Meshing for Annulus primitive (#12734)

# Objective

Related to #10572 
Allow the `Annulus` primitive to be meshed.

## Solution

We introduce a `Meshable` structure, `AnnulusMeshBuilder`, which allows
the `Annulus` primitive to be meshed, leaving optional configuration of
the number of angular sudivisions to the user. Here is a picture of the
annulus's UV-mapping:
<img width="1440" alt="Screenshot 2024-03-26 at 10 39 48 AM"
src="https://github.com/bevyengine/bevy/assets/2975848/b170291d-cba7-441b-90ee-2ad6841eaedb">

Other features are essentially identical to the implementations for
`Circle`/`Ellipse`.

---

## Changelog

- Introduced `AnnulusMeshBuilder`
- Implemented `Meshable` for `Annulus` with `Output =
AnnulusMeshBuilder`
- Implemented `From<Annulus>` and `From<AnnulusMeshBuilder>` for `Mesh`
- Added `impl_reflect!` declaration for `Annulus` and `Triangle3d` in
`bevy_reflect`

---

## Discussion

### Design considerations

The only interesting wrinkle here is that the existing UV-mapping of
`Ellipse` (and hence of `Circle` and `RegularPolygon`) is non-radial
(it's skew-free, created by situating the mesh in a bounding rectangle),
so the UV-mapping of `Annulus` doesn't limit to that of `Circle` as its
inner radius tends to zero, for instance. I don't see this as a real
issue for `Annulus`, which should almost certainly have this kind of
UV-mapping, but I think we ought to at least consider allowing mesh
configuration for `Circle`/`Ellipse` that performs radial UV-mapping
instead. (In these cases in particular, it would be especially easy,
since we wouldn't need a different parameter set in the builder.)

---------

Co-authored-by: Alice Cecile <alice.i.cecile@gmail.com>

crates/bevy_reflect/src/impls/math/primitives2d.rs

@@ -15,7 +15,16 @@ impl_reflect!(
     #[reflect(Debug, PartialEq, Serialize, Deserialize)]
     #[type_path = "bevy_math::primitives"]
     struct Ellipse {
-        pub half_size: Vec2,
+        half_size: Vec2,
+    }
+);
+
+impl_reflect!(
+    #[reflect(Debug, PartialEq, Serialize, Deserialize)]
+    #[type_path = "bevy_math::primitives"]
+    struct Annulus {
+        inner_circle: Circle,
+        outer_circle: Circle,
     }
 );
 

crates/bevy_reflect/src/impls/math/primitives3d.rs

@@ -44,6 +44,14 @@ impl_reflect!(
     }
 );
 
+impl_reflect!(
+    #[reflect(Debug, PartialEq, Serialize, Deserialize)]
+    #[type_path = "bevy_math::primitives"]
+    struct Triangle3d {
+        vertices: [Vec3; 3],
+    }
+);
+
 impl_reflect!(
     #[reflect(Debug, PartialEq, Serialize, Deserialize)]
     #[type_path = "bevy_math::primitives"]

crates/bevy_render/src/mesh/primitives/dim2.rs

@@ -5,7 +5,9 @@ use crate::{
 
 use super::Meshable;
 use bevy_math::{
-    primitives::{Capsule2d, Circle, Ellipse, Rectangle, RegularPolygon, Triangle2d, WindingOrder},
+    primitives::{
+        Annulus, Capsule2d, Circle, Ellipse, Rectangle, RegularPolygon, Triangle2d, WindingOrder,
+    },
     Vec2,
 };
 use wgpu::PrimitiveTopology;
@@ -193,6 +195,124 @@ impl From<EllipseMeshBuilder> for Mesh {
     }
 }
 
+/// A builder for creating a [`Mesh`] with an [`Annulus`] shape.
+pub struct AnnulusMeshBuilder {
+    /// The [`Annulus`] shape.
+    pub annulus: Annulus,
+
+    /// The number of vertices used in constructing each concentric circle of the annulus mesh.
+    /// The default is `32`.
+    pub resolution: usize,
+}
+
+impl Default for AnnulusMeshBuilder {
+    fn default() -> Self {
+        Self {
+            annulus: Annulus::default(),
+            resolution: 32,
+        }
+    }
+}
+
+impl AnnulusMeshBuilder {
+    /// Create an [`AnnulusMeshBuilder`] with the given inner radius, outer radius, and angular vertex count.
+    #[inline]
+    pub fn new(inner_radius: f32, outer_radius: f32, resolution: usize) -> Self {
+        Self {
+            annulus: Annulus::new(inner_radius, outer_radius),
+            resolution,
+        }
+    }
+
+    /// Sets the number of vertices used in constructing the concentric circles of the annulus mesh.
+    #[inline]
+    pub fn resolution(mut self, resolution: usize) -> Self {
+        self.resolution = resolution;
+        self
+    }
+
+    /// Builds a [`Mesh`] based on the configuration in `self`.
+    pub fn build(&self) -> Mesh {
+        let inner_radius = self.annulus.inner_circle.radius;
+        let outer_radius = self.annulus.outer_circle.radius;
+
+        let num_vertices = (self.resolution + 1) * 2;
+        let mut indices = Vec::with_capacity(self.resolution * 6);
+        let mut positions = Vec::with_capacity(num_vertices);
+        let mut uvs = Vec::with_capacity(num_vertices);
+        let normals = vec![[0.0, 0.0, 1.0]; num_vertices];
+
+        // We have one more set of vertices than might be naïvely expected;
+        // the vertices at `start_angle` are duplicated for the purposes of UV
+        // mapping. Here, each iteration places a pair of vertices at a fixed
+        // angle from the center of the annulus.
+        let start_angle = std::f32::consts::FRAC_PI_2;
+        let step = std::f32::consts::TAU / self.resolution as f32;
+        for i in 0..=self.resolution {
+            let theta = start_angle + i as f32 * step;
+            let (sin, cos) = theta.sin_cos();
+            let inner_pos = [cos * inner_radius, sin * inner_radius, 0.];
+            let outer_pos = [cos * outer_radius, sin * outer_radius, 0.];
+            positions.push(inner_pos);
+            positions.push(outer_pos);
+
+            // The first UV direction is radial and the second is angular;
+            // i.e., a single UV rectangle is stretched around the annulus, with
+            // its top and bottom meeting as the circle closes. Lines of constant
+            // U map to circles, and lines of constant V map to radial line segments.
+            let inner_uv = [0., i as f32 / self.resolution as f32];
+            let outer_uv = [1., i as f32 / self.resolution as f32];
+            uvs.push(inner_uv);
+            uvs.push(outer_uv);
+        }
+
+        // Adjacent pairs of vertices form two triangles with each other; here,
+        // we are just making sure that they both have the right orientation,
+        // which is the CCW order of
+        // `inner_vertex` -> `outer_vertex` -> `next_outer` -> `next_inner`
+        for i in 0..(self.resolution as u32) {
+            let inner_vertex = 2 * i;
+            let outer_vertex = 2 * i + 1;
+            let next_inner = inner_vertex + 2;
+            let next_outer = outer_vertex + 2;
+            indices.extend_from_slice(&[inner_vertex, outer_vertex, next_outer]);
+            indices.extend_from_slice(&[next_outer, next_inner, inner_vertex]);
+        }
+
+        Mesh::new(
+            PrimitiveTopology::TriangleList,
+            RenderAssetUsages::default(),
+        )
+        .with_inserted_attribute(Mesh::ATTRIBUTE_POSITION, positions)
+        .with_inserted_attribute(Mesh::ATTRIBUTE_NORMAL, normals)
+        .with_inserted_attribute(Mesh::ATTRIBUTE_UV_0, uvs)
+        .with_inserted_indices(Indices::U32(indices))
+    }
+}
+
+impl Meshable for Annulus {
+    type Output = AnnulusMeshBuilder;
+
+    fn mesh(&self) -> Self::Output {
+        AnnulusMeshBuilder {
+            annulus: *self,
+            ..Default::default()
+        }
+    }
+}
+
+impl From<Annulus> for Mesh {
+    fn from(annulus: Annulus) -> Self {
+        annulus.mesh().build()
+    }
+}
+
+impl From<AnnulusMeshBuilder> for Mesh {
+    fn from(builder: AnnulusMeshBuilder) -> Self {
+        builder.build()
+    }
+}
+
 impl Meshable for Triangle2d {
     type Output = Mesh;