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/*************************************************************************/
/* triangulate.cpp */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2018 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)
{
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;
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) {
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;
if (CMP_EPSILON > (((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)) 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[v] = v;
else
for (int v = 0; v < n; v++)
V[v] = (n - 1) - v;
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--)) {
//** Triangulate: ERROR - probable bad polygon!
return false;
}
/* 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)) {
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[s] = V[t];
nv--;
/* resest error detection counter */
count = 2 * nv;
}
}
return true;
}
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