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Diffstat (limited to 'core/math/delaunay_2d.h')
| -rw-r--r-- | core/math/delaunay_2d.h | 173 |
1 files changed, 173 insertions, 0 deletions
diff --git a/core/math/delaunay_2d.h b/core/math/delaunay_2d.h new file mode 100644 index 0000000000..b8252e9d16 --- /dev/null +++ b/core/math/delaunay_2d.h @@ -0,0 +1,173 @@ +/*************************************************************************/ +/* delaunay_2d.h */ +/*************************************************************************/ +/* 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. */ +/*************************************************************************/ + +#ifndef DELAUNAY_2D_H +#define DELAUNAY_2D_H + +#include "core/math/rect2.h" + +class Delaunay2D { +public: + struct Triangle { + + int points[3]; + bool bad; + Triangle() { bad = false; } + Triangle(int p_a, int p_b, int p_c) { + points[0] = p_a; + points[1] = p_b; + points[2] = p_c; + bad = false; + } + }; + + struct Edge { + int edge[2]; + bool bad; + Edge() { bad = false; } + Edge(int p_a, int p_b) { + bad = false; + edge[0] = p_a; + edge[1] = p_b; + } + }; + + static bool circum_circle_contains(const Vector<Vector2> &p_vertices, const Triangle &p_triangle, int p_vertex) { + + Vector2 p1 = p_vertices[p_triangle.points[0]]; + Vector2 p2 = p_vertices[p_triangle.points[1]]; + Vector2 p3 = p_vertices[p_triangle.points[2]]; + + real_t ab = p1.x * p1.x + p1.y * p1.y; + real_t cd = p2.x * p2.x + p2.y * p2.y; + real_t ef = p3.x * p3.x + p3.y * p3.y; + + Vector2 circum( + (ab * (p3.y - p2.y) + cd * (p1.y - p3.y) + ef * (p2.y - p1.y)) / (p1.x * (p3.y - p2.y) + p2.x * (p1.y - p3.y) + p3.x * (p2.y - p1.y)), + (ab * (p3.x - p2.x) + cd * (p1.x - p3.x) + ef * (p2.x - p1.x)) / (p1.y * (p3.x - p2.x) + p2.y * (p1.x - p3.x) + p3.y * (p2.x - p1.x))); + + circum *= 0.5; + float r = p1.distance_squared_to(circum); + float d = p_vertices[p_vertex].distance_squared_to(circum); + return d <= r; + } + + static bool edge_compare(const Vector<Vector2> &p_vertices, const Edge &p_a, const Edge &p_b) { + if (p_vertices[p_a.edge[0]].is_equal_approx(p_vertices[p_b.edge[0]]) && p_vertices[p_a.edge[1]].is_equal_approx(p_vertices[p_b.edge[1]])) { + return true; + } + + if (p_vertices[p_a.edge[0]].is_equal_approx(p_vertices[p_b.edge[1]]) && p_vertices[p_a.edge[1]].is_equal_approx(p_vertices[p_b.edge[0]])) { + return true; + } + + return false; + } + + static Vector<Triangle> triangulate(const Vector<Vector2> &p_points) { + + Vector<Vector2> points = p_points; + Vector<Triangle> triangles; + + Rect2 rect; + for (int i = 0; i < p_points.size(); i++) { + if (i == 0) { + rect.position = p_points[i]; + } else { + rect.expand_to(p_points[i]); + } + } + + float delta_max = MAX(rect.size.width, rect.size.height); + Vector2 center = rect.position + rect.size * 0.5; + + points.push_back(Vector2(center.x - 20 * delta_max, center.y - delta_max)); + points.push_back(Vector2(center.x, center.y + 20 * delta_max)); + points.push_back(Vector2(center.x + 20 * delta_max, center.y - delta_max)); + + triangles.push_back(Triangle(p_points.size() + 0, p_points.size() + 1, p_points.size() + 2)); + + for (int i = 0; i < p_points.size(); i++) { + + Vector<Edge> polygon; + + for (int j = 0; j < triangles.size(); j++) { + if (circum_circle_contains(points, triangles[j], i)) { + triangles.write[j].bad = true; + polygon.push_back(Edge(triangles[j].points[0], triangles[j].points[1])); + polygon.push_back(Edge(triangles[j].points[1], triangles[j].points[2])); + polygon.push_back(Edge(triangles[j].points[2], triangles[j].points[0])); + } + } + + for (int j = 0; j < triangles.size(); j++) { + if (triangles[j].bad) { + triangles.remove(j); + j--; + } + } + + for (int j = 0; j < polygon.size(); j++) { + for (int k = j + 1; k < polygon.size(); k++) { + if (edge_compare(points, polygon[j], polygon[k])) { + polygon.write[j].bad = true; + polygon.write[k].bad = true; + } + } + } + + for (int j = 0; j < polygon.size(); j++) { + + if (polygon[j].bad) { + continue; + } + triangles.push_back(Triangle(polygon[j].edge[0], polygon[j].edge[1], i)); + } + } + + for (int i = 0; i < triangles.size(); i++) { + bool invalid = false; + for (int j = 0; j < 3; j++) { + if (triangles[i].points[j] >= p_points.size()) { + invalid = true; + break; + } + } + if (invalid) { + triangles.remove(i); + i--; + } + } + + return triangles; + } +}; + +#endif // DELAUNAY_2D_H |