Delaunator GDScript

A GDScript port of Delaunator: A fast library for Delaunay triangulation of 2D points.

• Guide to data structures

This is a port of Mapbox's Delaunator.

Note: It seems like GDScript is not that fast (in reference of the slogan above, taken from the original library). See the performance benchmarks.

Delaunay triangulation

Voronoi cells

Usage

const Delaunator = preload("res://Delaunator.gd")

var points = PoolVector2Array([
  Vector2(0, 0), Vector2(1024, 0), Vector2(1024, 600), Vector2(0, 600), Vector2(29, 390), Vector2(859, 300), Vector2(65, 342), Vector2(86, 333), Vector2(962, 212), Vector2(211, 351), Vector2(3, 594), Vector2(421, 278), Vector2(608, 271), Vector2(230, 538), Vector2(870, 454), Vector2(850, 351), Vector2(583, 385), Vector2(907, 480), Vector2(749, 533), Vector2(877, 232), Vector2(720, 546), Vector2(1003, 541), Vector2(696, 594), Vector2(102, 306)
])

var delaunay = Delaunator.new(points)

print(delaunay.triangles)
# >> [11, 16, 12, 11, 13, 16, 22, 20, 16, 16, 15, 12, 20, 18, 16, 13, 22, 16, 20, 22, 18, 18, 15, 16, 15, 5, 12, 9, 13, 11, 8, 19, 5, 5, 19, 12, 12, 0, 11, 18, 14, 15, 15, 8, 5, 17, 14, 18, 0, 23, 11, 11, 23, 9, 9, 4, 13, 14, 17, 15, 21, 17, 2, 23, 7, 9, 23, 6, 7, 7, 4, 9, 17, 8, 15, 19, 1, 12, 6, 4, 7, 2, 17, 18, 17, 21, 8, 22, 2, 18, 21, 1, 8, 4, 10, 13, 13, 3, 22, 22, 3, 2, 4, 3, 10, 10, 3, 13, 2, 1, 21, 8, 1, 19, 1, 0, 12, 23, 0, 6, 6, 0, 4, 4, 0, 3]

print(delaunay.halfedges)
# >> [5, 11, 38, 28, 17, 0, 18, 14, 16, 22, 26, 1, 20, 23, 7, 98, 8, 4, 6, 89, 12, 41, 9, 13, 44, 35, 10, 56, 3, 53, 113, 33, 43, 31, 77, 25, 115, 50, 2, 46, 59, 21, 73, 32, 24, 57, 39, 82, 117, 51, 37, 49, 65, 29, 70, 95, 27, 45, 74, 40, 84, 81, 110, 68, 71, 52, 119, 80, 63, 79, 54, 64, 86, 42, 58, 112, 116, 34, 122, 69, 67, 61, 47, 88, 60, 92, 72, 101, 83, 19, 109, 111, 85, 104, 107, 55, 106, 99, 15, 97, -1, 87, 125, 105, 93, 103, 96, 94, -1, 90, 62, 91, 75, 30, -1, 36, 76, 48, 120, 66, 118, 123, 78, 121, -1, 102]

print(delaunay.hull)
# >> [1, 0, 3, 2]

print(delaunay.coords)
# >> [0, 0, 1024, 0, 1024, 600, 0, 600, 29, 390, 859, 300, 65, 342, 86, 333, 962, 212, 211, 351, 3, 594, 421, 278, 608, 271, 230, 538, 870, 454, 850, 351, 583, 385, 907, 480, 749, 533, 877, 232, 720, 546, 1003, 541, 696, 594, 102, 306]

API Reference

Delaunator.new(points)

Constructs a Delaunay triangulation object given an array of points (Vector2(x, y)). Duplicate points are skipped.

Delaunator.new(points).triangles

An array of triangle vertex indices (each group of three numbers forms a triangle). All triangles are directed counterclockwise.

To get the coordinates of all triangles, use:

var coordinates = []

for i in range(0, triangles.size(), 3):
  coordinates.append([
    points[triangles[i]],
    points[triangles[i + 1]],
    points[triangles[i + 2]]
  ])

Delaunator.new(points).halfedges

An array of triangle half-edge indices that allows you to traverse the triangulation. i-th half-edge in the array corresponds to vertex triangles[i] the half-edge is coming from. halfedges[i] is the index of a twin half-edge in an adjacent triangle (or -1 for outer half-edges on the convex hull).

The flat array-based data structures might be counterintuitive, but they're one of the key reasons this library is fast.

Delaunator.new(points).hull

An array of indices that reference points on the convex hull of the input data, counter-clockwise.

Delaunator.new(points).coords

An array of input coordinates in the form [x0, y0, x1, y1, ...], of the type provided in the constructor.

Delaunator.new(points).update()

Updates the triangulation if you modified Delaunator.new(points).coords values in place, avoiding expensive memory allocations. Useful for iterative relaxation algorithms such as Lloyd's.

Performance

Benchmark results performed on a Macbook Pro Retina 15" 2015 with Godot v3.2 and using this method:

var start = OS.get_ticks_msec()
var delaunay = Delaunator.new(points)
var elapsed = OS.get_ticks_msec() - start
print(elapsed)

Changelog

See CHANGELOG.

Authors

• Me 😛 hiulit.

Credits

Thanks to:

• Vladimir Agafonkin - For creating Delaunator, the original JavaScript library.
• Amit Patel - For the Delaunator guide, which my data structures guide is based of.
• Hakan Seven - For the Delaunator-Python port, which I used for some reference code.

License

MIT License.