Naturally coloring a Voronoi diagram using Mathematica
- To: mathgroup at smc.vnet.net
- 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. -- We're just a Bunch Of Regular Guys, a collective group that's trying to understand and assimilate technology. We feel that resistance to new ideas and technology is unwise and ultimately futile.
- Follow-Ups:
- Re: Naturally coloring a Voronoi diagram using Mathematica
- From: <ingolf.dahl@telia.com>
- Re: Naturally coloring a Voronoi diagram using Mathematica