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Voronoi Diagrams on Three-Dimensional Surfaces

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This Demonstration partitions the surface of a cylinder, cone, Möbius strip, sphere, or torus into Voronoi cells based on a set of up to 24 random points (sites) uniformly distributed over the surface.

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You can choose from three different distance functions (Euclidean, Manhattan, or chessboard). You can choose the cell colors according to eight color schemes.

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Contributed by: Erik Mahieu (July 2016)
Open content licensed under CC BY-NC-SA

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The regions are created using Mathematica's built-in function ParametricPlot3D. NearestFunction using the selected DistanceFunction is used as a MeshFunction to partition the regions into Voronoi cells.

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