New Navigation & Pathfinding support for 2D

-Added Navigation & NavigationPolygon nodes
-Added corresponding visual editor
-New pathfinding algorithm is modern and fast!
-Similar API to 3D Pathfinding (more coherent)

6 files changed, 1892 insertions, 0 deletions

diff --git a/core/bind/core_bind.cpp b/core/bind/core_bind.cpp
index 0c5d21b4f6..a03fd7fe4a 100644
--- a/core/bind/core_bind.cpp
+++ b/core/bind/core_bind.cpp
@@ -838,6 +838,12 @@ Variant _Geometry::segment_intersects_triangle( const Vector3& p_from, const Vec
 		return Variant();
 
 }
+
+bool _Geometry::point_is_inside_triangle(const Vector2& s, const Vector2& a, const Vector2& b, const Vector2& c) const {
+
+	return Geometry::is_point_in_triangle(s,a,b,c);
+}
+
 DVector<Vector3> _Geometry::segment_intersects_sphere( const Vector3& p_from, const Vector3& p_to, const Vector3& p_sphere_pos,real_t p_sphere_radius) {
 
 	DVector<Vector3> r;
@@ -938,6 +944,7 @@ void _Geometry::_bind_methods() {
 	ObjectTypeDB::bind_method(_MD("segment_intersects_sphere","from","to","spos","sradius"),&_Geometry::segment_intersects_sphere);
 	ObjectTypeDB::bind_method(_MD("segment_intersects_cylinder","from","to","height","radius"),&_Geometry::segment_intersects_cylinder);
 	ObjectTypeDB::bind_method(_MD("segment_intersects_convex","from","to","planes"),&_Geometry::segment_intersects_convex);
+	ObjectTypeDB::bind_method(_MD("point_is_inside_triangle","point","a","b","c"),&_Geometry::point_is_inside_triangle);
 
 	ObjectTypeDB::bind_method(_MD("triangulate_polygon","polygon"),&_Geometry::triangulate_polygon);
 
diff --git a/core/bind/core_bind.h b/core/bind/core_bind.h
index 12a4ae86eb..f5043ba71f 100644
--- a/core/bind/core_bind.h
+++ b/core/bind/core_bind.h
@@ -248,6 +248,8 @@ public:
 	Vector3 get_closest_point_to_segment(const Vector3& p_point, const Vector3& p_a,const Vector3& p_b);
 	Variant ray_intersects_triangle( const Vector3& p_from, const Vector3& p_dir, const Vector3& p_v0,const Vector3& p_v1,const Vector3& p_v2);
 	Variant segment_intersects_triangle( const Vector3& p_from, const Vector3& p_to, const Vector3& p_v0,const Vector3& p_v1,const Vector3& p_v2);
+	bool point_is_inside_triangle(const Vector2& s, const Vector2& a, const Vector2& b, const Vector2& c) const;
+
 	DVector<Vector3> segment_intersects_sphere( const Vector3& p_from, const Vector3& p_to, const Vector3& p_sphere_pos,real_t p_sphere_radius);
 	DVector<Vector3> segment_intersects_cylinder( const Vector3& p_from, const Vector3& p_to, float p_height,float p_radius);
 	DVector<Vector3> segment_intersects_convex(const Vector3& p_from, const Vector3& p_to,const Vector<Plane>& p_planes);
diff --git a/core/dvector.h b/core/dvector.h
index 72661882cd..29be417844 100644
--- a/core/dvector.h
+++ b/core/dvector.h
@@ -262,6 +262,23 @@ public:
 			w[bs+i]=r[i];
 	}
 
+
+	Error insert(int p_pos,const T& p_val) {
+
+		int s=size();
+		ERR_FAIL_INDEX_V(p_pos,s+1,ERR_INVALID_PARAMETER);
+		resize(s+1);
+		{
+			Write w = write();
+			for (int i=s;i>p_pos;i--)
+				w[i]=w[i-1];
+			w[p_pos]=p_val;
+		}
+
+		return OK;
+	}
+
+
 	bool is_locked() const { return mem.is_locked(); }
 	
 	inline const T operator[](int p_index) const;
diff --git a/core/math/geometry.h b/core/math/geometry.h
index 81530e30c0..7e0cc01a22 100644
--- a/core/math/geometry.h
+++ b/core/math/geometry.h
@@ -511,6 +511,20 @@ public:
 		else
 			return p_segment[0]+n*d; // inside
 	}
+
+	static bool is_point_in_triangle(const Vector2& s, const Vector2& a, const Vector2& b, const Vector2& c)
+	{
+	    int as_x = s.x-a.x;
+	    int as_y = s.y-a.y;
+
+	    bool s_ab = (b.x-a.x)*as_y-(b.y-a.y)*as_x > 0;
+
+	    if((c.x-a.x)*as_y-(c.y-a.y)*as_x > 0 == s_ab) return false;
+
+	    if((c.x-b.x)*(s.y-b.y)-(c.y-b.y)*(s.x-b.x) > 0 != s_ab) return false;
+
+	    return true;
+	}
 	static Vector2 get_closest_point_to_segment_uncapped_2d(const Vector2& p_point, const Vector2 *p_segment) {
 
 		Vector2 p=p_point-p_segment[0];
diff --git a/core/math/triangulator.cpp b/core/math/triangulator.cpp
new file mode 100644
index 0000000000..6be1cdb330
--- /dev/null
+++ b/core/math/triangulator.cpp
@@ -0,0 +1,1543 @@
+//Copyright (C) 2011 by Ivan Fratric
+//
+//Permission is hereby granted, free of charge, to any person obtaining a copy
+//of this software and associated documentation files (the "Software"), to deal
+//in the Software without restriction, including without limitation the rights
+//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//copies of the Software, and to permit persons to whom the Software is
+//furnished to do so, subject to the following conditions:
+//
+//The above copyright notice and this permission notice shall be included in
+//all copies or substantial portions of the Software.
+//
+//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+//THE SOFTWARE.
+
+
+#include <stdio.h>
+#include <string.h>
+#include <math.h>
+#include <algorithm>
+#include "triangulator.h"
+using namespace std;
+
+#define TRIANGULATOR_VERTEXTYPE_REGULAR 0
+#define TRIANGULATOR_VERTEXTYPE_START 1
+#define TRIANGULATOR_VERTEXTYPE_END 2
+#define TRIANGULATOR_VERTEXTYPE_SPLIT 3
+#define TRIANGULATOR_VERTEXTYPE_MERGE 4
+
+TriangulatorPoly::TriangulatorPoly() {
+	hole = false;
+	numpoints = 0;
+	points = NULL;
+}
+
+TriangulatorPoly::~TriangulatorPoly() {
+	if(points) delete [] points;
+}
+
+void TriangulatorPoly::Clear() {
+	if(points) delete [] points;
+	hole = false;
+	numpoints = 0;
+	points = NULL;
+}
+
+void TriangulatorPoly::Init(long numpoints) {
+	Clear();
+	this->numpoints = numpoints;
+	points = new Vector2[numpoints];
+}
+
+void TriangulatorPoly::Triangle(Vector2 &p1, Vector2 &p2, Vector2 &p3) {
+	Init(3);
+	points[0] = p1;
+	points[1] = p2;
+	points[2] = p3;
+}
+
+TriangulatorPoly::TriangulatorPoly(const TriangulatorPoly &src) {
+	hole = src.hole;
+	numpoints = src.numpoints;
+	points = new Vector2[numpoints];
+	memcpy(points, src.points, numpoints*sizeof(Vector2));
+}
+
+TriangulatorPoly& TriangulatorPoly::operator=(const TriangulatorPoly &src) {
+	Clear();
+	hole = src.hole;
+	numpoints = src.numpoints;
+	points = new Vector2[numpoints];
+	memcpy(points, src.points, numpoints*sizeof(Vector2));
+	return *this;
+}
+
+int TriangulatorPoly::GetOrientation() {
+	long i1,i2;
+	real_t area = 0;
+	for(i1=0; i1<numpoints; i1++) {
+		i2 = i1+1;
+		if(i2 == numpoints) i2 = 0;
+		area += points[i1].x * points[i2].y - points[i1].y * points[i2].x;
+	}
+	if(area>0) return TRIANGULATOR_CCW;
+	if(area<0) return TRIANGULATOR_CW;
+	return 0;
+}
+
+void TriangulatorPoly::SetOrientation(int orientation) {
+	int polyorientation = GetOrientation();
+	if(polyorientation&&(polyorientation!=orientation)) {
+		Invert();
+	}
+}
+
+void TriangulatorPoly::Invert() {
+	long i;
+	Vector2 *invpoints;
+
+	invpoints = new Vector2[numpoints];
+	for(i=0;i<numpoints;i++) {
+		invpoints[i] = points[numpoints-i-1];
+	}
+
+	delete [] points;
+	points = invpoints;
+}
+
+Vector2 TriangulatorPartition::Normalize(const Vector2 &p) {
+	Vector2 r;
+	real_t n = sqrt(p.x*p.x + p.y*p.y);
+	if(n!=0) {
+		r = p/n;
+	} else {
+		r.x = 0;
+		r.y = 0;
+	}
+	return r;
+}
+
+real_t TriangulatorPartition::Distance(const Vector2 &p1, const Vector2 &p2) {
+	real_t dx,dy;
+	dx = p2.x - p1.x;
+	dy = p2.y - p1.y;
+	return(sqrt(dx*dx + dy*dy));
+}
+
+//checks if two lines intersect
+int TriangulatorPartition::Intersects(Vector2 &p11, Vector2 &p12, Vector2 &p21, Vector2 &p22) {
+	if((p11.x == p21.x)&&(p11.y == p21.y)) return 0;
+	if((p11.x == p22.x)&&(p11.y == p22.y)) return 0;
+	if((p12.x == p21.x)&&(p12.y == p21.y)) return 0;
+	if((p12.x == p22.x)&&(p12.y == p22.y)) return 0;
+
+	Vector2 v1ort,v2ort,v;
+	real_t dot11,dot12,dot21,dot22;
+
+	v1ort.x = p12.y-p11.y;
+	v1ort.y = p11.x-p12.x;
+
+	v2ort.x = p22.y-p21.y;
+	v2ort.y = p21.x-p22.x;
+
+	v = p21-p11;
+	dot21 = v.x*v1ort.x + v.y*v1ort.y;
+	v = p22-p11;
+	dot22 = v.x*v1ort.x + v.y*v1ort.y;
+
+	v = p11-p21;
+	dot11 = v.x*v2ort.x + v.y*v2ort.y;
+	v = p12-p21;
+	dot12 = v.x*v2ort.x + v.y*v2ort.y;
+
+	if(dot11*dot12>0) return 0;
+	if(dot21*dot22>0) return 0;
+
+	return 1;
+}
+
+//removes holes from inpolys by merging them with non-holes
+int TriangulatorPartition::RemoveHoles(list<TriangulatorPoly> *inpolys, list<TriangulatorPoly> *outpolys) {
+	list<TriangulatorPoly> polys;
+	list<TriangulatorPoly>::iterator holeiter,polyiter,iter,iter2;
+	long i,i2,holepointindex,polypointindex;
+	Vector2 holepoint,polypoint,bestpolypoint;
+	Vector2 linep1,linep2;
+	Vector2 v1,v2;
+	TriangulatorPoly newpoly;
+	bool hasholes;
+	bool pointvisible;
+	bool pointfound;
+
+	//check for trivial case (no holes)
+	hasholes = false;
+	for(iter = inpolys->begin(); iter!=inpolys->end(); iter++) {
+		if(iter->IsHole()) {
+			hasholes = true;
+			break;
+		}
+	}
+	if(!hasholes) {
+		for(iter = inpolys->begin(); iter!=inpolys->end(); iter++) {
+			outpolys->push_back(*iter);
+		}
+		return 1;
+	}
+
+	polys = *inpolys;
+
+	while(1) {
+		//find the hole point with the largest x
+		hasholes = false;
+		for(iter = polys.begin(); iter!=polys.end(); iter++) {
+			if(!iter->IsHole()) continue;
+
+			if(!hasholes) {
+				hasholes = true;
+				holeiter = iter;
+				holepointindex = 0;
+			}
+
+			for(i=0; i < iter->GetNumPoints(); i++) {
+				if(iter->GetPoint(i).x > holeiter->GetPoint(holepointindex).x) {
+					holeiter = iter;
+					holepointindex = i;
+				}
+			}
+		}
+		if(!hasholes) break;
+		holepoint = holeiter->GetPoint(holepointindex);
+
+		pointfound = false;
+		for(iter = polys.begin(); iter!=polys.end(); iter++) {
+			if(iter->IsHole()) continue;
+			for(i=0; i < iter->GetNumPoints(); i++) {
+				if(iter->GetPoint(i).x <= holepoint.x) continue;
+				if(!InCone(iter->GetPoint((i+iter->GetNumPoints()-1)%(iter->GetNumPoints())),
+					   iter->GetPoint(i),
+					   iter->GetPoint((i+1)%(iter->GetNumPoints())),
+					   holepoint))
+					continue;
+				polypoint = iter->GetPoint(i);
+				if(pointfound) {
+					v1 = Normalize(polypoint-holepoint);
+					v2 = Normalize(bestpolypoint-holepoint);
+					if(v2.x > v1.x) continue;
+				}
+				pointvisible = true;
+				for(iter2 = polys.begin(); iter2!=polys.end(); iter2++) {
+					if(iter2->IsHole()) continue;
+					for(i2=0; i2 < iter2->GetNumPoints(); i2++) {
+						linep1 = iter2->GetPoint(i2);
+						linep2 = iter2->GetPoint((i2+1)%(iter2->GetNumPoints()));
+						if(Intersects(holepoint,polypoint,linep1,linep2)) {
+							pointvisible = false;
+							break;
+						}
+					}
+					if(!pointvisible) break;
+				}
+				if(pointvisible) {
+					pointfound = true;
+					bestpolypoint = polypoint;
+					polyiter = iter;
+					polypointindex = i;
+				}
+			}
+		}
+
+		if(!pointfound) return 0;
+
+		newpoly.Init(holeiter->GetNumPoints() + polyiter->GetNumPoints() + 2);
+		i2 = 0;
+		for(i=0;i<=polypointindex;i++) {
+			newpoly[i2] = polyiter->GetPoint(i);
+			i2++;
+		}
+		for(i=0;i<=holeiter->GetNumPoints();i++) {
+			newpoly[i2] = holeiter->GetPoint((i+holepointindex)%holeiter->GetNumPoints());
+			i2++;
+		}
+		for(i=polypointindex;i<polyiter->GetNumPoints();i++) {
+			newpoly[i2] = polyiter->GetPoint(i);
+			i2++;
+		}
+
+		polys.erase(holeiter);
+		polys.erase(polyiter);
+		polys.push_back(newpoly);
+	}
+
+	for(iter = polys.begin(); iter!=polys.end(); iter++) {
+		outpolys->push_back(*iter);
+	}
+
+	return 1;
+}
+
+bool TriangulatorPartition::IsConvex(Vector2& p1, Vector2& p2, Vector2& p3) {
+	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::IsReflex(Vector2& p1, Vector2& p2, Vector2& p3) {
+	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::IsInside(Vector2& p1, Vector2& p2, Vector2& p3, Vector2 &p) {
+	if(IsConvex(p1,p,p2)) return false;
+	if(IsConvex(p2,p,p3)) return false;
+	if(IsConvex(p3,p,p1)) return false;
+	return true;
+}
+
+bool TriangulatorPartition::InCone(Vector2 &p1, Vector2 &p2, Vector2 &p3, Vector2 &p) {
+	bool convex;
+
+	convex = IsConvex(p1,p2,p3);
+
+	if(convex) {
+		if(!IsConvex(p1,p2,p)) return false;
+		if(!IsConvex(p2,p3,p)) return false;
+		return true;
+	} else {
+		if(IsConvex(p1,p2,p)) return true;
+		if(IsConvex(p2,p3,p)) return true;
+		return false;
+	}
+}
+
+bool TriangulatorPartition::InCone(PartitionVertex *v, Vector2 &p) {
+	Vector2 p1,p2,p3;
+
+	p1 = v->previous->p;
+	p2 = v->p;
+	p3 = v->next->p;
+
+	return InCone(p1,p2,p3,p);
+}
+
+void TriangulatorPartition::UpdateVertexReflexity(PartitionVertex *v) {
+	PartitionVertex *v1,*v3;
+	v1 = v->previous;
+	v3 = v->next;
+	v->isConvex = !IsReflex(v1->p,v->p,v3->p);
+}
+
+void TriangulatorPartition::UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices) {
+	long i;
+	PartitionVertex *v1,*v3;
+	Vector2 vec1,vec3;
+
+	v1 = v->previous;
+	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>::iterator iter;
+
+	if(!RemoveHoles(inpolys,&outpolys)) return 0;
+	for(iter=outpolys.begin();iter!=outpolys.end();iter++) {
+		if(!Triangulate_EC(&(*iter),triangles)) return 0;
+	}
+	return 1;
+}
+
+int TriangulatorPartition::ConvexPartition_HM(TriangulatorPoly *poly, list<TriangulatorPoly> *parts) {
+	list<TriangulatorPoly> triangles;
+	list<TriangulatorPoly>::iterator 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.begin(); iter1 != triangles.end(); iter1++) {
+		poly1 = &(*iter1);
+		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 != triangles.end(); iter2++) {
+				if(iter1 == iter2) continue;
+				poly2 = &(*iter2);
+
+				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 = newpoly;
+			poly1 = &(*iter1);
+			i11 = -1;
+
+			continue;
+		}
+	}
+
+	for(iter1 = triangles.begin(); iter1 != triangles.end(); iter1++) {
+		parts->push_back(*iter1);
+	}
+
+	return 1;
+}
+
+int TriangulatorPartition::ConvexPartition_HM(list<TriangulatorPoly> *inpolys, list<TriangulatorPoly> *parts) {
+	list<TriangulatorPoly> outpolys;
+	list<TriangulatorPoly>::iterator iter;
+
+	if(!RemoveHoles(inpolys,&outpolys)) return 0;
+	for(iter=outpolys.begin();iter!=outpolys.end();iter++) {
+		if(!ConvexPartition_HM(&(*iter),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.begin());
+		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->begin()->index1)) return;
+		while((!pairs->empty())&&(pairs->begin()->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>::iterator 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 = pairs->end();
+		lastiter = pairs->end();
+		while(iter!=pairs->begin()) {
+			iter--;
+			if(!IsReflex(vertices[iter->index2].p,vertices[j].p,vertices[k].p)) lastiter = iter;
+			else break;
+		}
+		if(lastiter == pairs->end()) w++;
+		else {
+			if(IsReflex(vertices[k].p,vertices[i].p,vertices[lastiter->index1].p)) w++;
+			else top = lastiter->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>::iterator 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->begin();
+		if((!pairs->empty())&&(!IsReflex(vertices[i].p,vertices[j].p,vertices[iter->index1].p))) {
+			lastiter = iter;
+			while(iter!=pairs->end()) {
+				if(!IsReflex(vertices[i].p,vertices[j].p,vertices[iter->index1].p)) {
+					lastiter = iter;
+					iter++;
+				}
+				else break;
+			}
+			if(IsReflex(vertices[lastiter->index2].p,vertices[k].p,vertices[i].p)) w++;
+			else top = lastiter->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>::iterator iter,iter2;
+	int ret;
+	TriangulatorPoly newpoly;
+	list<long> indices;
+	list<long>::iterator 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.begin());
+		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->end();
+			iter--;
+			j = iter->index2;
+			newdiagonal.index1 = j;
+			newdiagonal.index2 = diagonal.index2;
+			diagonals.push_front(newdiagonal);
+			if((j - diagonal.index1)>1) {
+				if(iter->index1 != iter->index2) {
+					pairs2 = &(dpstates[diagonal.index1][j].pairs);
+					while(1) {
+						if(pairs2->empty()) {
+							ret = 0;
+							break;
+						}
+						iter2 = pairs2->end();
+						iter2--;
+						if(iter->index1 != iter2->index1) pairs2->pop_back();
+						else break;
+					}
+					if(ret == 0) break;
+				}
+				newdiagonal.index1 = diagonal.index1;
+				newdiagonal.index2 = j;
+				diagonals.push_front(newdiagonal);
+			}
+		} else {
+			iter = pairs->begin();
+			j = iter->index1;
+			newdiagonal.index1 = diagonal.index1;
+			newdiagonal.index2 = j;
+			diagonals.push_front(newdiagonal);
+			if((diagonal.index2 - j) > 1) {
+				if(iter->index1 != iter->index2) {
+					pairs2 = &(dpstates[j][diagonal.index2].pairs);
+					while(1) {
+						if(pairs2->empty()) {
+							ret = 0;
+							break;
+						}
+						iter2 = pairs2->begin();
+						if(iter->index2 != iter2->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.begin());
+		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.begin());
+			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->end();
+				iter--;
+				j = iter->index2;
+				if(iter->index1 != iter->index2) ijreal = false;
+			} else {
+				iter = pairs->begin();
+				j = iter->index1;
+				if(iter->index1 != iter->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.begin();iiter!=indices.end();iiter++) {
+			newpoly[k] = vertices[*iiter].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>::iterator 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->begin(); iter != inpolys->end(); iter++) {
+		numvertices += iter->GetNumPoints();
+	}
+
+	maxnumvertices = numvertices*3;
+	vertices = new MonotoneVertex[maxnumvertices];
+	newnumvertices = numvertices;
+
+	polystartindex = 0;
+	for(iter = inpolys->begin(); iter != inpolys->end(); iter++) {
+		poly = &(*iter);
+		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;
+	std::sort(priority,&(priority[numvertices]),VertexSorter(vertices));
+
+	//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>::iterator *edgeTreeIterators,edgeIter;
+	edgeTreeIterators = new set<ScanLineEdge>::iterator[maxnumvertices];
+	pair<set<ScanLineEdge>::iterator,bool> edgeTreeRet;
+	for(i = 0; i<numvertices; i++) edgeTreeIterators[i] = edgeTree.end();
+
+	//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;
+				edgeTreeRet = edgeTree.insert(newedge);
+				edgeTreeIterators[vindex] = edgeTreeRet.first;
+				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.begin()) {
+					error = true;
+					break;
+				}
+				edgeIter--;
+				//Insert the diagonal connecting vi to helper(ej) in D.
+				AddDiagonal(vertices,&newnumvertices,vindex,helpers[edgeIter->index],
+						vertextypes, edgeTreeIterators, &edgeTree, helpers);
+				vindex2 = newnumvertices-2;
+				v2 = &(vertices[vindex2]);
+				//helper(e j)�vi
+				helpers[edgeIter->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;
+				edgeTreeRet = edgeTree.insert(newedge);
+				edgeTreeIterators[vindex2] = edgeTreeRet.first;
+				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.begin()) {
+					error = true;
+					break;
+				}
+				edgeIter--;
+				//if helper(ej) is a merge vertex
+				if(vertextypes[helpers[edgeIter->index]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
+					//Insert the diagonal connecting vi to helper(e j) in D.
+					AddDiagonal(vertices,&newnumvertices,vindex2,helpers[edgeIter->index],
+							vertextypes, edgeTreeIterators, &edgeTree, helpers);
+				}
+				//helper(e j)�vi
+				helpers[edgeIter->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;
+					edgeTreeRet = edgeTree.insert(newedge);
+					edgeTreeIterators[vindex2] = edgeTreeRet.first;
+					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.begin()) {
+						error = true;
+						break;
+					}
+					edgeIter--;
+					//if helper(ej) is a merge vertex
+					if(vertextypes[helpers[edgeIter->index]]==TRIANGULATOR_VERTEXTYPE_MERGE) {
+						//Insert the diagonal connecting vi to helper(e j) in D.
+						AddDiagonal(vertices,&newnumvertices,vindex,helpers[edgeIter->index],
+								vertextypes, edgeTreeIterators, &edgeTree, helpers);
+					}
+					//helper(e j)�vi
+					helpers[edgeIter->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>::iterator *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] != edgeTree->end())
+		edgeTreeIterators[newindex1]->index = newindex1;
+	vertextypes[newindex2] = vertextypes[index2];
+	edgeTreeIterators[newindex2] = edgeTreeIterators[index2];
+	helpers[newindex2] = helpers[index2];
+	if(edgeTreeIterators[newindex2] != edgeTree->end())
+		edgeTreeIterators[newindex2]->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) {
+	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>::iterator iter;
+
+	if(!MonotonePartition(inpolys,&monotone)) return 0;
+	for(iter = monotone.begin(); iter!=monotone.end();iter++) {
+		if(!TriangulateMonotone(&(*iter),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);
+}
diff --git a/core/math/triangulator.h b/core/math/triangulator.h
new file mode 100644
index 0000000000..c34c445892
--- /dev/null
+++ b/core/math/triangulator.h
@@ -0,0 +1,309 @@
+//Copyright (C) 2011 by Ivan Fratric
+//
+//Permission is hereby granted, free of charge, to any person obtaining a copy
+//of this software and associated documentation files (the "Software"), to deal
+//in the Software without restriction, including without limitation the rights
+//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//copies of the Software, and to permit persons to whom the Software is
+//furnished to do so, subject to the following conditions:
+//
+//The above copyright notice and this permission notice shall be included in
+//all copies or substantial portions of the Software.
+//
+//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+//THE SOFTWARE.
+
+#ifndef TRIANGULATOR_H
+#define TRIANGULATOR_H
+
+#include "math_2d.h"
+#include <list>
+#include <set>
+
+//2D point structure
+
+
+#define TRIANGULATOR_CCW 1
+#define TRIANGULATOR_CW -1
+//Polygon implemented as an array of points with a 'hole' flag
+class TriangulatorPoly {
+protected:
+
+
+
+	Vector2 *points;
+	long numpoints;
+	bool hole;
+
+public:
+
+	//constructors/destructors
+	TriangulatorPoly();
+	~TriangulatorPoly();
+
+	TriangulatorPoly(const TriangulatorPoly &src);
+	TriangulatorPoly& operator=(const TriangulatorPoly &src);
+
+	//getters and setters
+	long GetNumPoints() {
+		return numpoints;
+	}
+
+	bool IsHole() {
+		return hole;
+	}
+
+	void SetHole(bool hole) {
+		this->hole = hole;
+	}
+
+	Vector2 &GetPoint(long i) {
+		return points[i];
+	}
+
+	Vector2 *GetPoints() {
+		return points;
+	}
+
+	Vector2& operator[] (int i) {
+		return points[i];
+	}
+
+	//clears the polygon points
+	void Clear();
+
+	//inits the polygon with numpoints vertices
+	void Init(long numpoints);
+
+	//creates a triangle with points p1,p2,p3
+	void Triangle(Vector2 &p1, Vector2 &p2, Vector2 &p3);
+
+	//inverts the orfer of vertices
+	void Invert();
+
+	//returns the orientation of the polygon
+	//possible values:
+	//   Triangulator_CCW : polygon vertices are in counter-clockwise order
+	//   Triangulator_CW : polygon vertices are in clockwise order
+	//       0 : the polygon has no (measurable) area
+	int GetOrientation();
+
+	//sets the polygon orientation
+	//orientation can be
+	//   Triangulator_CCW : sets vertices in counter-clockwise order
+	//   Triangulator_CW : sets vertices in clockwise order
+	void SetOrientation(int orientation);
+};
+
+class TriangulatorPartition {
+protected:
+	struct PartitionVertex {
+		bool isActive;
+		bool isConvex;
+		bool isEar;
+
+		Vector2 p;
+		real_t angle;
+		PartitionVertex *previous;
+		PartitionVertex *next;
+	};
+
+	struct MonotoneVertex {
+		Vector2 p;
+		long previous;
+		long next;
+	};
+
+	class VertexSorter{
+		MonotoneVertex *vertices;
+	public:
+		VertexSorter(MonotoneVertex *v) : vertices(v) {}
+		bool operator() (long index1, long index2);
+	};
+
+	struct Diagonal {
+		long index1;
+		long index2;
+	};
+
+	//dynamic programming state for minimum-weight triangulation
+	struct DPState {
+		bool visible;
+		real_t weight;
+		long bestvertex;
+	};
+
+	//dynamic programming state for convex partitioning
+	struct DPState2 {
+		bool visible;
+		long weight;
+		std::list<Diagonal> pairs;
+	};
+
+	//edge that intersects the scanline
+	struct ScanLineEdge {
+		mutable long index;
+		Vector2 p1;
+		Vector2 p2;
+
+		//determines if the edge is to the left of another edge
+		bool operator< (const ScanLineEdge & other) const;
+
+		bool IsConvex(const Vector2& p1, const Vector2& p2, const Vector2& p3) const;
+	};
+
+	//standard helper functions
+	bool IsConvex(Vector2& p1, Vector2& p2, Vector2& p3);
+	bool IsReflex(Vector2& p1, Vector2& p2, Vector2& p3);
+	bool IsInside(Vector2& p1, Vector2& p2, Vector2& p3, Vector2 &p);
+
+	bool InCone(Vector2 &p1, Vector2 &p2, Vector2 &p3, Vector2 &p);
+	bool InCone(PartitionVertex *v, Vector2 &p);
+
+	int Intersects(Vector2 &p11, Vector2 &p12, Vector2 &p21, Vector2 &p22);
+
+	Vector2 Normalize(const Vector2 &p);
+	real_t Distance(const Vector2 &p1, const Vector2 &p2);
+
+	//helper functions for Triangulate_EC
+	void UpdateVertexReflexity(PartitionVertex *v);
+	void UpdateVertex(PartitionVertex *v,PartitionVertex *vertices, long numvertices);
+
+	//helper functions for ConvexPartition_OPT
+	void UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates);
+	void TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates);
+	void TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates);
+
+	//helper functions for MonotonePartition
+	bool Below(Vector2 &p1, Vector2 &p2);
+	void AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
+			 char *vertextypes, std::set<ScanLineEdge>::iterator *edgeTreeIterators,
+			 std::set<ScanLineEdge> *edgeTree, long *helpers);
+
+	//triangulates a monotone polygon, used in Triangulate_MONO
+	int TriangulateMonotone(TriangulatorPoly *inPoly, std::list<TriangulatorPoly> *triangles);
+
+public:
+
+	//simple heuristic procedure for removing holes from a list of polygons
+	//works by creating a diagonal from the rightmost hole vertex to some visible vertex
+	//time complexity: O(h*(n^2)), h is the number of holes, n is the number of vertices
+	//space complexity: O(n)
+	//params:
+	//   inpolys : a list of polygons that can contain holes
+	//             vertices of all non-hole polys have to be in counter-clockwise order
+	//             vertices of all hole polys have to be in clockwise order
+	//   outpolys : a list of polygons without holes
+	//returns 1 on success, 0 on failure
+	int RemoveHoles(std::list<TriangulatorPoly> *inpolys, std::list<TriangulatorPoly> *outpolys);
+
+	//triangulates a polygon by ear clipping
+	//time complexity O(n^2), n is the number of vertices
+	//space complexity: O(n)
+	//params:
+	//   poly : an input polygon to be triangulated
+	//          vertices have to be in counter-clockwise order
+	//   triangles : a list of triangles (result)
+	//returns 1 on success, 0 on failure
+	int Triangulate_EC(TriangulatorPoly *poly, std::list<TriangulatorPoly> *triangles);
+
+	//triangulates a list of polygons that may contain holes by ear clipping algorithm
+	//first calls RemoveHoles to get rid of the holes, and then Triangulate_EC for each resulting polygon
+	//time complexity: O(h*(n^2)), h is the number of holes, n is the number of vertices
+	//space complexity: O(n)
+	//params:
+	//   inpolys : a list of polygons to be triangulated (can contain holes)
+	//             vertices of all non-hole polys have to be in counter-clockwise order
+	//             vertices of all hole polys have to be in clockwise order
+	//   triangles : a list of triangles (result)
+	//returns 1 on success, 0 on failure
+	int Triangulate_EC(std::list<TriangulatorPoly> *inpolys, std::list<TriangulatorPoly> *triangles);
+
+	//creates an optimal polygon triangulation in terms of minimal edge length
+	//time complexity: O(n^3), n is the number of vertices
+	//space complexity: O(n^2)
+	//params:
+	//   poly : an input polygon to be triangulated
+	//          vertices have to be in counter-clockwise order
+	//   triangles : a list of triangles (result)
+	//returns 1 on success, 0 on failure
+	int Triangulate_OPT(TriangulatorPoly *poly, std::list<TriangulatorPoly> *triangles);
+
+	//triangulates a polygons by firstly partitioning it into monotone polygons
+	//time complexity: O(n*log(n)), n is the number of vertices
+	//space complexity: O(n)
+	//params:
+	//   poly : an input polygon to be triangulated
+	//          vertices have to be in counter-clockwise order
+	//   triangles : a list of triangles (result)
+	//returns 1 on success, 0 on failure
+	int Triangulate_MONO(TriangulatorPoly *poly, std::list<TriangulatorPoly> *triangles);
+
+	//triangulates a list of polygons by firstly partitioning them into monotone polygons
+	//time complexity: O(n*log(n)), n is the number of vertices
+	//space complexity: O(n)
+	//params:
+	//   inpolys : a list of polygons to be triangulated (can contain holes)
+	//             vertices of all non-hole polys have to be in counter-clockwise order
+	//             vertices of all hole polys have to be in clockwise order
+	//   triangles : a list of triangles (result)
+	//returns 1 on success, 0 on failure
+	int Triangulate_MONO(std::list<TriangulatorPoly> *inpolys, std::list<TriangulatorPoly> *triangles);
+
+	//creates a monotone partition of a list of polygons that can contain holes
+	//time complexity: O(n*log(n)), n is the number of vertices
+	//space complexity: O(n)
+	//params:
+	//   inpolys : a list of polygons to be triangulated (can contain holes)
+	//             vertices of all non-hole polys have to be in counter-clockwise order
+	//             vertices of all hole polys have to be in clockwise order
+	//   monotonePolys : a list of monotone polygons (result)
+	//returns 1 on success, 0 on failure
+	int MonotonePartition(std::list<TriangulatorPoly> *inpolys, std::list<TriangulatorPoly> *monotonePolys);
+
+	//partitions a polygon into convex polygons by using Hertel-Mehlhorn algorithm
+	//the algorithm gives at most four times the number of parts as the optimal algorithm
+	//however, in practice it works much better than that and often gives optimal partition
+	//uses triangulation obtained by ear clipping as intermediate result
+	//time complexity O(n^2), n is the number of vertices
+	//space complexity: O(n)
+	//params:
+	//   poly : an input polygon to be partitioned
+	//          vertices have to be in counter-clockwise order
+	//   parts : resulting list of convex polygons
+	//returns 1 on success, 0 on failure
+	int ConvexPartition_HM(TriangulatorPoly *poly, std::list<TriangulatorPoly> *parts);
+
+	//partitions a list of polygons into convex parts by using Hertel-Mehlhorn algorithm
+	//the algorithm gives at most four times the number of parts as the optimal algorithm
+	//however, in practice it works much better than that and often gives optimal partition
+	//uses triangulation obtained by ear clipping as intermediate result
+	//time complexity O(n^2), n is the number of vertices
+	//space complexity: O(n)
+	//params:
+	//   inpolys : an input list of polygons to be partitioned
+	//             vertices of all non-hole polys have to be in counter-clockwise order
+	//             vertices of all hole polys have to be in clockwise order
+	//   parts : resulting list of convex polygons
+	//returns 1 on success, 0 on failure
+	int ConvexPartition_HM(std::list<TriangulatorPoly> *inpolys, std::list<TriangulatorPoly> *parts);
+
+	//optimal convex partitioning (in terms of number of resulting convex polygons)
+	//using the Keil-Snoeyink algorithm
+	//M. Keil, J. Snoeyink, "On the time bound for convex decomposition of simple polygons", 1998
+	//time complexity O(n^3), n is the number of vertices
+	//space complexity: O(n^3)
+	//   poly : an input polygon to be partitioned
+	//          vertices have to be in counter-clockwise order
+	//   parts : resulting list of convex polygons
+	//returns 1 on success, 0 on failure
+	int ConvexPartition_OPT(TriangulatorPoly *poly, std::list<TriangulatorPoly> *parts);
+};
+
+
+#endif