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.