Voronoi Explorer

This page allows you to explore generalised Voronoi diagrams.

There are two primary modes:

• Multiple points: in this mode, there are 16 points. The parameters (see below) are set at random.
• Double points: in this mode, there are 2 points. The parameters can be set manually for one of the points (it is the relative difference that matters, so it is only necessary to specify one set of parameters).

The diagram is generated by working out which source point would reach a given point first. The generalisation is to allow different growth functions which say how fast the region from a given source point expands outwards.

The growth function can be either linear or exponential. Each has certain parameters which are set either by the user (when there are 2 points) or at random (when there are 16 points). To work out which source point would reach a certain point first, we actually use the inverse of the growth formulae. Thus the formulae in use are:

• Linear: $a x + b$
• Exponential: $-a \log(1 - c x) + b$

where $a$ (the weight), $b$ (the delay), and $c$ (the extent) can vary with the source point.

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