A Bowyer-Watson algorithm implementation for Delaunay triangulation for Godot.
Also generates Voronoi diagram from triangulation, including neighbour cells scanning.
Written as a single GDScript file.
Algorithm returns list of triangles for given set of points.
To calculate it, Bowyer-Watson algorithm originally generates super-triangle that contains all points. Unfortunately, it wasn't giving good results on marginal points, so I've decided to implement "super-rectangle". It means that you need to specify a rectangle that will contain all points. If you won't specify such a rectangle, it will be calculated automatically
After that you can generate the list of triangles. That will also contain border triangles - triangles that share rectange corners.
Those triangles improve the Voronoi diagram generation but for the Delaunay triangulation you will most likely not want them. You can remove them with remove_border_triangles() or manually check is_border_triangle() while processing them in a loop.
Something similar happens after making Voronoi cells from triangles. Sites on rectangle edges tend to be quite stretched out and that's because there were no points behind to calculate it properly. You can remove such sites using remove_border_sites() function or manually check is_border_site() while processing them in a loop. In the future I plan to automatically clip such sites to rectangle boundary.
Check example.tscn which is a 2d scene with embedded with a full example script.
var delaunay = Delaunay.new(Rect2(0,0,1200,700))
#var delaunay = Delaunay.new() # use this to calculate rect automatically
for i in range(10):
for j in range(10):
delaunay.add_point(Vector2(50 + i*100 + rand_range(-15,15), 50 + j * 50 + rand_range(-15,15)))
var triangles = delaunay.triangulate()
for triangle in triangles:
if !delaunay.is_border_triangle(triangle): # do not render border triangles
show_triangle(triangle)
var sites = delaunay.make_voronoi(triangles)
for site in sites:
if !delaunay.is_border_site(site): # do not render border sites
show_site(site)
if site.neighbours.size() == site.source_triangles.size(): # sites on edges will have incomplete neighbours information
for neighbour_edge in site.neighbours:
show_neighbour(neighbour_edge)Check source code for more details
class_name Delaunay
# ==== CLASSES ====
class Edge: # Delaunay.Edge
var a: Vector2
var b: Vector2
func equals(edge: Edge) -> bool
func length() -> float
func center() -> Vector2
class Triangle: # Delaunay.Triangle
var a: Vector2
var b: Vector2
var c: Vector2
var edge_ab: Edge
var edge_bc: Edge
var edge_ca: Edge
var center: Vector2
var radius_sqr: float
func recalculate_circumcircle() -> void
func is_point_inside_circumcircle(point: Vector2) -> bool
func is_corner(point: Vector2) -> bool
func get_corner_opposite_edge(corner: Vector2) -> Edge
class VoronoiSite: # Delaunay.VoronoiSite
var center: Vector2
var polygon: PoolVector2Array # clockwise points in absolute position
var source_triangles: Array # of Triangle's that create this site internally, also clockwise
var neighbours: Array # of VoronoiEdge, also clockwise
func get_relative_polygon() -> PoolVector2Array # clockwise points in relative position to center
func get_boundary() -> Rect2:
class VoronoiEdge: # Delaunay.VoronoiEdge
var a: Vector2
var b: Vector2
var this: VoronoiSite
var other: VoronoiSite
func equals(edge: Edge) -> bool
func length() -> float
func center() -> Vector2
func normal() -> Vector2
# ==== PUBLIC STATIC FUNCTIONS ====
static func calculate_rect(points: PoolVector2Array, padding: float = 0.0)) -> Rect2:
# ==== PUBLIC VARIABLES ====
var points: PoolVector2Array
# ==== CONSTRUCTOR ====
func _init(rect: Rect2 = Rect2()) -> Delaunay # do not specify rectangle to calculate it automatically
# ==== PUBLIC FUNCTIONS ====
func add_point(point: Vector2) -> void
func set_rectangle(rect: Rect2) -> void:
func is_border_triangle(triangle: Triangle) -> bool
func remove_border_triangles(triangulation: Array) -> void
func is_border_site(site: VoronoiSite) -> bool:
func remove_border_sites(sites: Array) -> void
func get_polygon_site(site: VoronoiSite) -> PoolVector2Array: # return clipped polygon to Voronoi boundaries
func triangulate() -> Array # of Triangle
func make_voronoi(triangulation: Array) -> Array # of VoronoiSite- Implement Lloyd's relaxation algorithm
- Automatically clip border Voronoi cell polygons to rectangle border edges 1
-
Port to Godot 4- thanks to #6
Footnotes
-
possible by using
get_polygon_site()function manually ↩
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