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+//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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+
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+
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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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+
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+#include "triangulator.h"
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+
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+
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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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+
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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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+
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+TriangulatorPoly::~TriangulatorPoly() {
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+ if(points) delete [] points;
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+}
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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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+
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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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+
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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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+
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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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+
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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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+
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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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+
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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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+
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+void TriangulatorPoly::Invert() {
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+ long i;
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+ Vector2 *invpoints;
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+
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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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+
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+ delete [] points;
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+ points = invpoints;
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+}
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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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+
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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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+
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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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+
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+ Vector2 v1ort,v2ort,v;
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+ real_t dot11,dot12,dot21,dot22;
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+
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+ v1ort.x = p12.y-p11.y;
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+ v1ort.y = p11.x-p12.x;
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+
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+ v2ort.x = p22.y-p21.y;
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+ v2ort.y = p21.x-p22.x;
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+
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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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+
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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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+
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+ if(dot11*dot12>0) return 0;
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+ if(dot21*dot22>0) return 0;
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+
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+ return 1;
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+}
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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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+
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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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+
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+ polys = *inpolys;
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+
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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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+
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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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+
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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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+
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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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+
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+ if(!pointfound) return 0;
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+
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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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+
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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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+
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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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+
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+ return 1;
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+}
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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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+
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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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+
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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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+
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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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+
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+ convex = IsConvex(p1,p2,p3);
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+
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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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+
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+bool TriangulatorPartition::InCone(PartitionVertex *v, Vector2 &p) {
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+ Vector2 p1,p2,p3;
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+
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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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+
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+ return InCone(p1,p2,p3,p);
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+}
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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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+
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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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+
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+ v1 = v->previous;
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|
|
+ v3 = v->next;
|
|
|
|
+
|
|
|
|
+ v->isConvex = IsConvex(v1->p,v->p,v3->p);
|
|
|
|
+
|
|
|
|
+ vec1 = Normalize(v1->p - v->p);
|
|
|
|
+ vec3 = Normalize(v3->p - v->p);
|
|
|
|
+ v->angle = vec1.x*vec3.x + vec1.y*vec3.y;
|
|
|
|
+
|
|
|
|
+ if(v->isConvex) {
|
|
|
|
+ v->isEar = true;
|
|
|
|
+ for(i=0;i<numvertices;i++) {
|
|
|
|
+ if((vertices[i].p.x==v->p.x)&&(vertices[i].p.y==v->p.y)) continue;
|
|
|
|
+ if((vertices[i].p.x==v1->p.x)&&(vertices[i].p.y==v1->p.y)) continue;
|
|
|
|
+ if((vertices[i].p.x==v3->p.x)&&(vertices[i].p.y==v3->p.y)) continue;
|
|
|
|
+ if(IsInside(v1->p,v->p,v3->p,vertices[i].p)) {
|
|
|
|
+ v->isEar = false;
|
|
|
|
+ break;
|
|
|
|
+ }
|
|
|
|
+ }
|
|
|
|
+ } else {
|
|
|
|
+ v->isEar = false;
|
|
|
|
+ }
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+//triangulation by ear removal
|
|
|
|
+int TriangulatorPartition::Triangulate_EC(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) {
|
|
|
|
+ long numvertices;
|
|
|
|
+ PartitionVertex *vertices;
|
|
|
|
+ PartitionVertex *ear;
|
|
|
|
+ TriangulatorPoly triangle;
|
|
|
|
+ long i,j;
|
|
|
|
+ bool earfound;
|
|
|
|
+
|
|
|
|
+ if(poly->GetNumPoints() < 3) return 0;
|
|
|
|
+ if(poly->GetNumPoints() == 3) {
|
|
|
|
+ triangles->push_back(*poly);
|
|
|
|
+ return 1;
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ numvertices = poly->GetNumPoints();
|
|
|
|
+
|
|
|
|
+ vertices = new PartitionVertex[numvertices];
|
|
|
|
+ for(i=0;i<numvertices;i++) {
|
|
|
|
+ vertices[i].isActive = true;
|
|
|
|
+ vertices[i].p = poly->GetPoint(i);
|
|
|
|
+ if(i==(numvertices-1)) vertices[i].next=&(vertices[0]);
|
|
|
|
+ else vertices[i].next=&(vertices[i+1]);
|
|
|
|
+ if(i==0) vertices[i].previous = &(vertices[numvertices-1]);
|
|
|
|
+ else vertices[i].previous = &(vertices[i-1]);
|
|
|
|
+ }
|
|
|
|
+ for(i=0;i<numvertices;i++) {
|
|
|
|
+ UpdateVertex(&vertices[i],vertices,numvertices);
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ for(i=0;i<numvertices-3;i++) {
|
|
|
|
+ earfound = false;
|
|
|
|
+ //find the most extruded ear
|
|
|
|
+ for(j=0;j<numvertices;j++) {
|
|
|
|
+ if(!vertices[j].isActive) continue;
|
|
|
|
+ if(!vertices[j].isEar) continue;
|
|
|
|
+ if(!earfound) {
|
|
|
|
+ earfound = true;
|
|
|
|
+ ear = &(vertices[j]);
|
|
|
|
+ } else {
|
|
|
|
+ if(vertices[j].angle > ear->angle) {
|
|
|
|
+ ear = &(vertices[j]);
|
|
|
|
+ }
|
|
|
|
+ }
|
|
|
|
+ }
|
|
|
|
+ if(!earfound) {
|
|
|
|
+ delete [] vertices;
|
|
|
|
+ return 0;
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ triangle.Triangle(ear->previous->p,ear->p,ear->next->p);
|
|
|
|
+ triangles->push_back(triangle);
|
|
|
|
+
|
|
|
|
+ ear->isActive = false;
|
|
|
|
+ ear->previous->next = ear->next;
|
|
|
|
+ ear->next->previous = ear->previous;
|
|
|
|
+
|
|
|
|
+ if(i==numvertices-4) break;
|
|
|
|
+
|
|
|
|
+ UpdateVertex(ear->previous,vertices,numvertices);
|
|
|
|
+ UpdateVertex(ear->next,vertices,numvertices);
|
|
|
|
+ }
|
|
|
|
+ for(i=0;i<numvertices;i++) {
|
|
|
|
+ if(vertices[i].isActive) {
|
|
|
|
+ triangle.Triangle(vertices[i].previous->p,vertices[i].p,vertices[i].next->p);
|
|
|
|
+ triangles->push_back(triangle);
|
|
|
|
+ break;
|
|
|
|
+ }
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ delete [] vertices;
|
|
|
|
+
|
|
|
|
+ return 1;
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+int TriangulatorPartition::Triangulate_EC(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles) {
|
|
|
|
+ List<TriangulatorPoly> outpolys;
|
|
|
|
+ List<TriangulatorPoly>::Element*iter;
|
|
|
|
+
|
|
|
|
+ if(!RemoveHoles(inpolys,&outpolys)) return 0;
|
|
|
|
+ for(iter=outpolys.front();iter;iter=iter->next()) {
|
|
|
|
+ if(!Triangulate_EC(&(iter->get()),triangles)) return 0;
|
|
|
|
+ }
|
|
|
|
+ return 1;
|
|
|
|
+}
|
|
|
|
+
|
|
|
|
+int TriangulatorPartition::ConvexPartition_HM(TriangulatorPoly *poly, List<TriangulatorPoly> *parts) {
|
|
|
|
+ List<TriangulatorPoly> triangles;
|
|
|
|
+ List<TriangulatorPoly>::Element *iter1,*iter2;
|
|
|
|
+ TriangulatorPoly *poly1,*poly2;
|
|
|
|
+ TriangulatorPoly newpoly;
|
|
|
|
+ Vector2 d1,d2,p1,p2,p3;
|
|
|
|
+ long i11,i12,i21,i22,i13,i23,j,k;
|
|
|
|
+ bool isdiagonal;
|
|
|
|
+ long numreflex;
|
|
|
|
+
|
|
|
|
+ //check if the poly is already convex
|
|
|
|
+ numreflex = 0;
|
|
|
|
+ for(i11=0;i11<poly->GetNumPoints();i11++) {
|
|
|
|
+ if(i11==0) i12 = poly->GetNumPoints()-1;
|
|
|
|
+ else i12=i11-1;
|
|
|
|
+ if(i11==(poly->GetNumPoints()-1)) i13=0;
|
|
|
|
+ else i13=i11+1;
|
|
|
|
+ if(IsReflex(poly->GetPoint(i12),poly->GetPoint(i11),poly->GetPoint(i13))) {
|
|
|
|
+ numreflex = 1;
|
|
|
|
+ break;
|
|
|
|
+ }
|
|
|
|
+ }
|
|
|
|
+ if(numreflex == 0) {
|
|
|
|
+ parts->push_back(*poly);
|
|
|
|
+ return 1;
|
|
|
|
+ }
|
|
|
|
+
|
|
|
|
+ if(!Triangulate_EC(poly,&triangles)) return 0;
|
|
|
|
+
|
|
|
|
+ for(iter1 = triangles.front(); iter1 ; iter1=iter1->next()) {
|
|
|
|
+ poly1 = &(iter1->get());
|
|
|
|
+ for(i11=0;i11<poly1->GetNumPoints();i11++) {
|
|
|
|
+ d1 = poly1->GetPoint(i11);
|
|
|
|
+ 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)�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)�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)�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);
|
|
|
|
+}
|