*Uniform sampling of * is the problem of generating random
samples from with a uniform distribution.

In the following we assume that we are able to uniformly
sample a real interval. A general algorithm to uniformly
sample any set is to bound it with an axis-aligned box ,
draw samples from a uniform distribution on ,
and accept only those samples which are also
in . This is called *rejection sampling*. The
probability that a sample drawn from is also
in is the ratio of the measures of and .
Thus the efficiency is highly dependent on this
ratio. Unfortunately, this ratio is often low,
or even zero. For example, uniformly sampling
the surface of a sphere in would not succeed
using rejection sampling in the described manner.

Thus, more than often it is either necessary, or much more efficient, to generate uniform samplings via slightly more complex algorithms. Pastel implements efficient algorithms to uniform sample from:

- a box in
- a sphere (surface) in
- a ball in
- an annulus in

If instead you need to distort an existing uniform sampling from one shape to another, see the link below.