Reduce the size of MeshUniform to improve performance (#9416)

# Objective

- Significantly reduce the size of MeshUniform by only including
necessary data.

## Solution

Local to world, model transforms are affine. This means they only need a
4x3 matrix to represent them.

`MeshUniform` stores the current, and previous model transforms, and the
inverse transpose of the current model transform, all as 4x4 matrices.
Instead we can store the current, and previous model transforms as 4x3
matrices, and we only need the upper-left 3x3 part of the inverse
transpose of the current model transform. This change allows us to
reduce the serialized MeshUniform size from 208 bytes to 144 bytes,
which is over a 30% saving in data to serialize, and VRAM bandwidth and
space.

## Benchmarks

On an M1 Max, running `many_cubes -- sphere`, main is in yellow, this PR
is in red:
<img width="1484" alt="Screenshot 2023-08-11 at 02 36 43"
src="https://github.com/bevyengine/bevy/assets/302146/7d99c7b3-f2bb-4004-a8d0-4c00f755cb0d">
A reduction in frame time of ~14%.

---

## Changelog

- Changed: Redefined `MeshUniform` to improve performance by using 4x3
affine transforms and reconstructing 4x4 matrices in the shader. Helper
functions were added to `bevy_pbr::mesh_functions` to unpack the data.
`affine_to_square` converts the packed 4x3 in 3x4 matrix data to a 4x4
matrix. `mat2x4_f32_to_mat3x3` converts the 3x3 in mat2x4 + f32 matrix
data back into a 3x3.

## Migration Guide

Shader code before:
```
var model = mesh[instance_index].model;
```

Shader code after:
```
#import bevy_pbr::mesh_functions affine_to_square

var model = affine_to_square(mesh[instance_index].model);
```

assets/shaders/custom_vertex_attribute.wgsl

@@ -1,6 +1,5 @@
 #import bevy_pbr::mesh_bindings   mesh
-#import bevy_pbr::mesh_functions  mesh_position_local_to_clip
-#import bevy_render::instance_index
+#import bevy_pbr::mesh_functions  get_model_matrix, mesh_position_local_to_clip
 
 struct CustomMaterial {
     color: vec4<f32>,
@@ -23,7 +22,7 @@ struct VertexOutput {
 fn vertex(vertex: Vertex) -> VertexOutput {
     var out: VertexOutput;
     out.clip_position = mesh_position_local_to_clip(
-        mesh[bevy_render::instance_index::get_instance_index(vertex.instance_index)].model,
+        get_model_matrix(vertex.instance_index),
         vec4<f32>(vertex.position, 1.0),
     );
     out.blend_color = vertex.blend_color;

assets/shaders/instancing.wgsl

@@ -1,4 +1,4 @@
-#import bevy_pbr::mesh_functions  mesh_position_local_to_clip
+#import bevy_pbr::mesh_functions  get_model_matrix, mesh_position_local_to_clip
 #import bevy_pbr::mesh_bindings   mesh
 
 struct Vertex {
@@ -19,12 +19,12 @@ struct VertexOutput {
 fn vertex(vertex: Vertex) -> VertexOutput {
     let position = vertex.position * vertex.i_pos_scale.w + vertex.i_pos_scale.xyz;
     var out: VertexOutput;
-    // NOTE: The 0 index into the Mesh array is a hack for this example as the
-    // instance_index builtin would map to the wrong index in the Mesh array.
-    // This index could be passed in via another uniform instead but it's
-    // unnecessary for the example.
+    // NOTE: Passing 0 as the instance_index to get_model_matrix() is a hack
+    // for this example as the instance_index builtin would map to the wrong
+    // index in the Mesh array. This index could be passed in via another
+    // uniform instead but it's unnecessary for the example.
     out.clip_position = mesh_position_local_to_clip(
-        mesh[0].model,
+        get_model_matrix(0),
         vec4<f32>(position, 1.0)
     );
     out.color = vertex.i_color;

crates/bevy_math/src/affine3.rs

@@ -0,0 +1,29 @@
+use glam::{Affine3A, Mat3, Vec3};
+
+/// Reduced-size version of `glam::Affine3A` for use when storage has
+/// significant performance impact. Convert to `glam::Affine3A` to do
+/// non-trivial calculations.
+pub struct Affine3 {
+    /// Scaling, rotation, shears, and other non-translation affine transforms
+    pub matrix3: Mat3,
+    /// Translation
+    pub translation: Vec3,
+}
+
+impl From<&Affine3A> for Affine3 {
+    fn from(affine: &Affine3A) -> Self {
+        Self {
+            matrix3: affine.matrix3.into(),
+            translation: affine.translation.into(),
+        }
+    }
+}
+
+impl From<&Affine3> for Affine3A {
+    fn from(affine3: &Affine3) -> Self {
+        Self {
+            matrix3: affine3.matrix3.into(),
+            translation: affine3.translation.into(),
+        }
+    }
+}

crates/bevy_math/src/lib.rs

@@ -7,10 +7,12 @@
 #![allow(clippy::type_complexity)]
 #![warn(missing_docs)]
 
+mod affine3;
 pub mod cubic_splines;
 mod ray;
 mod rects;
 
+pub use affine3::*;
 pub use ray::Ray;
 pub use rects::*;
 

crates/bevy_pbr/src/light.rs

@@ -2025,7 +2025,7 @@ pub fn check_light_mesh_visibility(
                         view_frusta.iter().zip(view_visible_entities)
                     {
                         // Disable near-plane culling, as a shadow caster could lie before the near plane.
-                        if !frustum.intersects_obb(aabb, &transform.compute_matrix(), false, true) {
+                        if !frustum.intersects_obb(aabb, &transform.affine(), false, true) {
                             continue;
                         }
 
@@ -2098,7 +2098,7 @@ 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) {
-                        let model_to_world = transform.compute_matrix();
+                        let model_to_world = transform.affine();
                         // Do a cheap sphere vs obb test to prune out most meshes outside the sphere of the light
                         if !light_sphere.intersects_obb(aabb, &model_to_world) {
                             continue;
@@ -2162,7 +2162,7 @@ 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) {
-                        let model_to_world = transform.compute_matrix();
+                        let model_to_world = transform.affine();
                         // Do a cheap sphere vs obb test to prune out most meshes outside the sphere of the light
                         if !light_sphere.intersects_obb(aabb, &model_to_world) {
                             continue;

crates/bevy_pbr/src/material.rs

@@ -1,6 +1,6 @@
 use crate::{
     render, AlphaMode, DrawMesh, DrawPrepass, EnvironmentMapLight, MeshPipeline, MeshPipelineKey,
-    MeshUniform, PrepassPipelinePlugin, PrepassPlugin, RenderLightSystems,
+    MeshTransforms, MeshUniform, PrepassPipelinePlugin, PrepassPlugin, RenderLightSystems,
     ScreenSpaceAmbientOcclusionSettings, SetMeshBindGroup, SetMeshViewBindGroup, Shadow,
 };
 use bevy_app::{App, Plugin};
@@ -382,7 +382,7 @@ pub fn queue_material_meshes<M: Material>(
     material_meshes: Query<(
         &Handle<M>,
         &Handle<Mesh>,
-        &MeshUniform,
+        &MeshTransforms,
         &GpuArrayBufferIndex<MeshUniform>,
     )>,
     images: Res<RenderAssets<Image>>,
@@ -468,7 +468,7 @@ pub fn queue_material_meshes<M: Material>(
 
         let rangefinder = view.rangefinder3d();
         for visible_entity in &visible_entities.entities {
-            if let Ok((material_handle, mesh_handle, mesh_uniform, batch_indices)) =
+            if let Ok((material_handle, mesh_handle, mesh_transforms, batch_indices)) =
                 material_meshes.get(*visible_entity)
             {
                 if let (Some(mesh), Some(material)) = (
@@ -516,7 +516,8 @@ pub fn queue_material_meshes<M: Material>(
                         }
                     };
 
-                    let distance = rangefinder.distance(&mesh_uniform.transform)
+                    let distance = rangefinder
+                        .distance_translation(&mesh_transforms.transform.translation)
                         + material.properties.depth_bias;
                     match material.properties.alpha_mode {
                         AlphaMode::Opaque => {

crates/bevy_pbr/src/prepass/mod.rs

@@ -15,7 +15,7 @@ use bevy_ecs::{
         SystemParamItem,
     },
 };
-use bevy_math::Mat4;
+use bevy_math::{Affine3A, Mat4};
 use bevy_reflect::TypeUuid;
 use bevy_render::{
     globals::{GlobalsBuffer, GlobalsUniform},
@@ -46,8 +46,8 @@ use bevy_utils::tracing::error;
 
 use crate::{
     prepare_lights, setup_morph_and_skinning_defs, AlphaMode, DrawMesh, Material, MaterialPipeline,
-    MaterialPipelineKey, MeshLayouts, MeshPipeline, MeshPipelineKey, MeshUniform, RenderMaterials,
-    SetMaterialBindGroup, SetMeshBindGroup,
+    MaterialPipelineKey, MeshLayouts, MeshPipeline, MeshPipelineKey, MeshTransforms, MeshUniform,
+    RenderMaterials, SetMaterialBindGroup, SetMeshBindGroup,
 };
 
 use std::{hash::Hash, marker::PhantomData};
@@ -203,7 +203,7 @@ pub fn update_previous_view_projections(
 }
 
 #[derive(Component)]
-pub struct PreviousGlobalTransform(pub Mat4);
+pub struct PreviousGlobalTransform(pub Affine3A);
 
 pub fn update_mesh_previous_global_transforms(
     mut commands: Commands,
@@ -216,7 +216,7 @@ pub fn update_mesh_previous_global_transforms(
         for (entity, transform) in &meshes {
             commands
                 .entity(entity)
-                .insert(PreviousGlobalTransform(transform.compute_matrix()));
+                .insert(PreviousGlobalTransform(transform.affine()));
         }
     }
 }
@@ -762,7 +762,7 @@ pub fn queue_prepass_material_meshes<M: Material>(
     material_meshes: Query<(
         &Handle<M>,
         &Handle<Mesh>,
-        &MeshUniform,
+        &MeshTransforms,
         &GpuArrayBufferIndex<MeshUniform>,
     )>,
     mut views: Query<(
@@ -809,7 +809,7 @@ pub fn queue_prepass_material_meshes<M: Material>(
         let rangefinder = view.rangefinder3d();
 
         for visible_entity in &visible_entities.entities {
-            let Ok((material_handle, mesh_handle, mesh_uniform, batch_indices)) = material_meshes.get(*visible_entity) else {
+            let Ok((material_handle, mesh_handle, mesh_transforms, batch_indices)) = material_meshes.get(*visible_entity) else {
                 continue;
             };
 
@@ -852,8 +852,8 @@ pub fn queue_prepass_material_meshes<M: Material>(
                 }
             };
 
-            let distance =
-                rangefinder.distance(&mesh_uniform.transform) + material.properties.depth_bias;
+            let distance = rangefinder.distance_translation(&mesh_transforms.transform.translation)
+                + material.properties.depth_bias;
             match alpha_mode {
                 AlphaMode::Opaque => {
                     opaque_phase.add(Opaque3dPrepass {

crates/bevy_pbr/src/prepass/prepass.wgsl

@@ -3,7 +3,7 @@
 #import bevy_pbr::skinning
 #import bevy_pbr::morph
 #import bevy_pbr::mesh_bindings mesh
-#import bevy_render::instance_index
+#import bevy_render::instance_index get_instance_index
 
 // Most of these attributes are not used in the default prepass fragment shader, but they are still needed so we can
 // pass them to custom prepass shaders like pbr_prepass.wgsl.
@@ -92,7 +92,7 @@ fn vertex(vertex_no_morph: Vertex) -> VertexOutput {
 #else // SKINNED
     // Use vertex_no_morph.instance_index instead of vertex.instance_index to work around a wgpu dx12 bug.
     // See https://github.com/gfx-rs/naga/issues/2416
-    var model = mesh[bevy_render::instance_index::get_instance_index(vertex_no_morph.instance_index)].model;
+    var model = bevy_pbr::mesh_functions::get_model_matrix(vertex_no_morph.instance_index);
 #endif // SKINNED
 
     out.clip_position = bevy_pbr::mesh_functions::mesh_position_local_to_clip(model, vec4(vertex.position, 1.0));
@@ -113,7 +113,7 @@ fn vertex(vertex_no_morph: Vertex) -> VertexOutput {
         vertex.normal,
         // Use vertex_no_morph.instance_index instead of vertex.instance_index to work around a wgpu dx12 bug.
         // See https://github.com/gfx-rs/naga/issues/2416
-        bevy_render::instance_index::get_instance_index(vertex_no_morph.instance_index)
+        get_instance_index(vertex_no_morph.instance_index)
     );
 #endif // SKINNED
 
@@ -123,7 +123,7 @@ fn vertex(vertex_no_morph: Vertex) -> VertexOutput {
         vertex.tangent,
         // Use vertex_no_morph.instance_index instead of vertex.instance_index to work around a wgpu dx12 bug.
         // See https://github.com/gfx-rs/naga/issues/2416
-        bevy_render::instance_index::get_instance_index(vertex_no_morph.instance_index)
+        get_instance_index(vertex_no_morph.instance_index)
     );
 #endif // VERTEX_TANGENTS
 #endif // NORMAL_PREPASS
@@ -133,7 +133,7 @@ fn vertex(vertex_no_morph: Vertex) -> VertexOutput {
     // Use vertex_no_morph.instance_index instead of vertex.instance_index to work around a wgpu dx12 bug.
     // See https://github.com/gfx-rs/naga/issues/2416
     out.previous_world_position = bevy_pbr::mesh_functions::mesh_position_local_to_world(
-        mesh[bevy_render::instance_index::get_instance_index(vertex_no_morph.instance_index)].previous_model,
+        bevy_pbr::mesh_functions::get_previous_model_matrix(vertex_no_morph.instance_index),
         vec4<f32>(vertex.position, 1.0)
     );
 #endif // MOTION_VECTOR_PREPASS