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-rw-r--r--core/math/delaunay_2d.h127
1 files changed, 60 insertions, 67 deletions
diff --git a/core/math/delaunay_2d.h b/core/math/delaunay_2d.h
index 8d602da241..cf7ba8d48e 100644
--- a/core/math/delaunay_2d.h
+++ b/core/math/delaunay_2d.h
@@ -38,7 +38,8 @@ class Delaunay2D {
public:
struct Triangle {
int points[3];
- bool bad = false;
+ Vector2 circum_center;
+ real_t circum_radius_squared;
Triangle() {}
Triangle(int p_a, int p_b, int p_c) {
points[0] = p_a;
@@ -48,117 +49,109 @@ public:
};
struct Edge {
- int edge[2];
+ int points[2];
bool bad = false;
Edge() {}
Edge(int p_a, int p_b) {
- edge[0] = p_a;
- edge[1] = p_b;
+ // Store indices in a sorted manner to avoid having to check both orientations later.
+ if (p_a > p_b) {
+ points[0] = p_b;
+ points[1] = p_a;
+ } else {
+ points[0] = p_a;
+ points[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]];
+ static Triangle create_triangle(const Vector<Vector2> &p_vertices, const int &p_a, const int &p_b, const int &p_c) {
+ Triangle triangle = Triangle(p_a, p_b, p_c);
- 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;
+ // Get the values of the circumcircle and store them inside the triangle object.
+ Vector2 a = p_vertices[p_b] - p_vertices[p_a];
+ Vector2 b = p_vertices[p_c] - p_vertices[p_a];
- 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)));
+ Vector2 O = (b * a.length_squared() - a * b.length_squared()).orthogonal() / (a.cross(b) * 2.0f);
- circum *= 0.5;
- float r = p1.distance_squared_to(circum);
- float d = p_vertices[p_vertex].distance_squared_to(circum);
- return d <= r;
- }
+ triangle.circum_radius_squared = O.length_squared();
+ triangle.circum_center = O + p_vertices[p_a];
- 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;
+ return triangle;
}
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]);
- }
+ int point_count = p_points.size();
+ if (point_count <= 2) {
+ return triangles;
}
- float delta_max = MAX(rect.size.width, rect.size.height);
+ // Get a bounding rectangle.
+ Rect2 rect = Rect2(p_points[0], Size2());
+ for (int i = 1; i < point_count; i++) {
+ rect.expand_to(p_points[i]);
+ }
+
+ real_t delta_max = MAX(rect.size.width, rect.size.height);
Vector2 center = rect.get_center();
- 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));
+ // Construct a bounding triangle around the rectangle.
+ points.push_back(Vector2(center.x - delta_max * 16, center.y - delta_max));
+ points.push_back(Vector2(center.x, center.y + delta_max * 16));
+ points.push_back(Vector2(center.x + delta_max * 16, center.y - delta_max));
- triangles.push_back(Triangle(p_points.size() + 0, p_points.size() + 1, p_points.size() + 2));
+ Triangle bounding_triangle = create_triangle(points, point_count + 0, point_count + 1, point_count + 2);
+ triangles.push_back(bounding_triangle);
- for (int i = 0; i < p_points.size(); i++) {
+ for (int i = 0; i < point_count; 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;
+ // Save the edges of the triangles whose circumcircles contain the i-th vertex. Delete the triangles themselves.
+ for (int j = triangles.size() - 1; j >= 0; j--) {
+ if (points[i].distance_squared_to(triangles[j].circum_center) < triangles[j].circum_radius_squared) {
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_at(j);
- j--;
}
}
+ // Create a triangle for every unique edge.
for (int j = 0; j < polygon.size(); j++) {
+ if (polygon[j].bad) {
+ continue;
+ }
+
for (int k = j + 1; k < polygon.size(); k++) {
- if (edge_compare(points, polygon[j], polygon[k])) {
+ // Compare the edges.
+ if (polygon[k].points[0] == polygon[j].points[0] && polygon[k].points[1] == polygon[j].points[1]) {
polygon.write[j].bad = true;
polygon.write[k].bad = true;
+
+ break; // Since no more than two triangles can share an edge, no more than two edges can share vertices.
}
}
- }
- for (int j = 0; j < polygon.size(); j++) {
- if (polygon[j].bad) {
- continue;
+ // Create triangles out of good edges.
+ if (!polygon[j].bad) {
+ triangles.push_back(create_triangle(points, polygon[j].points[0], polygon[j].points[1], i));
}
- 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_at(i);
- i--;
+ // Filter out the triangles containing vertices of the bounding triangle.
+ int preserved_count = 0;
+ Triangle *triangles_ptrw = triangles.ptrw();
+ for (int i = 0; i < triangles.size() - 1; i++) {
+ if (!(triangles[i].points[0] >= point_count || triangles[i].points[1] >= point_count || triangles[i].points[2] >= point_count)) {
+ triangles_ptrw[preserved_count] = triangles[i];
+ preserved_count++;
}
}
+ triangles.resize(preserved_count);
return triangles;
}