307 lines
11 KiB
C++
307 lines
11 KiB
C++
//Copyright (C) 2011 by Ivan Fratric
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//
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//Permission is hereby granted, free of charge, to any person obtaining a copy
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//of this software and associated documentation files (the "Software"), to deal
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//in the Software without restriction, including without limitation the rights
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//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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//copies of the Software, and to permit persons to whom the Software is
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//furnished to do so, subject to the following conditions:
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//
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//The above copyright notice and this permission notice shall be included in
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//all copies or substantial portions of the Software.
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//
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//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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//THE SOFTWARE.
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#ifndef TRIANGULATOR_H
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#define TRIANGULATOR_H
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#include "core/templates/list.h"
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#include "core/math/vector2.h"
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#include "core/templates/set.h"
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//2D point structure
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#define TRIANGULATOR_CCW 1
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#define TRIANGULATOR_CW -1
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//Polygon implemented as an array of points with a 'hole' flag
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class TriangulatorPoly {
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protected:
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Vector2 *points;
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long numpoints;
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bool hole;
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public:
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//constructors/destructors
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TriangulatorPoly();
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~TriangulatorPoly();
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TriangulatorPoly(const TriangulatorPoly &src);
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TriangulatorPoly& operator=(const TriangulatorPoly &src);
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//getters and setters
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long GetNumPoints() {
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return numpoints;
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}
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bool IsHole() {
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return hole;
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}
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void SetHole(bool hole) {
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this->hole = hole;
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}
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Vector2 &GetPoint(long i) {
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return points[i];
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}
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Vector2 *GetPoints() {
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return points;
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}
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Vector2& operator[] (int i) {
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return points[i];
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}
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//clears the polygon points
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void Clear();
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//inits the polygon with numpoints vertices
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void Init(long numpoints);
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//creates a triangle with points p1,p2,p3
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void Triangle(Vector2 &p1, Vector2 &p2, Vector2 &p3);
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//inverts the orfer of vertices
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void Invert();
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//returns the orientation of the polygon
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//possible values:
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// Triangulator_CCW : polygon vertices are in counter-clockwise order
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// Triangulator_CW : polygon vertices are in clockwise order
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// 0 : the polygon has no (measurable) area
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int GetOrientation();
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//sets the polygon orientation
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//orientation can be
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// Triangulator_CCW : sets vertices in counter-clockwise order
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// Triangulator_CW : sets vertices in clockwise order
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void SetOrientation(int orientation);
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};
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class TriangulatorPartition {
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protected:
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struct PartitionVertex {
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bool isActive;
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bool isConvex;
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bool isEar;
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Vector2 p;
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real_t angle;
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PartitionVertex *previous;
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PartitionVertex *next;
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};
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struct MonotoneVertex {
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Vector2 p;
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long previous;
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long next;
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};
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struct VertexSorter{
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mutable MonotoneVertex *vertices;
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bool operator() (long index1, long index2) const;
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};
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struct Diagonal {
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long index1;
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long index2;
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};
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//dynamic programming state for minimum-weight triangulation
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struct DPState {
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bool visible;
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real_t weight;
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long bestvertex;
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};
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//dynamic programming state for convex partitioning
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struct DPState2 {
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bool visible;
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long weight;
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List<Diagonal> pairs;
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};
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//edge that intersects the scanline
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struct ScanLineEdge {
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mutable long index;
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Vector2 p1;
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Vector2 p2;
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//determines if the edge is to the left of another edge
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bool operator< (const ScanLineEdge & other) const;
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bool IsConvex(const Vector2& p1, const Vector2& p2, const Vector2& p3) const;
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};
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//standard helper functions
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bool IsConvex(Vector2& p1, Vector2& p2, Vector2& p3);
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bool IsReflex(Vector2& p1, Vector2& p2, Vector2& p3);
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bool IsInside(Vector2& p1, Vector2& p2, Vector2& p3, Vector2 &p);
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bool InCone(Vector2 &p1, Vector2 &p2, Vector2 &p3, Vector2 &p);
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bool InCone(PartitionVertex *v, Vector2 &p);
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int Intersects(Vector2 &p11, Vector2 &p12, Vector2 &p21, Vector2 &p22);
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Vector2 Normalize(const Vector2 &p);
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real_t Distance(const Vector2 &p1, const Vector2 &p2);
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//helper functions for Triangulate_EC
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void UpdateVertexReflexity(PartitionVertex *v);
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void UpdateVertex(PartitionVertex *v,PartitionVertex *vertices, long numvertices);
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//helper functions for ConvexPartition_OPT
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void UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates);
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void TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates);
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void TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates);
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//helper functions for MonotonePartition
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bool Below(Vector2 &p1, Vector2 &p2);
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void AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
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char *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators,
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Set<ScanLineEdge> *edgeTree, long *helpers);
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//triangulates a monotone polygon, used in Triangulate_MONO
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int TriangulateMonotone(TriangulatorPoly *inPoly, List<TriangulatorPoly> *triangles);
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public:
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//simple heuristic procedure for removing holes from a list of polygons
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//works by creating a diagonal from the rightmost hole vertex to some visible vertex
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//time complexity: O(h*(n^2)), h is the number of holes, n is the number of vertices
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//space complexity: O(n)
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//params:
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// inpolys : a list of polygons that can contain holes
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// vertices of all non-hole polys have to be in counter-clockwise order
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// vertices of all hole polys have to be in clockwise order
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// outpolys : a list of polygons without holes
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//returns 1 on success, 0 on failure
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int RemoveHoles(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *outpolys);
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//triangulates a polygon by ear clipping
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//time complexity O(n^2), n is the number of vertices
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//space complexity: O(n)
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//params:
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// poly : an input polygon to be triangulated
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// vertices have to be in counter-clockwise order
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// triangles : a list of triangles (result)
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//returns 1 on success, 0 on failure
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int Triangulate_EC(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles);
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//triangulates a list of polygons that may contain holes by ear clipping algorithm
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//first calls RemoveHoles to get rid of the holes, and then Triangulate_EC for each resulting polygon
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//time complexity: O(h*(n^2)), h is the number of holes, n is the number of vertices
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//space complexity: O(n)
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//params:
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// inpolys : a list of polygons to be triangulated (can contain holes)
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// vertices of all non-hole polys have to be in counter-clockwise order
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// vertices of all hole polys have to be in clockwise order
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// triangles : a list of triangles (result)
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//returns 1 on success, 0 on failure
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int Triangulate_EC(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles);
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//creates an optimal polygon triangulation in terms of minimal edge length
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//time complexity: O(n^3), n is the number of vertices
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//space complexity: O(n^2)
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//params:
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// poly : an input polygon to be triangulated
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// vertices have to be in counter-clockwise order
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// triangles : a list of triangles (result)
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//returns 1 on success, 0 on failure
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int Triangulate_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles);
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//triangulates a polygons by firstly partitioning it into monotone polygons
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//time complexity: O(n*log(n)), n is the number of vertices
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//space complexity: O(n)
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//params:
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// poly : an input polygon to be triangulated
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// vertices have to be in counter-clockwise order
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// triangles : a list of triangles (result)
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//returns 1 on success, 0 on failure
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int Triangulate_MONO(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles);
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//triangulates a list of polygons by firstly partitioning them into monotone polygons
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//time complexity: O(n*log(n)), n is the number of vertices
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//space complexity: O(n)
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//params:
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// inpolys : a list of polygons to be triangulated (can contain holes)
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// vertices of all non-hole polys have to be in counter-clockwise order
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// vertices of all hole polys have to be in clockwise order
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// triangles : a list of triangles (result)
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//returns 1 on success, 0 on failure
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int Triangulate_MONO(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles);
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//creates a monotone partition of a list of polygons that can contain holes
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//time complexity: O(n*log(n)), n is the number of vertices
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//space complexity: O(n)
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//params:
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// inpolys : a list of polygons to be triangulated (can contain holes)
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// vertices of all non-hole polys have to be in counter-clockwise order
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// vertices of all hole polys have to be in clockwise order
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// monotonePolys : a list of monotone polygons (result)
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//returns 1 on success, 0 on failure
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int MonotonePartition(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *monotonePolys);
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//partitions a polygon into convex polygons by using Hertel-Mehlhorn algorithm
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//the algorithm gives at most four times the number of parts as the optimal algorithm
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//however, in practice it works much better than that and often gives optimal partition
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//uses triangulation obtained by ear clipping as intermediate result
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//time complexity O(n^2), n is the number of vertices
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//space complexity: O(n)
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//params:
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// poly : an input polygon to be partitioned
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// vertices have to be in counter-clockwise order
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// parts : resulting list of convex polygons
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//returns 1 on success, 0 on failure
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int ConvexPartition_HM(TriangulatorPoly *poly, List<TriangulatorPoly> *parts);
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//partitions a list of polygons into convex parts by using Hertel-Mehlhorn algorithm
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//the algorithm gives at most four times the number of parts as the optimal algorithm
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//however, in practice it works much better than that and often gives optimal partition
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//uses triangulation obtained by ear clipping as intermediate result
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//time complexity O(n^2), n is the number of vertices
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//space complexity: O(n)
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//params:
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// inpolys : an input list of polygons to be partitioned
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// vertices of all non-hole polys have to be in counter-clockwise order
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// vertices of all hole polys have to be in clockwise order
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// parts : resulting list of convex polygons
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//returns 1 on success, 0 on failure
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int ConvexPartition_HM(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *parts);
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//optimal convex partitioning (in terms of number of resulting convex polygons)
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//using the Keil-Snoeyink algorithm
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//M. Keil, J. Snoeyink, "On the time bound for convex decomposition of simple polygons", 1998
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//time complexity O(n^3), n is the number of vertices
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//space complexity: O(n^3)
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// poly : an input polygon to be partitioned
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// vertices have to be in counter-clockwise order
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// parts : resulting list of convex polygons
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//returns 1 on success, 0 on failure
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int ConvexPartition_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *parts);
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};
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#endif
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