Faster view frustum culling (bevyengine#4181)

# Objective

- Reduce time spent in the `check_visibility` system

## Solution

- Use `Vec3A` for all bounding volume types to leverage SIMD optimisations and to avoid repeated runtime conversions from `Vec3` to `Vec3A`
- Inline all bounding volume intersection methods
- Add on-the-fly calculated `Aabb` -> `Sphere` and do `Sphere`-`Frustum` intersection tests before `Aabb`-`Frustum` tests. This is faster for `many_cubes` but could be slower in other cases where the sphere test gives a false-positive that the `Aabb` test discards. Also, I tested precalculating the `Sphere`s and inserting them alongside the `Aabb` but this was slower. 
- Do not test meshes against the far plane. Apparently games don't do this anymore with infinite projections, and it's one fewer plane to test against. I made it optional and still do the test for culling lights but that is up for discussion.
- These collectively reduce `check_visibility` execution time in `many_cubes -- sphere` from 2.76ms to 1.48ms and increase frame rate from ~42fps to ~44fps

crates/bevy_pbr/src/light.rs

@@ -2,7 +2,7 @@ use std::collections::HashSet;
 
 use bevy_asset::Assets;
 use bevy_ecs::prelude::*;
-use bevy_math::{Mat4, UVec2, UVec3, Vec2, Vec3, Vec3Swizzles, Vec4, Vec4Swizzles};
+use bevy_math::{Mat4, UVec2, UVec3, Vec2, Vec3, Vec3A, Vec3Swizzles, Vec4, Vec4Swizzles};
 use bevy_reflect::Reflect;
 use bevy_render::{
     camera::{Camera, CameraProjection, OrthographicProjection},
@@ -640,8 +640,8 @@ fn cluster_space_light_aabb(
     light_sphere: &Sphere,
 ) -> (Vec3, Vec3) {
     let light_aabb_view = Aabb {
-        center: (inverse_view_transform * light_sphere.center.extend(1.0)).xyz(),
-        half_extents: Vec3::splat(light_sphere.radius),
+        center: Vec3A::from(inverse_view_transform * light_sphere.center.extend(1.0)),
+        half_extents: Vec3A::splat(light_sphere.radius),
     };
     let (mut light_aabb_view_min, mut light_aabb_view_max) =
         (light_aabb_view.min(), light_aabb_view.max());
@@ -798,13 +798,13 @@ pub(crate) fn assign_lights_to_clusters(
                 false
             } else {
                 let light_sphere = Sphere {
-                    center: light.translation,
+                    center: Vec3A::from(light.translation),
                     radius: light.range,
                 };
 
                 let light_in_view = frusta
                     .iter()
-                    .any(|frustum| frustum.intersects_sphere(&light_sphere));
+                    .any(|frustum| frustum.intersects_sphere(&light_sphere, true));
 
                 if light_in_view {
                     lights_in_view_count += 1;
@@ -875,12 +875,12 @@ pub(crate) fn assign_lights_to_clusters(
             let mut cluster_index_estimate = 0.0;
             for light in lights.iter() {
                 let light_sphere = Sphere {
-                    center: light.translation,
+                    center: Vec3A::from(light.translation),
                     radius: light.range,
                 };
 
                 // Check if the light is within the view frustum
-                if !frustum.intersects_sphere(&light_sphere) {
+                if !frustum.intersects_sphere(&light_sphere, true) {
                     continue;
                 }
 
@@ -965,12 +965,12 @@ pub(crate) fn assign_lights_to_clusters(
 
         for light in lights.iter() {
             let light_sphere = Sphere {
-                center: light.translation,
+                center: Vec3A::from(light.translation),
                 radius: light.range,
             };
 
             // Check if the light is within the view frustum
-            if !frustum.intersects_sphere(&light_sphere) {
+            if !frustum.intersects_sphere(&light_sphere, true) {
                 continue;
             }
 
@@ -1174,7 +1174,7 @@ pub fn check_light_mesh_visibility(
 
             // If we have an aabb and transform, do frustum culling
             if let (Some(aabb), Some(transform)) = (maybe_aabb, maybe_transform) {
-                if !frustum.intersects_obb(aabb, &transform.compute_matrix()) {
+                if !frustum.intersects_obb(aabb, &transform.compute_matrix(), true) {
                     continue;
                 }
             }
@@ -1209,7 +1209,7 @@ pub fn check_light_mesh_visibility(
 
                 let view_mask = maybe_view_mask.copied().unwrap_or_default();
                 let light_sphere = Sphere {
-                    center: transform.translation,
+                    center: Vec3A::from(transform.translation),
                     radius: point_light.range,
                 };
 
@@ -1242,7 +1242,7 @@ pub fn check_light_mesh_visibility(
                             .iter()
                             .zip(cubemap_visible_entities.iter_mut())
                         {
-                            if frustum.intersects_obb(aabb, &model_to_world) {
+                            if frustum.intersects_obb(aabb, &model_to_world, true) {
                                 computed_visibility.is_visible = true;
                                 visible_entities.entities.push(entity);
                             }

crates/bevy_render/src/primitives/mod.rs

@@ -6,12 +6,15 @@ use bevy_reflect::Reflect;
 #[derive(Component, Clone, Debug, Default, Reflect)]
 #[reflect(Component)]
 pub struct Aabb {
-    pub center: Vec3,
-    pub half_extents: Vec3,
+    pub center: Vec3A,
+    pub half_extents: Vec3A,
 }
 
 impl Aabb {
+    #[inline]
     pub fn from_min_max(minimum: Vec3, maximum: Vec3) -> Self {
+        let minimum = Vec3A::from(minimum);
+        let maximum = Vec3A::from(maximum);
         let center = 0.5 * (maximum + minimum);
         let half_extents = 0.5 * (maximum - minimum);
         Self {
@@ -21,9 +24,10 @@ impl Aabb {
     }
 
     /// Calculate the relative radius of the AABB with respect to a plane
+    #[inline]
     pub fn relative_radius(&self, p_normal: &Vec3A, axes: &[Vec3A]) -> f32 {
         // NOTE: dot products on Vec3A use SIMD and even with the overhead of conversion are net faster than Vec3
-        let half_extents = Vec3A::from(self.half_extents);
+        let half_extents = self.half_extents;
         Vec3A::new(
             p_normal.dot(axes[0]),
             p_normal.dot(axes[1]),
@@ -33,39 +37,43 @@ impl Aabb {
         .dot(half_extents)
     }
 
-    pub fn min(&self) -> Vec3 {
+    #[inline]
+    pub fn min(&self) -> Vec3A {
         self.center - self.half_extents
     }
 
-    pub fn max(&self) -> Vec3 {
+    #[inline]
+    pub fn max(&self) -> Vec3A {
         self.center + self.half_extents
     }
 }
 
 impl From<Sphere> for Aabb {
+    #[inline]
     fn from(sphere: Sphere) -> Self {
         Self {
             center: sphere.center,
-            half_extents: Vec3::splat(sphere.radius),
+            half_extents: Vec3A::splat(sphere.radius),
         }
     }
 }
 
 #[derive(Debug, Default)]
 pub struct Sphere {
-    pub center: Vec3,
+    pub center: Vec3A,
     pub radius: f32,
 }
 
 impl Sphere {
+    #[inline]
     pub fn intersects_obb(&self, aabb: &Aabb, local_to_world: &Mat4) -> bool {
         let aabb_center_world = *local_to_world * aabb.center.extend(1.0);
         let axes = [
             Vec3A::from(local_to_world.x_axis),
             Vec3A::from(local_to_world.y_axis),
             Vec3A::from(local_to_world.z_axis),
         ];
-        let v = Vec3A::from(aabb_center_world) - Vec3A::from(self.center);
+        let v = Vec3A::from(aabb_center_world) - self.center;
         let d = v.length();
         let relative_radius = aabb.relative_radius(&(v / d), &axes);
         d < self.radius + relative_radius
@@ -96,8 +104,8 @@ impl Plane {
 
     /// `Plane` unit normal
     #[inline]
-    pub fn normal(&self) -> Vec3 {
-        self.normal_d.xyz()
+    pub fn normal(&self) -> Vec3A {
+        Vec3A::from(self.normal_d)
     }
 
     /// Signed distance from the origin along the unit normal such that n.p + d = 0 for point p in
@@ -127,6 +135,7 @@ impl Frustum {
     // projection matrix is from Foundations of Game Engine Development 2
     // Rendering by Lengyel. Slight modification has been made for when
     // the far plane is infinite but we still want to cull to a far plane.
+    #[inline]
     pub fn from_view_projection(
         view_projection: &Mat4,
         view_translation: &Vec3,
@@ -148,24 +157,29 @@ impl Frustum {
         Self { planes }
     }
 
-    pub fn intersects_sphere(&self, sphere: &Sphere) -> bool {
-        for plane in &self.planes {
-            if plane.normal_d().dot(sphere.center.extend(1.0)) + sphere.radius <= 0.0 {
+    #[inline]
+    pub fn intersects_sphere(&self, sphere: &Sphere, intersect_far: bool) -> bool {
+        let sphere_center = sphere.center.extend(1.0);
+        let max = if intersect_far { 6 } else { 5 };
+        for plane in &self.planes[..max] {
+            if plane.normal_d().dot(sphere_center) + sphere.radius <= 0.0 {
                 return false;
             }
         }
         true
     }
 
-    pub fn intersects_obb(&self, aabb: &Aabb, model_to_world: &Mat4) -> bool {
-        let aabb_center_world = *model_to_world * aabb.center.extend(1.0);
+    #[inline]
+    pub fn intersects_obb(&self, aabb: &Aabb, model_to_world: &Mat4, intersect_far: bool) -> bool {
+        let aabb_center_world = model_to_world.transform_point3a(aabb.center).extend(1.0);
         let axes = [
             Vec3A::from(model_to_world.x_axis),
             Vec3A::from(model_to_world.y_axis),
             Vec3A::from(model_to_world.z_axis),
         ];
 
-        for plane in &self.planes {
+        let max = if intersect_far { 6 } else { 5 };
+        for plane in &self.planes[..max] {
             let p_normal = Vec3A::from(plane.normal_d());
             let relative_radius = aabb.relative_radius(&p_normal, &axes);
             if plane.normal_d().dot(aabb_center_world) + relative_radius <= 0.0 {
@@ -215,21 +229,21 @@ mod tests {
         // Sphere outside frustum
         let frustum = big_frustum();
         let sphere = Sphere {
-            center: Vec3::new(0.9167, 0.0000, 0.0000),
+            center: Vec3A::new(0.9167, 0.0000, 0.0000),
             radius: 0.7500,
         };
-        assert!(!frustum.intersects_sphere(&sphere));
+        assert!(!frustum.intersects_sphere(&sphere, true));
     }
 
     #[test]
     fn intersects_sphere_big_frustum_intersect() {
         // Sphere intersects frustum boundary
         let frustum = big_frustum();
         let sphere = Sphere {
-            center: Vec3::new(7.9288, 0.0000, 2.9728),
+            center: Vec3A::new(7.9288, 0.0000, 2.9728),
             radius: 2.0000,
         };
-        assert!(frustum.intersects_sphere(&sphere));
+        assert!(frustum.intersects_sphere(&sphere, true));
     }
 
     // A frustum
@@ -251,65 +265,65 @@ mod tests {
         // Sphere surrounds frustum
         let frustum = frustum();
         let sphere = Sphere {
-            center: Vec3::new(0.0000, 0.0000, 0.0000),
+            center: Vec3A::new(0.0000, 0.0000, 0.0000),
             radius: 3.0000,
         };
-        assert!(frustum.intersects_sphere(&sphere));
+        assert!(frustum.intersects_sphere(&sphere, true));
     }
 
     #[test]
     fn intersects_sphere_frustum_contained() {
         // Sphere is contained in frustum
         let frustum = frustum();
         let sphere = Sphere {
-            center: Vec3::new(0.0000, 0.0000, 0.0000),
+            center: Vec3A::new(0.0000, 0.0000, 0.0000),
             radius: 0.7000,
         };
-        assert!(frustum.intersects_sphere(&sphere));
+        assert!(frustum.intersects_sphere(&sphere, true));
     }
 
     #[test]
     fn intersects_sphere_frustum_intersects_plane() {
         // Sphere intersects a plane
         let frustum = frustum();
         let sphere = Sphere {
-            center: Vec3::new(0.0000, 0.0000, 0.9695),
+            center: Vec3A::new(0.0000, 0.0000, 0.9695),
             radius: 0.7000,
         };
-        assert!(frustum.intersects_sphere(&sphere));
+        assert!(frustum.intersects_sphere(&sphere, true));
     }
 
     #[test]
     fn intersects_sphere_frustum_intersects_2_planes() {
         // Sphere intersects 2 planes
         let frustum = frustum();
         let sphere = Sphere {
-            center: Vec3::new(1.2037, 0.0000, 0.9695),
+            center: Vec3A::new(1.2037, 0.0000, 0.9695),
             radius: 0.7000,
         };
-        assert!(frustum.intersects_sphere(&sphere));
+        assert!(frustum.intersects_sphere(&sphere, true));
     }
 
     #[test]
     fn intersects_sphere_frustum_intersects_3_planes() {
         // Sphere intersects 3 planes
         let frustum = frustum();
         let sphere = Sphere {
-            center: Vec3::new(1.2037, -1.0988, 0.9695),
+            center: Vec3A::new(1.2037, -1.0988, 0.9695),
             radius: 0.7000,
         };
-        assert!(frustum.intersects_sphere(&sphere));
+        assert!(frustum.intersects_sphere(&sphere, true));
     }
 
     #[test]
     fn intersects_sphere_frustum_dodges_1_plane() {
         // Sphere avoids intersecting the frustum by 1 plane
         let frustum = frustum();
         let sphere = Sphere {
-            center: Vec3::new(-1.7020, 0.0000, 0.0000),
+            center: Vec3A::new(-1.7020, 0.0000, 0.0000),
             radius: 0.7000,
         };
-        assert!(!frustum.intersects_sphere(&sphere));
+        assert!(!frustum.intersects_sphere(&sphere, true));
     }
 
     // A long frustum.
@@ -331,20 +345,20 @@ mod tests {
         // Sphere outside frustum
         let frustum = long_frustum();
         let sphere = Sphere {
-            center: Vec3::new(-4.4889, 46.9021, 0.0000),
+            center: Vec3A::new(-4.4889, 46.9021, 0.0000),
             radius: 0.7500,
         };
-        assert!(!frustum.intersects_sphere(&sphere));
+        assert!(!frustum.intersects_sphere(&sphere, true));
     }
 
     #[test]
     fn intersects_sphere_long_frustum_intersect() {
         // Sphere intersects frustum boundary
         let frustum = long_frustum();
         let sphere = Sphere {
-            center: Vec3::new(-4.9957, 0.0000, -0.7396),
+            center: Vec3A::new(-4.9957, 0.0000, -0.7396),
             radius: 4.4094,
         };
-        assert!(frustum.intersects_sphere(&sphere));
+        assert!(frustum.intersects_sphere(&sphere, true));
     }
 }

crates/bevy_render/src/view/visibility/mod.rs

@@ -1,5 +1,6 @@
 mod render_layers;
 
+use bevy_math::Vec3A;
 pub use render_layers::*;
 
 use bevy_app::{CoreStage, Plugin};
@@ -12,7 +13,7 @@ use bevy_transform::TransformSystem;
 use crate::{
     camera::{Camera, CameraProjection, OrthographicProjection, PerspectiveProjection},
     mesh::Mesh,
-    primitives::{Aabb, Frustum},
+    primitives::{Aabb, Frustum, Sphere},
 };
 
 /// User indication of whether an entity is visible
@@ -181,10 +182,20 @@ pub fn check_visibility(
             }
 
             // If we have an aabb and transform, do frustum culling
-            if let (Some(aabb), None, Some(transform)) =
+            if let (Some(model_aabb), None, Some(transform)) =
                 (maybe_aabb, maybe_no_frustum_culling, maybe_transform)
             {
-                if !frustum.intersects_obb(aabb, &transform.compute_matrix()) {
+                let model = transform.compute_matrix();
+                let model_sphere = Sphere {
+                    center: model.transform_point3a(model_aabb.center),
+                    radius: (Vec3A::from(transform.scale) * model_aabb.half_extents).length(),
+                };
+                // Do quick sphere-based frustum culling
+                if !frustum.intersects_sphere(&model_sphere, false) {
+                    continue;
+                }
+                // If we have an aabb, do aabb-based frustum culling
+                if !frustum.intersects_obb(model_aabb, &model, false) {
                     continue;
                 }
             }