virtualx-engine/thirdparty/misc/polypartition.h
reduz 746dddc067 Replace most uses of Map by HashMap
* Map is unnecessary and inefficient in almost every case.
* Replaced by the new HashMap.
* Renamed Map to RBMap and Set to RBSet for cases that still make sense
  (order matters) but use is discouraged.

There were very few cases where replacing by HashMap was undesired because
keeping the key order was intended.
I tried to keep those (as RBMap) as much as possible, but might have missed
some. Review appreciated!
2022-05-16 10:37:48 +02:00

378 lines
13 KiB
C++

/*************************************************************************/
/* Copyright (c) 2011-2021 Ivan Fratric and contributors. */
/* */
/* 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 */
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/* 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.*/
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/*************************************************************************/
#ifndef POLYPARTITION_H
#define POLYPARTITION_H
#include "core/math/vector2.h"
#include "core/templates/list.h"
#include "core/templates/rb_set.h"
typedef double tppl_float;
enum TPPLOrientation {
TPPL_ORIENTATION_CW = -1,
TPPL_ORIENTATION_NONE = 0,
TPPL_ORIENTATION_CCW = 1,
};
enum TPPLVertexType {
TPPL_VERTEXTYPE_REGULAR = 0,
TPPL_VERTEXTYPE_START = 1,
TPPL_VERTEXTYPE_END = 2,
TPPL_VERTEXTYPE_SPLIT = 3,
TPPL_VERTEXTYPE_MERGE = 4,
};
// 2D point structure.
typedef Vector2 TPPLPoint;
// Polygon implemented as an array of points with a "hole" flag.
class TPPLPoly {
protected:
TPPLPoint *points;
long numpoints;
bool hole;
public:
// Constructors and destructors.
TPPLPoly();
~TPPLPoly();
TPPLPoly(const TPPLPoly &src);
TPPLPoly &operator=(const TPPLPoly &src);
// Getters and setters.
long GetNumPoints() const {
return numpoints;
}
bool IsHole() const {
return hole;
}
void SetHole(bool hole) {
this->hole = hole;
}
TPPLPoint &GetPoint(long i) {
return points[i];
}
const TPPLPoint &GetPoint(long i) const {
return points[i];
}
TPPLPoint *GetPoints() {
return points;
}
TPPLPoint &operator[](int i) {
return points[i];
}
const TPPLPoint &operator[](int i) const {
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, and p3.
void Triangle(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3);
// Inverts the orfer of vertices.
void Invert();
// Returns the orientation of the polygon.
// Possible values:
// TPPL_ORIENTATION_CCW: Polygon vertices are in counter-clockwise order.
// TPPL_ORIENTATION_CW: Polygon vertices are in clockwise order.
// TPPL_ORIENTATION_NONE: The polygon has no (measurable) area.
TPPLOrientation GetOrientation() const;
// Sets the polygon orientation.
// Possible values:
// TPPL_ORIENTATION_CCW: Sets vertices in counter-clockwise order.
// TPPL_ORIENTATION_CW: Sets vertices in clockwise order.
// TPPL_ORIENTATION_NONE: Reverses the orientation of the vertices if there
// is one, otherwise does nothing (if orientation is already NONE).
void SetOrientation(TPPLOrientation orientation);
// Checks whether a polygon is valid or not.
inline bool Valid() const { return this->numpoints >= 3; }
};
#ifdef TPPL_ALLOCATOR
typedef List<TPPLPoly, TPPL_ALLOCATOR(TPPLPoly)> TPPLPolyList;
#else
typedef List<TPPLPoly> TPPLPolyList;
#endif
class TPPLPartition {
protected:
struct PartitionVertex {
bool isActive;
bool isConvex;
bool isEar;
TPPLPoint p;
tppl_float angle;
PartitionVertex *previous;
PartitionVertex *next;
PartitionVertex();
};
struct MonotoneVertex {
TPPLPoint 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;
};
#ifdef TPPL_ALLOCATOR
typedef List<Diagonal, TPPL_ALLOCATOR(Diagonal)> DiagonalList;
#else
typedef List<Diagonal> DiagonalList;
#endif
// Dynamic programming state for minimum-weight triangulation.
struct DPState {
bool visible;
tppl_float weight;
long bestvertex;
};
// Dynamic programming state for convex partitioning.
struct DPState2 {
bool visible;
long weight;
DiagonalList pairs;
};
// Edge that intersects the scanline.
struct ScanLineEdge {
mutable long index;
TPPLPoint p1;
TPPLPoint p2;
// Determines if the edge is to the left of another edge.
bool operator<(const ScanLineEdge &other) const;
bool IsConvex(const TPPLPoint &p1, const TPPLPoint &p2, const TPPLPoint &p3) const;
};
// Standard helper functions.
bool IsConvex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3);
bool IsReflex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3);
bool IsInside(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p);
bool InCone(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p);
bool InCone(PartitionVertex *v, TPPLPoint &p);
int Intersects(TPPLPoint &p11, TPPLPoint &p12, TPPLPoint &p21, TPPLPoint &p22);
TPPLPoint Normalize(const TPPLPoint &p);
tppl_float Distance(const TPPLPoint &p1, const TPPLPoint &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(TPPLPoint &p1, TPPLPoint &p2);
void AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
TPPLVertexType *vertextypes, RBSet<ScanLineEdge>::Element **edgeTreeIterators,
RBSet<ScanLineEdge> *edgeTree, long *helpers);
// Triangulates a monotone polygon, used in Triangulate_MONO.
int TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles);
public:
// Simple heuristic procedure for removing holes from a list of polygons.
// It works by creating a diagonal from the right-most hole vertex
// to some other visible vertex.
// Time complexity: O(h*(n^2)), h is the # of holes, n is the # 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(TPPLPolyList *inpolys, TPPLPolyList *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(TPPLPoly *poly, TPPLPolyList *triangles);
// Triangulates a list of polygons that may contain holes by ear clipping
// algorithm. It first calls RemoveHoles to get rid of the holes, and then
// calls Triangulate_EC for each resulting polygon.
// Time complexity: O(h*(n^2)), h is the # of holes, n is the # 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(TPPLPolyList *inpolys, TPPLPolyList *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(TPPLPoly *poly, TPPLPolyList *triangles);
// Triangulates a polygon by first 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(TPPLPoly *poly, TPPLPolyList *triangles);
// Triangulates a list of polygons by first
// 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(TPPLPolyList *inpolys, TPPLPolyList *triangles);
// Creates a monotone partition of a list of polygons that
// can contain holes. Triangulates a set of polygons by
// first 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.
// monotonePolys:
// A list of monotone polygons (result).
// Returns 1 on success, 0 on failure.
int MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monotonePolys);
// Partitions a polygon into convex polygons by using the
// 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.
// It 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(TPPLPoly *poly, TPPLPolyList *parts);
// Partitions a list of polygons into convex parts by using the
// 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.
// It 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(TPPLPolyList *inpolys, TPPLPolyList *parts);
// Optimal convex partitioning (in terms of number of resulting
// convex polygons) using the Keil-Snoeyink algorithm.
// For reference, see 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)
// 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_OPT(TPPLPoly *poly, TPPLPolyList *parts);
};
#endif