Optimize 2D Delaunay and make it more readable
Co-authored-by: Dimitri Tabatadze <tabatadzedima@protonmail.com>
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VolTer
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@ -38,7 +38,8 @@ class Delaunay2D {
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public:
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struct Triangle {
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int points[3];
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bool bad = false;
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Vector2 circum_center;
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real_t circum_radius_squared;
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Triangle() {}
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Triangle(int p_a, int p_b, int p_c) {
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points[0] = p_a;
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@ -48,117 +49,109 @@ public:
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};
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struct Edge {
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int edge[2];
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int points[2];
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bool bad = false;
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Edge() {}
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Edge(int p_a, int p_b) {
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edge[0] = p_a;
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edge[1] = p_b;
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// Store indices in a sorted manner to avoid having to check both orientations later.
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if (p_a > p_b) {
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points[0] = p_b;
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points[1] = p_a;
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} else {
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points[0] = p_a;
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points[1] = p_b;
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}
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}
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};
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static bool circum_circle_contains(const Vector<Vector2> &p_vertices, const Triangle &p_triangle, int p_vertex) {
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Vector2 p1 = p_vertices[p_triangle.points[0]];
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Vector2 p2 = p_vertices[p_triangle.points[1]];
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Vector2 p3 = p_vertices[p_triangle.points[2]];
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static Triangle create_triangle(const Vector<Vector2> &p_vertices, const int &p_a, const int &p_b, const int &p_c) {
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Triangle triangle = Triangle(p_a, p_b, p_c);
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real_t ab = p1.x * p1.x + p1.y * p1.y;
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real_t cd = p2.x * p2.x + p2.y * p2.y;
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real_t ef = p3.x * p3.x + p3.y * p3.y;
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// Get the values of the circumcircle and store them inside the triangle object.
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Vector2 a = p_vertices[p_b] - p_vertices[p_a];
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Vector2 b = p_vertices[p_c] - p_vertices[p_a];
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Vector2 circum(
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(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)),
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(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)));
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Vector2 O = (b * a.length_squared() - a * b.length_squared()).orthogonal() / (a.cross(b) * 2.0f);
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circum *= 0.5;
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float r = p1.distance_squared_to(circum);
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float d = p_vertices[p_vertex].distance_squared_to(circum);
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return d <= r;
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}
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triangle.circum_radius_squared = O.length_squared();
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triangle.circum_center = O + p_vertices[p_a];
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static bool edge_compare(const Vector<Vector2> &p_vertices, const Edge &p_a, const Edge &p_b) {
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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]])) {
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return true;
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}
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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]])) {
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return true;
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}
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return false;
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return triangle;
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}
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static Vector<Triangle> triangulate(const Vector<Vector2> &p_points) {
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Vector<Vector2> points = p_points;
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Vector<Triangle> triangles;
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Rect2 rect;
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for (int i = 0; i < p_points.size(); i++) {
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if (i == 0) {
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rect.position = p_points[i];
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} else {
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rect.expand_to(p_points[i]);
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}
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int point_count = p_points.size();
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if (point_count <= 2) {
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return triangles;
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}
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float delta_max = MAX(rect.size.width, rect.size.height);
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// Get a bounding rectangle.
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Rect2 rect = Rect2(p_points[0], Size2());
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for (int i = 1; i < point_count; i++) {
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rect.expand_to(p_points[i]);
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}
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real_t delta_max = MAX(rect.size.width, rect.size.height);
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Vector2 center = rect.get_center();
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points.push_back(Vector2(center.x - 20 * delta_max, center.y - delta_max));
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points.push_back(Vector2(center.x, center.y + 20 * delta_max));
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points.push_back(Vector2(center.x + 20 * delta_max, center.y - delta_max));
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// Construct a bounding triangle around the rectangle.
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points.push_back(Vector2(center.x - delta_max * 16, center.y - delta_max));
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points.push_back(Vector2(center.x, center.y + delta_max * 16));
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points.push_back(Vector2(center.x + delta_max * 16, center.y - delta_max));
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triangles.push_back(Triangle(p_points.size() + 0, p_points.size() + 1, p_points.size() + 2));
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Triangle bounding_triangle = create_triangle(points, point_count + 0, point_count + 1, point_count + 2);
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triangles.push_back(bounding_triangle);
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for (int i = 0; i < p_points.size(); i++) {
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for (int i = 0; i < point_count; i++) {
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Vector<Edge> polygon;
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for (int j = 0; j < triangles.size(); j++) {
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if (circum_circle_contains(points, triangles[j], i)) {
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triangles.write[j].bad = true;
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// Save the edges of the triangles whose circumcircles contain the i-th vertex. Delete the triangles themselves.
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for (int j = triangles.size() - 1; j >= 0; j--) {
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if (points[i].distance_squared_to(triangles[j].circum_center) < triangles[j].circum_radius_squared) {
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polygon.push_back(Edge(triangles[j].points[0], triangles[j].points[1]));
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polygon.push_back(Edge(triangles[j].points[1], triangles[j].points[2]));
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polygon.push_back(Edge(triangles[j].points[2], triangles[j].points[0]));
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}
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}
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for (int j = 0; j < triangles.size(); j++) {
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if (triangles[j].bad) {
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triangles.remove_at(j);
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j--;
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}
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}
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for (int j = 0; j < polygon.size(); j++) {
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for (int k = j + 1; k < polygon.size(); k++) {
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if (edge_compare(points, polygon[j], polygon[k])) {
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polygon.write[j].bad = true;
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polygon.write[k].bad = true;
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}
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}
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}
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// Create a triangle for every unique edge.
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for (int j = 0; j < polygon.size(); j++) {
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if (polygon[j].bad) {
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continue;
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}
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triangles.push_back(Triangle(polygon[j].edge[0], polygon[j].edge[1], i));
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for (int k = j + 1; k < polygon.size(); k++) {
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// Compare the edges.
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if (polygon[k].points[0] == polygon[j].points[0] && polygon[k].points[1] == polygon[j].points[1]) {
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polygon.write[j].bad = true;
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polygon.write[k].bad = true;
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break; // Since no more than two triangles can share an edge, no more than two edges can share vertices.
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}
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}
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// Create triangles out of good edges.
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if (!polygon[j].bad) {
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triangles.push_back(create_triangle(points, polygon[j].points[0], polygon[j].points[1], i));
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}
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}
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}
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for (int i = 0; i < triangles.size(); i++) {
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bool invalid = false;
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for (int j = 0; j < 3; j++) {
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if (triangles[i].points[j] >= p_points.size()) {
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invalid = true;
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break;
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}
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}
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if (invalid) {
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triangles.remove_at(i);
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i--;
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// Filter out the triangles containing vertices of the bounding triangle.
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int preserved_count = 0;
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Triangle *triangles_ptrw = triangles.ptrw();
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for (int i = 0; i < triangles.size() - 1; i++) {
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if (!(triangles[i].points[0] >= point_count || triangles[i].points[1] >= point_count || triangles[i].points[2] >= point_count)) {
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triangles_ptrw[preserved_count] = triangles[i];
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preserved_count++;
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}
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}
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triangles.resize(preserved_count);
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return triangles;
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}
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