Random points in triangle
- To: mathgroup at smc.vnet.net
- Subject: [mg111573] Random points in triangle
- From: "S. B. Gray" <stevebg at ROADRUNNER.COM>
- Date: Fri, 6 Aug 2010 06:55:22 -0400 (EDT)
- Reply-to: stevebg at ROADRUNNER.COM
I was looking for a simple way to place random points inside a triangle with uniform distribution. Here's a good way: newtri := Module[{x}, ptri = RandomReal[{-5, +5}, {3, 2}]; tredg = Subsets[ptri, {2}]; ] newpts[nump_] := Module[{wts}, inpoints = {}; Do [ wts = RandomReal[GammaDistribution[1, 2], 3]; wts = wts/Total[wts]; newin = Total[ptri*wts]; inpoints = Append[inpoints, newin], {nump}]; ] shotri := Module[{x}, Graphics[{Blue, Line[tredg], Red, Point[inpoints]}, ImageSize -> 500] ] The same idea works for points in a tetrahedron; they will be uniformly distributed if you use args such as GammaDistribution[.6,.1]. Steve Gray