Re: Random points in triangle

*To*: mathgroup at smc.vnet.net*Subject*: [mg111619] Re: Random points in triangle*From*: Ray Koopman <koopman at sfu.ca>*Date*: Sat, 7 Aug 2010 06:22:15 -0400 (EDT)*References*: <i3gpmj$2rm$1@smc.vnet.net>

On Aug 6, 3:55 am, "S. B. Gray" <stev... at ROADRUNNER.COM> wrote: > 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]. The scale parameter in the call to GammaDistribution doesn't matter, because the scale gets divided out when you take wts/Total[wts], but the shape parameter should always be 1. Values other than 1 will give either too many or too few points near the vertices, according as the shape parameter is less than or greater than 1.