Delaunay / Voronoï diagrams (Delaunoï)

Delaunoï is a 2D library to construct Delaunay triangulations and Voronoï diagrams using QuadEdge datastructure as described by Leonidas J. Guibas and Jorge Stolfi in the paper Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams.

This library targets .NET framework 4.6.1.

Applications:

• Delaunay triangulation on plane / sphere
• Voronoi / Centroid / Incenter diagram on plane / sphere
• Random points sampling (Uniform, Halton, Poisson, Fibonnaci) on plane / sphere

Getting started:

Unity examples can be found in:

• Plane: Assets/Scenes/GuibasStolfiTest
• Sphere: Assets/Scenes/SphereSamplerTest
• Poisson sampling: Assets/Scenes/PoissonDiskTest

In order to please Unity you must update your Scripting Runtime Version to 4.X (Edit/ProjectSettings/Player/OtherSettings)

References:

Delaunay triangulation:

• Guibas and Stolfi paper
• Delaunay
• Star shape polygon
• Stereographic projection
• Interactive projection

Voronoï diagrams:

• Voronoi diagram
• Geometry predicates
• 3D circumcenter

Generators:

• Halton low-discrepancy sequence
• Poisson disk sampling
• Low-discrepancy sequence
• Spherical Fibonacci Mapping