godot/core/math/triangulator.h

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//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