block by Kcnarf dacd1d9d2f0e69cf93c68ecf32f7896d

Voronoï playground : interactive weighted Voronoï study

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This block experiments weighted Voronoï diagram. Weighted Voronoï diagram comes in severall flavours (additive/multiplicative, powered/not-powered, 2D/3D and highier dimensions, …), but this block focuses on the 2D additive weighted power diagram. It helps me to understand the basics (properties, underlying computations, meanings, …) of such diagram.

From Wikipedia, the additively weighted power diagram is defined when positive weights are subtracted from the squared euclidian distances between points. The distance of a pixel from a site is the additive weighted power distance, further references as awp-distance. For any point of the 2D plan, the closest site is the one with the minimal awp-distance.

I choose this kind of weighted Voronoï diagram because the resulting tessellation is made of concave polygons/cells with straight borders, as the default Voronoï diagram does. Using non-squared distances results in hyperbolic borders.

What are you seeing ?

User interactions :

Unobvious things I’ve discovered :

Acknowledgments to: