1 = Distance(poly->GetPoint(i),poly->GetPoint(k));
|
||
if(j<=(k+1)) d2=0;
|
||
else d2 = Distance(poly->GetPoint(k),poly->GetPoint(j));
|
||
|
||
weight = dpstates[k][i].weight + dpstates[j][k].weight + d1 + d2;
|
||
|
||
if((bestvertex == -1)||(weight<minweight)) {
|
||
bestvertex = k;
|
||
minweight = weight;
|
||
}
|
||
}
|
||
if(bestvertex == -1) {
|
||
for(i=1;i<n;i++) {
|
||
delete [] dpstates[i];
|
||
}
|
||
delete [] dpstates;
|
||
|
||
return 0;
|
||
}
|
||
|
||
dpstates[j][i].bestvertex = bestvertex;
|
||
dpstates[j][i].weight = minweight;
|
||
}
|
||
}
|
||
|
||
newdiagonal.index1 = 0;
|
||
newdiagonal.index2 = n-1;
|
||
diagonals.push_back(newdiagonal);
|
||
while(!diagonals.empty()) {
|
||
diagonal = (diagonals.front()->get());
|
||
diagonals.pop_front();
|
||
bestvertex = dpstates[diagonal.index2][diagonal.index1].bestvertex;
|
||
if(bestvertex == -1) {
|
||
ret = 0;
|
||
break;
|
||
}
|
||
triangle.Triangle(poly->GetPoint(diagonal.index1),poly->GetPoint(bestvertex),poly->GetPoint(diagonal.index2));
|
||
triangles->push_back(triangle);
|
||
if(bestvertex > (diagonal.index1+1)) {
|
||
newdiagonal.index1 = diagonal.index1;
|
||
newdiagonal.index2 = bestvertex;
|
||
diagonals.push_back(newdiagonal);
|
||
}
|
||
if(diagonal.index2 > (bestvertex+1)) {
|
||
newdiagonal.index1 = bestvertex;
|
||
newdiagonal.index2 = diagonal.index2;
|
||
diagonals.push_back(newdiagonal);
|
||
}
|
||
}
|
||
|
||
for(i=1;i<n;i++) {
|
||
delete [] dpstates[i];
|
||
}
|
||
delete [] dpstates;
|
||
|
||
return ret;
|
||
}
|
||
|
||
void TriangulatorPartition::UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates) {
|
||
Diagonal newdiagonal;
|
||
List<Diagonal> *pairs;
|
||
long w2;
|
||
|
||
w2 = dpstates[a][b].weight;
|
||
if(w>w2) return;
|
||
|
||
pairs = &(dpstates[a][b].pairs);
|
||
newdiagonal.index1 = i;
|
||
newdiagonal.index2 = j;
|
||
|
||
if(w<w2) {
|
||
pairs->clear();
|
||
pairs->push_front(newdiagonal);
|
||
dpstates[a][b].weight = w;
|
||
} else {
|
||
if((!pairs->empty())&&(i <= pairs->front()->get().index1)) return;
|
||
while((!pairs->empty())&&(pairs->front()->get().index2 >= j)) pairs->pop_front();
|
||
pairs->push_front(newdiagonal);
|
||
}
|
||
}
|
||
|
||
void TriangulatorPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
|
||
List<Diagonal> *pairs;
|
||
List<Diagonal>::Element *iter,*lastiter;
|
||
long top;
|
||
long w;
|
||
|
||
if(!dpstates[i][j].visible) return;
|
||
top = j;
|
||
w = dpstates[i][j].weight;
|
||
if(k-j > 1) {
|
||
if (!dpstates[j][k].visible) return;
|
||
w += dpstates[j][k].weight + 1;
|
||
}
|
||
if(j-i > 1) {
|
||
pairs = &(dpstates[i][j].pairs);
|
||
iter = NULL;
|
||
lastiter = NULL;
|
||
while(iter!=pairs->front()) {
|
||
if (!iter)
|
||
iter=pairs->back();
|
||
else
|
||
iter=iter->prev();
|
||
|
||
if(!IsReflex(vertices[iter->get().index2].p,vertices[j].p,vertices[k].p)) lastiter = iter;
|
||
else break;
|
||
}
|
||
if(lastiter == NULL) w++;
|
||
else {
|
||
if(IsReflex(vertices[k].p,vertices[i].p,vertices[lastiter->get().index1].p)) w++;
|
||
else top = lastiter->get().index1;
|
||
}
|
||
}
|
||
UpdateState(i,k,w,top,j,dpstates);
|
||
}
|
||
|
||
void TriangulatorPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
|
||
List<Diagonal> *pairs;
|
||
List<Diagonal>::Element* iter,*lastiter;
|
||
long top;
|
||
long w;
|
||
|
||
if(!dpstates[j][k].visible) return;
|
||
top = j;
|
||
w = dpstates[j][k].weight;
|
||
|
||
if (j-i > 1) {
|
||
if (!dpstates[i][j].visible) return;
|
||
w += dpstates[i][j].weight + 1;
|
||
}
|
||
if (k-j > 1) {
|
||
pairs = &(dpstates[j][k].pairs);
|
||
|
||
iter = pairs->front();
|
||
if((!pairs->empty())&&(!IsReflex(vertices[i].p,vertices[j].p,vertices[iter->get().index1].p))) {
|
||
lastiter = iter;
|
||
while(iter!=NULL) {
|
||
if(!IsReflex(vertices[i].p,vertices[j].p,vertices[iter->get().index1].p)) {
|
||
lastiter = iter;
|
||
iter=iter->next();
|
||
}
|
||
else break;
|
||
}
|
||
if(IsReflex(vertices[lastiter->get().index2].p,vertices[k].p,vertices[i].p)) w++;
|
||
else top = lastiter->get().index2;
|
||
} else w++;
|
||
}
|
||
UpdateState(i,k,w,j,top,dpstates);
|
||
}
|
||
|
||
int TriangulatorPartition::ConvexPartition_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *parts) {
|
||
Vector2 p1,p2,p3,p4;
|
||
PartitionVertex *vertices;
|
||
DPState2 **dpstates;
|
||
long i,j,k,n,gap;
|
||
List<Diagonal> diagonals,diagonals2;
|
||
Diagonal diagonal,newdiagonal;
|
||
List<Diagonal> *pairs,*pairs2;
|
||
List<Diagonal>::Element* iter,*iter2;
|
||
int ret;
|
||
TriangulatorPoly newpoly;
|
||
List<long> indices;
|
||
List<long>::Element* iiter;
|
||
bool ijreal,jkreal;
|
||
|
||
n = poly->GetNumPoints();
|
||
vertices = new PartitionVertex[n];
|
||
|
||
dpstates = new DPState2 *[n];
|
||
for(i=0;i<n;i++) {
|
||
dpstates[i] = new DPState2[n];
|
||
}
|
||
|
||
//init vertex information
|
||
for(i=0;i<n;i++) {
|
||
vertices[i].p = poly->GetPoint(i);
|
||
vertices[i].isActive = true;
|
||
if(i==0) vertices[i].previous = &(vertices[n-1]);
|
||
else vertices[i].previous = &(vertices[i-1]);
|
||
if(i==(poly->GetNumPoints()-1)) vertices[i].next = &(vertices[0]);
|
||
else vertices[i].next = &(vertices[i+1]);
|
||
}
|
||
for(i=1;i<n;i++) {
|
||
UpdateVertexReflexity(&(vertices[i]));
|
||
}
|
||
|
||
//init states and visibility
|
||
for(i=0;i<(n-1);i++) {
|
||
p1 = poly->GetPoint(i);
|
||
for(j=i+1;j<n;j++) {
|
||
dpstates[i][j].visible = true;
|
||
if(j==i+1) {
|
||
dpstates[i][j].weight = 0;
|
||
} else {
|
||
dpstates[i][j].weight = 2147483647;
|
||
}
|
||
if(j!=(i+1)) {
|
||
p2 = poly->GetPoint(j);
|
||
|
||
//visibility check
|
||
if(!InCone(&vertices[i],p2)) {
|
||
dpstates[i][j].visible = false;
|
||
continue;
|
||
}
|
||
if(!InCone(&vertices[j],p1)) {
|
||
dpstates[i][j].visible = false;
|
||
continue;
|
||
}
|
||
|
||
for(k=0;k<n;k++) {
|
||
p3 = poly->GetPoint(k);
|
||
if(k==(n-1)) p4 = poly->GetPoint(0);
|
||
else p4 = poly->GetPoint(k+1);
|
||
if(Intersects(p1,p2,p3,p4)) {
|
||
dpstates[i][j].visible = false;
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
for(i=0;i<(n-2);i++) {
|
||
j = i+2;
|
||
if(dpstates[i][j].visible) {
|
||
dpstates[i][j].weight = 0;
|
||
newdiagonal.index1 = i+1;
|
||
newdiagonal.index2 = i+1;
|
||
dpstates[i][j].pairs.push_back(newdiagonal);
|
||
}
|
||
}
|
||
|
||
dpstates[0][n-1].visible = true;
|
||
vertices[0].isConvex = false; //by convention
|
||
|
||
for(gap=3; gap<n; gap++) {
|
||
for(i=0;i<n-gap;i++) {
|
||
if(vertices[i].isConvex) continue;
|
||
k = i+gap;
|
||
if(dpstates[i][k].visible) {
|
||
if(!vertices[k].isConvex) {
|
||
for(j=i+1;j<k;j++) TypeA(i,j,k,vertices,dpstates);
|
||
} else {
|
||
for(j=i+1;j<(k-1);j++) {
|
||
if(vertices[j].isConvex) continue;
|
||
TypeA(i,j,k,vertices,dpstates);
|
||
}
|
||
TypeA(i,k-1,k,vertices,dpstates);
|
||
}
|
||
}
|
||
}
|
||
for(k=gap;k<n;k++) {
|
||
if(vertices[k].isConvex) continue;
|
||
i = k-gap;
|
||
if((vertices[i].isConvex)&&(dpstates[i][k].visible)) {
|
||
TypeB(i,i+1,k,vertices,dpstates);
|
||
for(j=i+2;j<k;j++) {
|
||
if(vertices[j].isConvex) continue;
|
||
TypeB(i,j,k,vertices,dpstates);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
|
||
//recover solution
|
||
ret = 1;
|
||
newdiagonal.index1 = 0;
|
||
newdiagonal.index2 = n-1;
|
||
diagonals.push_front(newdiagonal);
|
||
while(!diagonals.empty()) {
|
||
diagonal = (diagonals.front()->get());
|
||
diagonals.pop_front();
|
||
if((diagonal.index2 - diagonal.index1) <=1) continue;
|
||
pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
|
||
if(pairs->empty()) {
|
||
ret = 0;
|
||
break;
|
||
}
|
||
if(!vertices[diagonal.index1].isConvex) {
|
||
iter = pairs->back();
|
||
|
||
j = iter->get().index2;
|
||
newdiagonal.index1 = j;
|
||
newdiagonal.index2 = diagonal.index2;
|
||
diagonals.push_front(newdiagonal);
|
||
if((j - diagonal.index1)>1) {
|
||
if(iter->get().index1 != iter->get().index2) {
|
||
pairs2 = &(dpstates[diagonal.index1][j].pairs);
|
||
while(1) {
|
||
if(pairs2->empty()) {
|
||
ret = 0;
|
||
break;
|
||
}
|
||
iter2 = pairs2->back();
|
||
|
||
if(iter->get().index1 != iter2->get().index1) pairs2->pop_back();
|
||
else break;
|
||
}
|
||
if(ret == 0) break;
|
||
}
|
||
newdiagonal.index1 = diagonal.index1;
|
||
newdiagonal.index2 = j;
|
||
diagonals.push_front(newdiagonal);
|
||
}
|
||
} else {
|
||
iter = pairs->front();
|
||
j = iter->get().index1;
|
||
newdiagonal.index1 = diagonal.index1;
|
||
newdiagonal.index2 = j;
|
||
diagonals.push_front(newdiagonal);
|
||
if((diagonal.index2 - j) > 1) {
|
||
if(iter->get().index1 != iter->get().index2) {
|
||
pairs2 = &(dpstates[j][diagonal.index2].pairs);
|
||
while(1) {
|
||
if(pairs2->empty()) {
|
||
ret = 0;
|
||
break;
|
||
}
|
||
iter2 = pairs2->front();
|
||
if(iter->get().index2 != iter2->get().index2) pairs2->pop_front();
|
||
else break;
|
||
}
|
||
if(ret == 0) break;
|
||
}
|
||
newdiagonal.index1 = j;
|
||
newdiagonal.index2 = diagonal.index2;
|
||
diagonals.push_front(newdiagonal);
|
||
}
|
||
}
|
||
}
|
||
|
||
if(ret == 0) {
|
||
for(i=0;i<n;i++) {
|
||
delete [] dpstates[i];
|
||
}
|
||
delete [] dpstates;
|
||
delete [] vertices;
|
||
|
||
return ret;
|
||
}
|
||
|
||
newdiagonal.index1 = 0;
|
||
newdiagonal.index2 = n-1;
|
||
diagonals.push_front(newdiagonal);
|
||
while(!diagonals.empty()) {
|
||
diagonal = (diagonals.front())->get();
|
||
diagonals.pop_front();
|
||
if((diagonal.index2 - diagonal.index1) <= 1) continue;
|
||
|
||
indices.clear();
|
||
diagonals2.clear();
|
||
indices.push_back(diagonal.index1);
|
||
indices.push_back(diagonal.index2);
|
||
diagonals2.push_front(diagonal);
|
||
|
||
while(!diagonals2.empty()) {
|
||
diagonal = (diagonals2.front()->get());
|
||
diagonals2.pop_front();
|
||
if((diagonal.index2 - diagonal.index1) <= 1) continue;
|
||
ijreal = true;
|
||
jkreal = true;
|
||
pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
|
||
if(!vertices[diagonal.index1].isConvex) {
|
||
iter = pairs->back();
|
||
j = iter->get().index2;
|
||
if(iter->get().index1 != iter->get().index2) ijreal = false;
|
||
} else {
|
||
iter = pairs->front();
|
||
j = iter->get().index1;
|
||
if(iter->get().index1 != iter->get().index2) jkreal = false;
|
||
}
|
||
|
||
newdiagonal.index1 = diagonal.index1;
|
||
newdiagonal.index2 = j;
|
||
if(ijreal) {
|
||
diagonals.push_back(newdiagonal);
|
||
} else {
|
||
diagonals2.push_back(newdiagonal);
|
||
}
|
||
|
||
newdiagonal.index1 = j;
|
||
newdiagonal.index2 = diagonal.index2;
|
||
if(jkreal) {
|
||
diagonals.push_back(newdiagonal);
|
||
} else {
|
||
diagonals2.push_back(newdiagonal);
|
||
}
|
||
|
||
indices.push_back(j);
|
||
}
|
||
|
||
indices.sort();
|
||
newpoly.Init((long)indices.size());
|
||
k=0;
|
||
for(iiter = indices.front();iiter;iiter=iiter->next()) {
|
||
newpoly[k] = vertices[iiter->get()].p;
|
||
k++;
|
||
}
|
||
parts->push_back(newpoly);
|
||
}
|
||
|
||
for(i=0;i<n;i++) {
|
||
delete [] dpstates[i];
|
||
}
|
||
delete [] dpstates;
|
||
delete [] vertices;
|
||
|
||
return ret;
|
||
}
|
||
|
||
//triangulates a set of polygons by first partitioning them into monotone polygons
|
||
//O(n*log(n)) time complexity, O(n) space complexity
|
||
//the algorithm used here is outlined in the book
|
||
//"Computational Geometry: Algorithms and Applications"
|
||
//by Mark de Berg, Otfried Cheong, Marc van Kreveld and Mark Overmars
|
||
int TriangulatorPartition::MonotonePartition(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *monotonePolys) {
|
||
List<TriangulatorPoly>::Element *iter;
|
||
MonotoneVertex *vertices;
|
||
long i,numvertices,vindex,vindex2,newnumvertices,maxnumvertices;
|
||
long polystartindex, polyendindex;
|
||
TriangulatorPoly *poly;
|
||
MonotoneVertex *v,*v2,*vprev,*vnext;
|
||
ScanLineEdge newedge;
|
||
bool error = false;
|
||
|
||
numvertices = 0;
|
||
for(iter = inpolys->front(); iter ; iter=iter->next()) {
|
||
numvertices += iter->get().GetNumPoints();
|
||
}
|
||
|
||
maxnumvertices = numvertices*3;
|
||
vertices = new MonotoneVertex[maxnumvertices];
|
||
newnumvertices = numvertices;
|
||
|
||
polystartindex = 0;
|
||
for(iter = inpolys->front(); iter ; iter=iter->next()) {
|
||
poly = &(iter->get());
|
||
polyendindex = polystartindex + poly->GetNumPoints()-1;
|
||
for(i=0;i<poly->GetNumPoints();i++) {
|
||
vertices[i+polystartindex].p = poly->GetPoint(i);
|
||
if(i==0) vertices[i+polystartindex].previous = polyendindex;
|
||
else vertices[i+polystartindex].previous = i+polystartindex-1;
|
||
if(i==(poly->GetNumPoints()-1)) vertices[i+polystartindex].next = polystartindex;
|
||
else vertices[i+polystartindex].next = i+polystartindex+1;
|
||
}
|
||
polystartindex = polyendindex+1;
|
||
}
|
||
|
||
//construct the priority queue
|
||
long *priority = new long [numvertices];
|
||
for(i=0;i<numvertices;i++) priority[i] = i;
|
||
SortArray<long,VertexSorter> sorter;
|
||
sorter.compare.vertices=vertices;
|
||
sorter.sort(priority,numvertices);
|
||
|
||
//determine vertex types
|
||
char *vertextypes = new char[maxnumvertices];
|
||
for(i=0;i<numvertices;i++) {
|
||
v = &(vertices[i]);
|
||
vprev = &(vertices[v->previous]);
|
||
vnext = &(vertices[v->next]);
|
||
|
||
if(Below(vprev->p,v->p)&&Below(vnext->p,v->p)) {
|
||
if(IsConvex(vnext->p,vprev->p,v->p)) {
|
||
vertextypes[i] = TRIANGULATOR_VERTEXTYPE_START;
|
||
} else {
|
||
vertextypes[i] = TRIANGULATOR_VERTEXTYPE_SPLIT;
|
||
}
|
||
} else if(Below(v->p,vprev->p)&&Below(v->p,vnext->p)) {
|
||
if(IsConvex(vnext->p,vprev->p,v->p))
|
||
{
|
||
vertextypes[i] = TRIANGULATOR_VERTEXTYPE_END;
|
||
} else {
|
||
vertextypes[i] = TRIANGULATOR_VERTEXTYPE_MERGE;
|
||
}
|
||
} else {
|
||
vertextypes[i] = TRIANGULATOR_VERTEXTYPE_REGULAR;
|
||
}
|
||
}
|
||
|
||
//helpers
|
||
long *helpers = new long[maxnumvertices];
|
||
|
||
//binary search tree that holds edges intersecting the scanline
|
||
//note that while set doesn't actually have to be implemented as a tree
|
||
//complexity requirements for operations are the same as for the balanced binary search tree
|
||
Set<ScanLineEdge> edgeTree;
|
||
//store iterators to the edge tree elements
|
||
//this makes deleting existing edges much faster
|
||
Set<ScanLineEdge>::Element **edgeTreeIterators,*edgeIter;
|
||
edgeTreeIterators = new Set<ScanLineEdge>::Element*[maxnumvertices];
|
||
//Pair<Set<ScanLineEdge>::Element*,bool> edgeTreeRet;
|
||
for(i = 0; i<numvertices; i++) edgeTreeIterators[i] = NULL;
|
||
|
||
//for each vertex
|
||
for(i=0;i<numvertices;i++) {
|
||
vindex = priority[i];
|
||
v = &(vertices[vindex]);
|
||
vindex2 = vindex;
|
||
v2 = v;
|
||
|
||
//depending on the vertex type, do the appropriate action
|
||
//comments in the following sections are copied from "Computational Geometry: Algorithms and Applications"
|
||
switch(vertextypes[vindex]) {
|
||
case TRIANGULATOR_VERTEXTYPE_START:
|
||
//Insert ei in T and set helper(ei) to vi.
|
||
newedge.p1 = v->p;
|
||
newedge.p2 = vertices[v->next].p;
|
||
newedge.index = vindex;
|
||
edgeTreeIterators[vindex] = edgeTree.insert(newedge);
|
||
helpers[vindex] = vindex;
|
||
break;
|
||
|
||
case TRIANGULATOR_VERTEXTYPE_END:
|
||
//if helper(ei-1) is a merge vertex
|
||
if(vertextypes[helpers[v->previous]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
|
||
//Insert the diagonal connecting vi to helper(ei-1) in D.
|
||
AddDiagonal(vertices,&newnumvertices,vindex,helpers[v->previous],
|
||
vertextypes, edgeTreeIterators, &edgeTree, helpers);
|
||
}
|
||
//Delete ei-1 from T
|
||
edgeTree.erase(edgeTreeIterators[v->previous]);
|
||
break;
|
||
|
||
case TRIANGULATOR_VERTEXTYPE_SPLIT:
|
||
//Search in T to find the edge e j directly left of vi.
|
||
newedge.p1 = v->p;
|
||
newedge.p2 = v->p;
|
||
edgeIter = edgeTree.lower_bound(newedge);
|
||
if(edgeIter == edgeTree.front()) {
|
||
error = true;
|
||
break;
|
||
}
|
||
edgeIter=edgeIter->prev();
|
||
//Insert the diagonal connecting vi to helper(ej) in D.
|
||
AddDiagonal(vertices,&newnumvertices,vindex,helpers[edgeIter->get().index],
|
||
vertextypes, edgeTreeIterators, &edgeTree, helpers);
|
||
vindex2 = newnumvertices-2;
|
||
v2 = &(vertices[vindex2]);
|
||
//helper(e j)<29>vi
|
||
helpers[edgeIter->get().index] = vindex;
|
||
//Insert ei in T and set helper(ei) to vi.
|
||
newedge.p1 = v2->p;
|
||
newedge.p2 = vertices[v2->next].p;
|
||
newedge.index = vindex2;
|
||
|
||
edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
|
||
helpers[vindex2] = vindex2;
|
||
break;
|
||
|
||
case TRIANGULATOR_VERTEXTYPE_MERGE:
|
||
//if helper(ei-1) is a merge vertex
|
||
if(vertextypes[helpers[v->previous]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
|
||
//Insert the diagonal connecting vi to helper(ei-1) in D.
|
||
AddDiagonal(vertices,&newnumvertices,vindex,helpers[v->previous],
|
||
vertextypes, edgeTreeIterators, &edgeTree, helpers);
|
||
vindex2 = newnumvertices-2;
|
||
v2 = &(vertices[vindex2]);
|
||
}
|
||
//Delete ei-1 from T.
|
||
edgeTree.erase(edgeTreeIterators[v->previous]);
|
||
//Search in T to find the edge e j directly left of vi.
|
||
newedge.p1 = v->p;
|
||
newedge.p2 = v->p;
|
||
edgeIter = edgeTree.lower_bound(newedge);
|
||
if(edgeIter == edgeTree.front()) {
|
||
error = true;
|
||
break;
|
||
}
|
||
edgeIter=edgeIter->prev();
|
||
//if helper(ej) is a merge vertex
|
||
if(vertextypes[helpers[edgeIter->get().index]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
|
||
//Insert the diagonal connecting vi to helper(e j) in D.
|
||
AddDiagonal(vertices,&newnumvertices,vindex2,helpers[edgeIter->get().index],
|
||
vertextypes, edgeTreeIterators, &edgeTree, helpers);
|
||
}
|
||
//helper(e j)<29>vi
|
||
helpers[edgeIter->get().index] = vindex2;
|
||
break;
|
||
|
||
case TRIANGULATOR_VERTEXTYPE_REGULAR:
|
||
//if the interior of P lies to the right of vi
|
||
if(Below(v->p,vertices[v->previous].p)) {
|
||
//if helper(ei-1) is a merge vertex
|
||
if(vertextypes[helpers[v->previous]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
|
||
//Insert the diagonal connecting vi to helper(ei-1) in D.
|
||
AddDiagonal(vertices,&newnumvertices,vindex,helpers[v->previous],
|
||
vertextypes, edgeTreeIterators, &edgeTree, helpers);
|
||
vindex2 = newnumvertices-2;
|
||
v2 = &(vertices[vindex2]);
|
||
}
|
||
//Delete ei-1 from T.
|
||
edgeTree.erase(edgeTreeIterators[v->previous]);
|
||
//Insert ei in T and set helper(ei) to vi.
|
||
newedge.p1 = v2->p;
|
||
newedge.p2 = vertices[v2->next].p;
|
||
newedge.index = vindex2;
|
||
edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
|
||
helpers[vindex2] = vindex;
|
||
} else {
|
||
//Search in T to find the edge ej directly left of vi.
|
||
newedge.p1 = v->p;
|
||
newedge.p2 = v->p;
|
||
edgeIter = edgeTree.lower_bound(newedge);
|
||
if(edgeIter == edgeTree.front()) {
|
||
error = true;
|
||
break;
|
||
}
|
||
edgeIter=edgeIter->prev();
|
||
//if helper(ej) is a merge vertex
|
||
if(vertextypes[helpers[edgeIter->get().index]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
|
||
//Insert the diagonal connecting vi to helper(e j) in D.
|
||
AddDiagonal(vertices,&newnumvertices,vindex,helpers[edgeIter->get().index],
|
||
vertextypes, edgeTreeIterators, &edgeTree, helpers);
|
||
}
|
||
//helper(e j)<29>vi
|
||
helpers[edgeIter->get().index] = vindex;
|
||
}
|
||
break;
|
||
}
|
||
|
||
if(error) break;
|
||
}
|
||
|
||
char *used = new char[newnumvertices];
|
||
memset(used,0,newnumvertices*sizeof(char));
|
||
|
||
if(!error) {
|
||
//return result
|
||
long size;
|
||
TriangulatorPoly mpoly;
|
||
for(i=0;i<newnumvertices;i++) {
|
||
if(used[i]) continue;
|
||
v = &(vertices[i]);
|
||
vnext = &(vertices[v->next]);
|
||
size = 1;
|
||
while(vnext!=v) {
|
||
vnext = &(vertices[vnext->next]);
|
||
size++;
|
||
}
|
||
mpoly.Init(size);
|
||
v = &(vertices[i]);
|
||
mpoly[0] = v->p;
|
||
vnext = &(vertices[v->next]);
|
||
size = 1;
|
||
used[i] = 1;
|
||
used[v->next] = 1;
|
||
while(vnext!=v) {
|
||
mpoly[size] = vnext->p;
|
||
used[vnext->next] = 1;
|
||
vnext = &(vertices[vnext->next]);
|
||
size++;
|
||
}
|
||
monotonePolys->push_back(mpoly);
|
||
}
|
||
}
|
||
|
||
//cleanup
|
||
delete [] vertices;
|
||
delete [] priority;
|
||
delete [] vertextypes;
|
||
delete [] edgeTreeIterators;
|
||
delete [] helpers;
|
||
delete [] used;
|
||
|
||
if(error) {
|
||
return 0;
|
||
} else {
|
||
return 1;
|
||
}
|
||
}
|
||
|
||
//adds a diagonal to the doubly-connected list of vertices
|
||
void TriangulatorPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
|
||
char *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators,
|
||
Set<ScanLineEdge> *edgeTree, long *helpers)
|
||
{
|
||
long newindex1,newindex2;
|
||
|
||
newindex1 = *numvertices;
|
||
(*numvertices)++;
|
||
newindex2 = *numvertices;
|
||
(*numvertices)++;
|
||
|
||
vertices[newindex1].p = vertices[index1].p;
|
||
vertices[newindex2].p = vertices[index2].p;
|
||
|
||
vertices[newindex2].next = vertices[index2].next;
|
||
vertices[newindex1].next = vertices[index1].next;
|
||
|
||
vertices[vertices[index2].next].previous = newindex2;
|
||
vertices[vertices[index1].next].previous = newindex1;
|
||
|
||
vertices[index1].next = newindex2;
|
||
vertices[newindex2].previous = index1;
|
||
|
||
vertices[index2].next = newindex1;
|
||
vertices[newindex1].previous = index2;
|
||
|
||
//update all relevant structures
|
||
vertextypes[newindex1] = vertextypes[index1];
|
||
edgeTreeIterators[newindex1] = edgeTreeIterators[index1];
|
||
helpers[newindex1] = helpers[index1];
|
||
if(edgeTreeIterators[newindex1] != NULL)
|
||
edgeTreeIterators[newindex1]->get().index = newindex1;
|
||
vertextypes[newindex2] = vertextypes[index2];
|
||
edgeTreeIterators[newindex2] = edgeTreeIterators[index2];
|
||
helpers[newindex2] = helpers[index2];
|
||
if(edgeTreeIterators[newindex2] != NULL)
|
||
edgeTreeIterators[newindex2]->get().index = newindex2;
|
||
}
|
||
|
||
bool TriangulatorPartition::Below(Vector2 &p1, Vector2 &p2) {
|
||
if(p1.y < p2.y) return true;
|
||
else if(p1.y == p2.y) {
|
||
if(p1.x < p2.x) return true;
|
||
}
|
||
return false;
|
||
}
|
||
|
||
|
||
|
||
|
||
|
||
//sorts in the falling order of y values, if y is equal, x is used instead
|
||
bool TriangulatorPartition::VertexSorter::operator() (long index1, long index2) const {
|
||
if(vertices[index1].p.y > vertices[index2].p.y) return true;
|
||
else if(vertices[index1].p.y == vertices[index2].p.y) {
|
||
if(vertices[index1].p.x > vertices[index2].p.x) return true;
|
||
}
|
||
return false;
|
||
}
|
||
|
||
bool TriangulatorPartition::ScanLineEdge::IsConvex(const Vector2& p1, const Vector2& p2, const Vector2& p3) const {
|
||
real_t tmp;
|
||
tmp = (p3.y-p1.y)*(p2.x-p1.x)-(p3.x-p1.x)*(p2.y-p1.y);
|
||
if(tmp>0) return 1;
|
||
else return 0;
|
||
}
|
||
|
||
bool TriangulatorPartition::ScanLineEdge::operator < (const ScanLineEdge & other) const {
|
||
if(other.p1.y == other.p2.y) {
|
||
if(p1.y == p2.y) {
|
||
if(p1.y < other.p1.y) return true;
|
||
else return false;
|
||
}
|
||
if(IsConvex(p1,p2,other.p1)) return true;
|
||
else return false;
|
||
} else if(p1.y == p2.y) {
|
||
if(IsConvex(other.p1,other.p2,p1)) return false;
|
||
else return true;
|
||
} else if(p1.y < other.p1.y) {
|
||
if(IsConvex(other.p1,other.p2,p1)) return false;
|
||
else return true;
|
||
} else {
|
||
if(IsConvex(p1,p2,other.p1)) return true;
|
||
else return false;
|
||
}
|
||
}
|
||
|
||
//triangulates monotone polygon
|
||
//O(n) time, O(n) space complexity
|
||
int TriangulatorPartition::TriangulateMonotone(TriangulatorPoly *inPoly, List<TriangulatorPoly> *triangles) {
|
||
long i,i2,j,topindex,bottomindex,leftindex,rightindex,vindex;
|
||
Vector2 *points;
|
||
long numpoints;
|
||
TriangulatorPoly triangle;
|
||
|
||
numpoints = inPoly->GetNumPoints();
|
||
points = inPoly->GetPoints();
|
||
|
||
//trivial calses
|
||
if(numpoints < 3) return 0;
|
||
if(numpoints == 3) {
|
||
triangles->push_back(*inPoly);
|
||
}
|
||
|
||
topindex = 0; bottomindex=0;
|
||
for(i=1;i<numpoints;i++) {
|
||
if(Below(points[i],points[bottomindex])) bottomindex = i;
|
||
if(Below(points[topindex],points[i])) topindex = i;
|
||
}
|
||
|
||
//check if the poly is really monotone
|
||
i = topindex;
|
||
while(i!=bottomindex) {
|
||
i2 = i+1; if(i2>=numpoints) i2 = 0;
|
||
if(!Below(points[i2],points[i])) return 0;
|
||
i = i2;
|
||
}
|
||
i = bottomindex;
|
||
while(i!=topindex) {
|
||
i2 = i+1; if(i2>=numpoints) i2 = 0;
|
||
if(!Below(points[i],points[i2])) return 0;
|
||
i = i2;
|
||
}
|
||
|
||
char *vertextypes = new char[numpoints];
|
||
long *priority = new long[numpoints];
|
||
|
||
//merge left and right vertex chains
|
||
priority[0] = topindex;
|
||
vertextypes[topindex] = 0;
|
||
leftindex = topindex+1; if(leftindex>=numpoints) leftindex = 0;
|
||
rightindex = topindex-1; if(rightindex<0) rightindex = numpoints-1;
|
||
for(i=1;i<(numpoints-1);i++) {
|
||
if(leftindex==bottomindex) {
|
||
priority[i] = rightindex;
|
||
rightindex--; if(rightindex<0) rightindex = numpoints-1;
|
||
vertextypes[priority[i]] = -1;
|
||
} else if(rightindex==bottomindex) {
|
||
priority[i] = leftindex;
|
||
leftindex++; if(leftindex>=numpoints) leftindex = 0;
|
||
vertextypes[priority[i]] = 1;
|
||
} else {
|
||
if(Below(points[leftindex],points[rightindex])) {
|
||
priority[i] = rightindex;
|
||
rightindex--; if(rightindex<0) rightindex = numpoints-1;
|
||
vertextypes[priority[i]] = -1;
|
||
} else {
|
||
priority[i] = leftindex;
|
||
leftindex++; if(leftindex>=numpoints) leftindex = 0;
|
||
vertextypes[priority[i]] = 1;
|
||
}
|
||
}
|
||
}
|
||
priority[i] = bottomindex;
|
||
vertextypes[bottomindex] = 0;
|
||
|
||
long *stack = new long[numpoints];
|
||
long stackptr = 0;
|
||
|
||
stack[0] = priority[0];
|
||
stack[1] = priority[1];
|
||
stackptr = 2;
|
||
|
||
//for each vertex from top to bottom trim as many triangles as possible
|
||
for(i=2;i<(numpoints-1);i++) {
|
||
vindex = priority[i];
|
||
if(vertextypes[vindex]!=vertextypes[stack[stackptr-1]]) {
|
||
for(j=0;j<(stackptr-1);j++) {
|
||
if(vertextypes[vindex]==1) {
|
||
triangle.Triangle(points[stack[j+1]],points[stack[j]],points[vindex]);
|
||
} else {
|
||
triangle.Triangle(points[stack[j]],points[stack[j+1]],points[vindex]);
|
||
}
|
||
triangles->push_back(triangle);
|
||
}
|
||
stack[0] = priority[i-1];
|
||
stack[1] = priority[i];
|
||
stackptr = 2;
|
||
} else {
|
||
stackptr--;
|
||
while(stackptr>0) {
|
||
if(vertextypes[vindex]==1) {
|
||
if(IsConvex(points[vindex],points[stack[stackptr-1]],points[stack[stackptr]])) {
|
||
triangle.Triangle(points[vindex],points[stack[stackptr-1]],points[stack[stackptr]]);
|
||
triangles->push_back(triangle);
|
||
stackptr--;
|
||
} else {
|
||
break;
|
||
}
|
||
} else {
|
||
if(IsConvex(points[vindex],points[stack[stackptr]],points[stack[stackptr-1]])) {
|
||
triangle.Triangle(points[vindex],points[stack[stackptr]],points[stack[stackptr-1]]);
|
||
triangles->push_back(triangle);
|
||
stackptr--;
|
||
} else {
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
stackptr++;
|
||
stack[stackptr] = vindex;
|
||
stackptr++;
|
||
}
|
||
}
|
||
vindex = priority[i];
|
||
for(j=0;j<(stackptr-1);j++) {
|
||
if(vertextypes[stack[j+1]]==1) {
|
||
triangle.Triangle(points[stack[j]],points[stack[j+1]],points[vindex]);
|
||
} else {
|
||
triangle.Triangle(points[stack[j+1]],points[stack[j]],points[vindex]);
|
||
}
|
||
triangles->push_back(triangle);
|
||
}
|
||
|
||
delete [] priority;
|
||
delete [] vertextypes;
|
||
delete [] stack;
|
||
|
||
return 1;
|
||
}
|
||
|
||
int TriangulatorPartition::Triangulate_MONO(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles) {
|
||
List<TriangulatorPoly> monotone;
|
||
List<TriangulatorPoly>::Element* iter;
|
||
|
||
if(!MonotonePartition(inpolys,&monotone)) return 0;
|
||
for(iter = monotone.front(); iter;iter=iter->next()) {
|
||
if(!TriangulateMonotone(&(iter->get()),triangles)) return 0;
|
||
}
|
||
return 1;
|
||
}
|
||
|
||
int TriangulatorPartition::Triangulate_MONO(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) {
|
||
List<TriangulatorPoly> polys;
|
||
polys.push_back(*poly);
|
||
|
||
return Triangulate_MONO(&polys, triangles);
|
||
}
|