[figomore]

If you are not interested in the edges, only painting the sites with different colors, you can use a variation of flood fill starting with the seeds and only stacking the pixel if that color has distance lower than the one already painted that pixel.

[mikhailfranco]

Build a 3D scene of distinctly colored right circular cones with their apexes at the 2D planar vertices, and their axes perpendicular to the plane.

Render a 2D orthographic view from 'above' the apexes.

The z-buffer will preserve pixels from the nearest apex.

(Yes, I now there are shadery ways to do this, but the classic 3D cones demo is trivial to understand and implement).

[alejohausner]

You don't have to use cones. Paraboloids work too.