Annulus sampling (#13471)

# Objective

Add random sampling for the `Annulus` primitive. This is part of ongoing
work to bring the various `bevy_math` primitives to feature parity.

## Solution

`Annulus` implements `ShapeSample`. Boundary sampling is implemented in
the obvious way, and interior sampling works exactly as in the
implementation for `Circle`, using the fact that the square of the
radius should be taken uniformly from between r^2 and R^2, where r and R
are the inner and outer radii respectively.

## Testing

I generated a bunch of random points and rendered them. Here's 1000
points on the interior of the default annulus:
<img width="1440" alt="Screenshot 2024-05-22 at 8 01 34 AM"
src="https://github.com/bevyengine/bevy/assets/2975848/19c31bb0-edba-477f-b247-2b12d854afae">

This looks kind of weird around the edges, but I verified that they're
all actually inside the annulus, so I assume it has to do with the fact
that the rendered circles have some radius.
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Matty 2024-05-22 09:13:04 -04:00 committed by GitHub
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@ -191,6 +191,35 @@ impl ShapeSample for Sphere {
}
}
impl ShapeSample for Annulus {
type Output = Vec2;
fn sample_interior<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::Output {
let inner_radius = self.inner_circle.radius;
let outer_radius = self.outer_circle.radius;
// Like random sampling for a circle, radius is weighted by the square.
let r_squared = rng.gen_range((inner_radius * inner_radius)..(outer_radius * outer_radius));
let r = r_squared.sqrt();
let theta = rng.gen_range(0.0..TAU);
Vec2::new(r * theta.cos(), r * theta.sin())
}
fn sample_boundary<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::Output {
let total_perimeter = self.inner_circle.perimeter() + self.outer_circle.perimeter();
let inner_prob = (self.inner_circle.perimeter() / total_perimeter) as f64;
// Sample from boundary circles, choosing which one by weighting by perimeter:
let inner = rng.gen_bool(inner_prob);
if inner {
self.inner_circle.sample_boundary(rng)
} else {
self.outer_circle.sample_boundary(rng)
}
}
}
impl ShapeSample for Rectangle {
type Output = Vec2;