[nowdnbmi] Blending many images

Blend 2 images with a gray mask controlling the weight between the two pictures: 1 degree of freedom.  Alpha channel.

N images require weights in a (N-1)-dimensional linear combination subspace.  The challenge is to randomly sample this subspace uniformly.

Sample X, Y, Z uniformly independently between [0,1].  Is X/s, Y/s, Z/s where s=X+Y+Z a uniform sample in the equilateral triangle-shaped subspace?  (I'm guessing not.)

We'd actually prefer to sample less than uniformly to avoid gray, preferring saturated colors.