-Removed FuncRef, since Callable makes it obsolete -Removed int_types.h as its obsolete in c++11+ -Changed color names code
306 lines
11 KiB
C++
306 lines
11 KiB
C++
//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 "core/templates/list.h"
|
|
#include "core/math/vector2.h"
|
|
#include "core/templates/set.h"
|
|
|
|
//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;
|
|
};
|
|
|
|
struct VertexSorter{
|
|
mutable MonotoneVertex *vertices;
|
|
bool operator() (long index1, long index2) const;
|
|
};
|
|
|
|
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;
|
|
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, Set<ScanLineEdge>::Element **edgeTreeIterators,
|
|
Set<ScanLineEdge> *edgeTree, long *helpers);
|
|
|
|
//triangulates a monotone polygon, used in Triangulate_MONO
|
|
int TriangulateMonotone(TriangulatorPoly *inPoly, 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(List<TriangulatorPoly> *inpolys, 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, 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(List<TriangulatorPoly> *inpolys, 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, 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, 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(List<TriangulatorPoly> *inpolys, 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(List<TriangulatorPoly> *inpolys, 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, 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(List<TriangulatorPoly> *inpolys, 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, List<TriangulatorPoly> *parts);
|
|
};
|
|
|
|
|
|
#endif
|