1/**************************************************************************/
2/* triangulate.cpp */
3/**************************************************************************/
4/* This file is part of: */
5/* GODOT ENGINE */
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8/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
9/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
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29/**************************************************************************/
30
31#include "triangulate.h"
32
33real_t Triangulate::get_area(const Vector<Vector2> &contour) {
34 int n = contour.size();
35 const Vector2 *c = &contour[0];
36
37 real_t A = 0.0;
38
39 for (int p = n - 1, q = 0; q < n; p = q++) {
40 A += c[p].cross(c[q]);
41 }
42 return A * 0.5f;
43}
44
45/* `is_inside_triangle` decides if a point P is inside the triangle
46 * defined by A, B, C. */
47bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay,
48 real_t Bx, real_t By,
49 real_t Cx, real_t Cy,
50 real_t Px, real_t Py,
51 bool include_edges) {
52 real_t ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
53 real_t cCROSSap, bCROSScp, aCROSSbp;
54
55 ax = Cx - Bx;
56 ay = Cy - By;
57 bx = Ax - Cx;
58 by = Ay - Cy;
59 cx = Bx - Ax;
60 cy = By - Ay;
61 apx = Px - Ax;
62 apy = Py - Ay;
63 bpx = Px - Bx;
64 bpy = Py - By;
65 cpx = Px - Cx;
66 cpy = Py - Cy;
67
68 aCROSSbp = ax * bpy - ay * bpx;
69 cCROSSap = cx * apy - cy * apx;
70 bCROSScp = bx * cpy - by * cpx;
71
72 if (include_edges) {
73 return ((aCROSSbp > 0.0f) && (bCROSScp > 0.0f) && (cCROSSap > 0.0f));
74 } else {
75 return ((aCROSSbp >= 0.0f) && (bCROSScp >= 0.0f) && (cCROSSap >= 0.0f));
76 }
77}
78
79bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V, bool relaxed) {
80 int p;
81 real_t Ax, Ay, Bx, By, Cx, Cy, Px, Py;
82 const Vector2 *contour = &p_contour[0];
83
84 Ax = contour[V[u]].x;
85 Ay = contour[V[u]].y;
86
87 Bx = contour[V[v]].x;
88 By = contour[V[v]].y;
89
90 Cx = contour[V[w]].x;
91 Cy = contour[V[w]].y;
92
93 // It can happen that the triangulation ends up with three aligned vertices to deal with.
94 // In this scenario, making the check below strict may reject the possibility of
95 // forming a last triangle with these aligned vertices, preventing the triangulation
96 // from completing.
97 // To avoid that we allow zero-area triangles if all else failed.
98 float threshold = relaxed ? -CMP_EPSILON : CMP_EPSILON;
99
100 if (threshold > (((Bx - Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax)))) {
101 return false;
102 }
103
104 for (p = 0; p < n; p++) {
105 if ((p == u) || (p == v) || (p == w)) {
106 continue;
107 }
108 Px = contour[V[p]].x;
109 Py = contour[V[p]].y;
110 if (is_inside_triangle(Ax, Ay, Bx, By, Cx, Cy, Px, Py, relaxed)) {
111 return false;
112 }
113 }
114
115 return true;
116}
117
118bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &result) {
119 /* allocate and initialize list of Vertices in polygon */
120
121 int n = contour.size();
122 if (n < 3) {
123 return false;
124 }
125
126 Vector<int> V;
127 V.resize(n);
128
129 /* we want a counter-clockwise polygon in V */
130
131 if (0.0f < get_area(contour)) {
132 for (int v = 0; v < n; v++) {
133 V.write[v] = v;
134 }
135 } else {
136 for (int v = 0; v < n; v++) {
137 V.write[v] = (n - 1) - v;
138 }
139 }
140
141 bool relaxed = false;
142
143 int nv = n;
144
145 /* remove nv-2 Vertices, creating 1 triangle every time */
146 int count = 2 * nv; /* error detection */
147
148 for (int v = nv - 1; nv > 2;) {
149 /* if we loop, it is probably a non-simple polygon */
150 if (0 >= (count--)) {
151 if (relaxed) {
152 //** Triangulate: ERROR - probable bad polygon!
153 return false;
154 } else {
155 // There may be aligned vertices that the strict
156 // checks prevent from triangulating. In this situation
157 // we are better off adding flat triangles than
158 // failing, so we relax the checks and try one last
159 // round.
160 // Only relaxing the constraints as a last resort avoids
161 // degenerate triangles when they aren't necessary.
162 count = 2 * nv;
163 relaxed = true;
164 }
165 }
166
167 /* three consecutive vertices in current polygon, <u,v,w> */
168 int u = v;
169 if (nv <= u) {
170 u = 0; /* previous */
171 }
172 v = u + 1;
173 if (nv <= v) {
174 v = 0; /* new v */
175 }
176 int w = v + 1;
177 if (nv <= w) {
178 w = 0; /* next */
179 }
180
181 if (snip(contour, u, v, w, nv, V, relaxed)) {
182 int a, b, c, s, t;
183
184 /* true names of the vertices */
185 a = V[u];
186 b = V[v];
187 c = V[w];
188
189 /* output Triangle */
190 result.push_back(a);
191 result.push_back(b);
192 result.push_back(c);
193
194 /* remove v from remaining polygon */
195 for (s = v, t = v + 1; t < nv; s++, t++) {
196 V.write[s] = V[t];
197 }
198
199 nv--;
200
201 /* reset error detection counter */
202 count = 2 * nv;
203 }
204 }
205
206 return true;
207}
208