UnitCircle including the inside

[kuviman]

I would like to produce random points inside a circle.

A UnitCircleInside and UnitSphereInside distributions would be great to have.

Also, there is currently UnitCircle distribution, but it only produces points on edge. And this is not obvious since there is also UnitSphereSurface which states such fact in the name. So, ideally UnitCircle could be renamed to UnitCircleEdge.

[dhardy]

Actually, we already discussed the names: 'circle' typically refers to just the edge, while 'disc' refers to the internal area. For a sphere, the edge might be called a 'shell', but that name appeared more confusing, hence the desicision to use UnitSphereSurface. So we can use:

• UnitDisc
• UnitSphereInterior

See the discussion in #567. Implementing these should be straightforward, and I don't see why they shouldn't be added (to rand_distr), but @vks may also wish to comment.

[kuviman]

Hm, 'sphere' also usually refers to the shell, and the interior is called 'ball', I think?

[vks]

Sampling from inside a circle or sphere is most efficiently done using rejection sampling, so it is very easy to implement (see the corresponding benchmarks). I'm fine with adding them to rand_distr. They were not yet added, because I was not sure how useful it would be, and because their implementations are much more straightforward than for sampling from the surface.

[dhardy]

Those appear to be the terms used by Wikipedia and Wolfram at least; I'm happy to switch to this terminology. @vks? This is actually a good time to rename UnitSphere since rand_distr already has breaking changes.

Another thing occuring to me is that we could abstract over dimensions as follows, though probably this is more confusing than useful:

impl Distribution<[f64; 2]> for UnitSphere { .. }
impl Distribution<[f64; 3]> for UnitSphere { .. }