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/*************************************************************************/
/* 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 = false;
Triangle() {}
Triangle(int p_a, int p_b, int p_c) {
points[0] = p_a;
points[1] = p_b;
points[2] = p_c;
}
};
struct Edge {
int edge[2];
bool bad = false;
Edge() {}
Edge(int p_a, int p_b) {
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
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