RE: Random spherical troubles

*To*: mathgroup at smc.vnet.net*Subject*: [mg25180] RE: [mg25170] Random spherical troubles*From*: "Ingolf Dahl" <ingolf.dahl at telia.com>*Date*: Tue, 12 Sep 2000 21:24:24 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Barbara DaVinci wants to generate a set of directions randomly distributed over the whole solid angle. Hi Barbara! There is a better way. Load <<Statistics`ContinuousDistributions` and generate three random numbers from the Normal distribution: Table[Random[NormalDistribution[0, 1]], {3}] If you want to be on the sure side, check that not all of these numbers are zero. If we see these numbers as the rectangular (Cartesian) coordinates for a vector, then this vector is randomly distributed over the whole solid angle. That follows from the fact that an orthogonal transformation of a number of independent normal distributed [0,1] random variables gives a new set of independent normal distributed variables with the same parameters. You can then normalize the vector to unit length if you like, or convert it to spherical coordinates. Ingolf Dahl MINA, Chalmers University f9aid at fy.chalmers.se