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Naturally coloring a Voronoi diagram using Mathematica

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  • Subject: [mg105591] Naturally coloring a Voronoi diagram using Mathematica
  • From: Kelly Jones <kelly.terry.jones at gmail.com>
  • Date: Thu, 10 Dec 2009 04:57:24 -0500 (EST)

I've defined 0 <= f[x] <= 1 for 1000 x's in the unit square, and now
want to extend f as a uniformly continuous function on the entire unit
square as follows:

 % For any two points x and y in the unit square, and 0<=k<=1:

f[k*x + (1-k)*y] = k*f[x] + (1-k)*f[y]

Note that x and y are points in the unit square, not real numbers.

 % The equation above applies to the 1000 points I originally defined,
 but also to any two other points in the unit square.

 % I want to compute f efficiently.

Essentially, I have a Voronoi diagram and have assigned a different
hue to each point (but saturation=value=1, so we're only dealing w/
1-dimensional color), and now want to color the entire diagram
efficiently in a "reasonable" way.

Ideally, I'd like to find a *function* that does this, but if
Mathematica can do this w/ Graphics (eg, some sort of color
gradient?), that's fine too.

I do realize I'm probably limited to coloring the convex hull of my
original points.

PS: Thanks to everyone who replies to my other questions. I'm bad
about replying, but do appreciate the answers and do learn from them.

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