1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
|
/*************************************************************************/
/* triangulate.cpp */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md). */
/* */
/* 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. */
/*************************************************************************/
#include "triangulate.h"
real_t Triangulate::get_area(const Vector<Vector2> &contour) {
int n = contour.size();
const Vector2 *c = &contour[0];
real_t A = 0.0;
for (int p = n - 1, q = 0; q < n; p = q++) {
A += c[p].cross(c[q]);
}
return A * 0.5;
}
/*
is_inside_triangle decides if a point P is Inside of the triangle
defined by A, B, C.
*/
bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay,
real_t Bx, real_t By,
real_t Cx, real_t Cy,
real_t Px, real_t Py,
bool include_edges)
{
real_t ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
real_t cCROSSap, bCROSScp, aCROSSbp;
ax = Cx - Bx;
ay = Cy - By;
bx = Ax - Cx;
by = Ay - Cy;
cx = Bx - Ax;
cy = By - Ay;
apx = Px - Ax;
apy = Py - Ay;
bpx = Px - Bx;
bpy = Py - By;
cpx = Px - Cx;
cpy = Py - Cy;
aCROSSbp = ax * bpy - ay * bpx;
cCROSSap = cx * apy - cy * apx;
bCROSScp = bx * cpy - by * cpx;
if (include_edges) {
return ((aCROSSbp > 0.0) && (bCROSScp > 0.0) && (cCROSSap > 0.0));
} else {
return ((aCROSSbp >= 0.0) && (bCROSScp >= 0.0) && (cCROSSap >= 0.0));
}
};
bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V, bool relaxed) {
int p;
real_t Ax, Ay, Bx, By, Cx, Cy, Px, Py;
const Vector2 *contour = &p_contour[0];
Ax = contour[V[u]].x;
Ay = contour[V[u]].y;
Bx = contour[V[v]].x;
By = contour[V[v]].y;
Cx = contour[V[w]].x;
Cy = contour[V[w]].y;
// It can happen that the triangulation ends up with three aligned vertices to deal with.
// In this scenario, making the check below strict may reject the possibility of
// forming a last triangle with these aligned vertices, preventing the triangulatiom
// from completing.
// To avoid that we allow zero-area triangles if all else failed.
float threshold = relaxed ? -CMP_EPSILON : CMP_EPSILON;
if (threshold > (((Bx - Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax)))) return false;
for (p = 0; p < n; p++) {
if ((p == u) || (p == v) || (p == w)) continue;
Px = contour[V[p]].x;
Py = contour[V[p]].y;
if (is_inside_triangle(Ax, Ay, Bx, By, Cx, Cy, Px, Py, relaxed)) return false;
}
return true;
}
bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &result) {
/* allocate and initialize list of Vertices in polygon */
int n = contour.size();
if (n < 3) return false;
Vector<int> V;
V.resize(n);
/* we want a counter-clockwise polygon in V */
if (0.0 < get_area(contour))
for (int v = 0; v < n; v++)
V.write[v] = v;
else
for (int v = 0; v < n; v++)
V.write[v] = (n - 1) - v;
bool relaxed = false;
int nv = n;
/* remove nv-2 Vertices, creating 1 triangle every time */
int count = 2 * nv; /* error detection */
for (int v = nv - 1; nv > 2;) {
/* if we loop, it is probably a non-simple polygon */
if (0 >= (count--)) {
if (relaxed) {
//** Triangulate: ERROR - probable bad polygon!
return false;
} else {
// There may be aligned vertices that the strict
// checks prevent from triangulating. In this situation
// we are better off adding flat triangles than
// failing, so we relax the checks and try one last
// round.
// Only relaxing the constraints as a last resort avoids
// degenerate triangles when they aren't necessary.
count = 2 * nv;
relaxed = true;
}
}
/* three consecutive vertices in current polygon, <u,v,w> */
int u = v;
if (nv <= u) u = 0; /* previous */
v = u + 1;
if (nv <= v) v = 0; /* new v */
int w = v + 1;
if (nv <= w) w = 0; /* next */
if (snip(contour, u, v, w, nv, V, relaxed)) {
int a, b, c, s, t;
/* true names of the vertices */
a = V[u];
b = V[v];
c = V[w];
/* output Triangle */
result.push_back(a);
result.push_back(b);
result.push_back(c);
/* remove v from remaining polygon */
for (s = v, t = v + 1; t < nv; s++, t++)
V.write[s] = V[t];
nv--;
/* reset error detection counter */
count = 2 * nv;
}
}
return true;
}
|
