bevy_pbr: Fix tangent and normal normalization (bevyengine#5666)

# Objective

- Morten Mikkelsen clarified that the world normal and tangent must be normalized in the vertex stage and the interpolated values must not be normalized in the fragment stage. This is in order to match the mikktspace approach exactly.
- Fixes bevyengine#5514 by ensuring the tangent basis matrix (TBN) is orthonormal

## Solution

- Normalize the world normal in the vertex stage and not the fragment stage
- Normalize the world tangent xyz in the vertex stage
- Take into account the sign of the determinant of the local to world matrix when calculating the bitangent

---

## Changelog

- Fixed - scaling a model that uses normal mapping now has correct lighting again

crates/bevy_pbr/src/render/mesh.rs

@@ -9,7 +9,7 @@ use bevy_ecs::{
     prelude::*,
     system::{lifetimeless::*, SystemParamItem, SystemState},
 };
-use bevy_math::{Mat4, Vec2};
+use bevy_math::{Mat3A, Mat4, Vec2};
 use bevy_reflect::TypeUuid;
 use bevy_render::{
     extract_component::{ComponentUniforms, DynamicUniformIndex, UniformComponentPlugin},
@@ -117,6 +117,9 @@ bitflags::bitflags! {
     #[repr(transparent)]
     struct MeshFlags: u32 {
         const SHADOW_RECEIVER            = (1 << 0);
+        // Indicates the sign of the determinant of the 3x3 model matrix. If the sign is positive,
+        // then the flag should be set, else it should not be set.
+        const SIGN_DETERMINANT_MODEL_3X3 = (1 << 31);
         const NONE                       = 0;
         const UNINITIALIZED              = 0xFFFF;
     }
@@ -143,13 +146,16 @@ pub fn extract_meshes(
 
     for (entity, _, transform, handle, not_receiver, not_caster) in visible_meshes {
         let transform = transform.compute_matrix();
-        let shadow_receiver_flags = if not_receiver.is_some() {
-            MeshFlags::empty().bits
+        let mut flags = if not_receiver.is_some() {
+            MeshFlags::empty()
         } else {
-            MeshFlags::SHADOW_RECEIVER.bits
+            MeshFlags::SHADOW_RECEIVER
         };
+        if Mat3A::from_mat4(transform).determinant().is_sign_positive() {
+            flags |= MeshFlags::SIGN_DETERMINANT_MODEL_3X3;
+        }
         let uniform = MeshUniform {
-            flags: shadow_receiver_flags,
+            flags: flags.bits,
             transform,
             inverse_transpose_model: transform.inverse().transpose(),
         };

crates/bevy_pbr/src/render/mesh_functions.wgsl

@@ -17,20 +17,47 @@ fn mesh_position_local_to_clip(model: mat4x4<f32>, vertex_position: vec4<f32>) -
 }
 
 fn mesh_normal_local_to_world(vertex_normal: vec3<f32>) -> vec3<f32> {
-    return mat3x3<f32>(
-        mesh.inverse_transpose_model[0].xyz,
-        mesh.inverse_transpose_model[1].xyz,
-        mesh.inverse_transpose_model[2].xyz
-    ) * vertex_normal;
+    // NOTE: The mikktspace method of normal mapping requires that the world normal is
+    // re-normalized in the vertex shader to match the way mikktspace bakes vertex tangents
+    // and normal maps so that the exact inverse process is applied when shading. Blender, Unity,
+    // Unreal Engine, Godot, and more all use the mikktspace method. Do not change this code
+    // unless you really know what you are doing.
+    // http://www.mikktspace.com/
+    return normalize(
+        mat3x3<f32>(
+            mesh.inverse_transpose_model[0].xyz,
+            mesh.inverse_transpose_model[1].xyz,
+            mesh.inverse_transpose_model[2].xyz
+        ) * vertex_normal
+    );
+}
+
+// Calculates the sign of the determinant of the 3x3 model matrix based on a
+// mesh flag
+fn sign_determinant_model_3x3() -> f32 {
+    // bool(u32) is false if 0u else true
+    // f32(bool) is 1.0 if true else 0.0
+    // * 2.0 - 1.0 remaps 0.0 or 1.0 to -1.0 or 1.0 respectively
+    return f32(bool(mesh.flags & MESH_FLAGS_SIGN_DETERMINANT_MODEL_3X3_BIT)) * 2.0 - 1.0;
 }
 
 fn mesh_tangent_local_to_world(model: mat4x4<f32>, vertex_tangent: vec4<f32>) -> vec4<f32> {
+    // NOTE: The mikktspace method of normal mapping requires that the world tangent is
+    // re-normalized in the vertex shader to match the way mikktspace bakes vertex tangents
+    // and normal maps so that the exact inverse process is applied when shading. Blender, Unity,
+    // Unreal Engine, Godot, and more all use the mikktspace method. Do not change this code
+    // unless you really know what you are doing.
+    // http://www.mikktspace.com/
     return vec4<f32>(
-        mat3x3<f32>(
-            model[0].xyz,
-            model[1].xyz,
-            model[2].xyz
-        ) * vertex_tangent.xyz,
-        vertex_tangent.w
+        normalize(
+            mat3x3<f32>(
+                model[0].xyz,
+                model[1].xyz,
+                model[2].xyz
+            ) * vertex_tangent.xyz
+        ),
+        // NOTE: Multiplying by the sign of the determinant of the 3x3 model matrix accounts for
+        // situations such as negative scaling.
+        vertex_tangent.w * sign_determinant_model_3x3()
     );
 }

crates/bevy_pbr/src/render/mesh_types.wgsl

@@ -14,3 +14,5 @@ struct SkinnedMesh {
 #endif
 
 let MESH_FLAGS_SHADOW_RECEIVER_BIT: u32 = 1u;
+// 2^31 - if the flag is set, the sign is positive, else it is negative
+let MESH_FLAGS_SIGN_DETERMINANT_MODEL_3X3_BIT: u32 = 2147483648u;

crates/bevy_pbr/src/render/pbr_functions.wgsl

@@ -15,7 +15,13 @@ fn prepare_normal(
 #endif
     is_front: bool,
 ) -> vec3<f32> {
-    var N: vec3<f32> = normalize(world_normal);
+    // NOTE: The mikktspace method of normal mapping explicitly requires that the world normal NOT
+    // be re-normalized in the fragment shader. This is primarily to match the way mikktspace
+    // bakes vertex tangents and normal maps so that this is the exact inverse. Blender, Unity,
+    // Unreal Engine, Godot, and more all use the mikktspace method. Do not change this code
+    // unless you really know what you are doing.
+    // http://www.mikktspace.com/
+    var N: vec3<f32> = world_normal;
 
 #ifdef VERTEX_TANGENTS
 #ifdef STANDARDMATERIAL_NORMAL_MAP
@@ -236,7 +242,7 @@ fn pbr(
 fn tone_mapping(in: vec4<f32>) -> vec4<f32> {
     // tone_mapping
     return vec4<f32>(reinhard_luminance(in.rgb), in.a);
-    
+
     // Gamma correction.
     // Not needed with sRGB buffer
     // output_color.rgb = pow(output_color.rgb, vec3(1.0 / 2.2));