Generate gaussian random points in 3D space with a given mean position.

Given a point in 3D space, m = (x,y,z), I would like to generate a series of gaussian random points with a mean position of m and a given standard deviation, s (s is the same for all directions). Any ideas on the easiest way to do this?

My first thought is to pick random unit vectors, d=(dx,dy,dz) with equal probability of pointing in any direction(I think this is equivalent to randomly picking points on a unit sphere). Then get random radii with a gaussian distribution of mean=0 and std=s. The random points then become p=m+r*d; This seems like a lot of work and I wonder if anyone has a more clever way to do this.

Thanks, Justin

Answer 1

[Iman Ansari]

m = [2 0 2];
s = 1;
n = bsxfun(@plus,m,s.*randn(100,3));
plot3(n(:,1),n(:,2),n(:,3),'.r')

M = mean(n,1)
S = std(n,1)