195 lines
6.1 KiB
C++
195 lines
6.1 KiB
C++
/*************************************************************************/
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/* triangulate.cpp */
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/*************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2019 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2019 Godot Engine contributors (cf. AUTHORS.md) */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in 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, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/*************************************************************************/
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#include "triangulate.h"
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real_t Triangulate::get_area(const Vector<Vector2> &contour) {
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int n = contour.size();
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const Vector2 *c = &contour[0];
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real_t A = 0.0;
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for (int p = n - 1, q = 0; q < n; p = q++) {
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A += c[p].cross(c[q]);
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}
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return A * 0.5;
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}
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/*
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is_inside_triangle decides if a point P is Inside of the triangle
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defined by A, B, C.
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*/
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bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay,
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real_t Bx, real_t By,
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real_t Cx, real_t Cy,
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real_t Px, real_t Py,
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bool include_edges)
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{
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real_t ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
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real_t cCROSSap, bCROSScp, aCROSSbp;
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ax = Cx - Bx;
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ay = Cy - By;
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bx = Ax - Cx;
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by = Ay - Cy;
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cx = Bx - Ax;
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cy = By - Ay;
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apx = Px - Ax;
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apy = Py - Ay;
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bpx = Px - Bx;
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bpy = Py - By;
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cpx = Px - Cx;
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cpy = Py - Cy;
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aCROSSbp = ax * bpy - ay * bpx;
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cCROSSap = cx * apy - cy * apx;
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bCROSScp = bx * cpy - by * cpx;
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if (include_edges) {
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return ((aCROSSbp > 0.0) && (bCROSScp > 0.0) && (cCROSSap > 0.0));
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} else {
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return ((aCROSSbp >= 0.0) && (bCROSScp >= 0.0) && (cCROSSap >= 0.0));
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}
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};
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bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V, bool relaxed) {
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int p;
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real_t Ax, Ay, Bx, By, Cx, Cy, Px, Py;
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const Vector2 *contour = &p_contour[0];
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Ax = contour[V[u]].x;
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Ay = contour[V[u]].y;
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Bx = contour[V[v]].x;
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By = contour[V[v]].y;
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Cx = contour[V[w]].x;
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Cy = contour[V[w]].y;
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// It can happen that the triangulation ends up with three aligned vertices to deal with.
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// In this scenario, making the check below strict may reject the possibility of
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// forming a last triangle with these aligned vertices, preventing the triangulatiom
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// from completing.
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// To avoid that we allow zero-area triangles if all else failed.
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float threshold = relaxed ? -CMP_EPSILON : CMP_EPSILON;
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if (threshold > (((Bx - Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax)))) return false;
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for (p = 0; p < n; p++) {
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if ((p == u) || (p == v) || (p == w)) continue;
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Px = contour[V[p]].x;
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Py = contour[V[p]].y;
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if (is_inside_triangle(Ax, Ay, Bx, By, Cx, Cy, Px, Py, relaxed)) return false;
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}
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return true;
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}
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bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &result) {
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/* allocate and initialize list of Vertices in polygon */
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int n = contour.size();
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if (n < 3) return false;
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Vector<int> V;
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V.resize(n);
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/* we want a counter-clockwise polygon in V */
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if (0.0 < get_area(contour))
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for (int v = 0; v < n; v++)
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V.write[v] = v;
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else
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for (int v = 0; v < n; v++)
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V.write[v] = (n - 1) - v;
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bool relaxed = false;
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int nv = n;
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/* remove nv-2 Vertices, creating 1 triangle every time */
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int count = 2 * nv; /* error detection */
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for (int v = nv - 1; nv > 2;) {
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/* if we loop, it is probably a non-simple polygon */
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if (0 >= (count--)) {
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if (relaxed) {
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//** Triangulate: ERROR - probable bad polygon!
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return false;
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} else {
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// There may be aligned vertices that the strict
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// checks prevent from triangulating. In this situation
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// we are better off adding flat triangles than
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// failing, so we relax the checks and try one last
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// round.
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// Only relaxing the constraints as a last resort avoids
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// degenerate triangles when they aren't necessary.
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count = 2 * nv;
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relaxed = true;
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}
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}
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/* three consecutive vertices in current polygon, <u,v,w> */
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int u = v;
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if (nv <= u) u = 0; /* previous */
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v = u + 1;
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if (nv <= v) v = 0; /* new v */
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int w = v + 1;
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if (nv <= w) w = 0; /* next */
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if (snip(contour, u, v, w, nv, V, relaxed)) {
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int a, b, c, s, t;
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/* true names of the vertices */
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a = V[u];
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b = V[v];
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c = V[w];
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/* output Triangle */
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result.push_back(a);
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result.push_back(b);
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result.push_back(c);
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/* remove v from remaining polygon */
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for (s = v, t = v + 1; t < nv; s++, t++)
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V.write[s] = V[t];
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nv--;
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/* reset error detection counter */
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count = 2 * nv;
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}
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}
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return true;
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}
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