/*************************************************************************/ /* triangulate.cpp */ /*************************************************************************/ /* This file is part of: */ /* GODOT ENGINE */ /* https://godotengine.org */ /*************************************************************************/ /* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */ /* Copyright (c) 2014-2022 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 * 0.5f; } /* `is_inside_triangle` decides if a point P is inside 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 > 0.0f) && (bCROSScp > 0.0f) && (cCROSSap > 0.0f)); } else { return ((aCROSSbp >= 0.0f) && (bCROSScp >= 0.0f) && (cCROSSap >= 0.0f)); } } 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 triangulation // 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 (0.0f < 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; }