feat(3d): Support non-uniform scale and shadows on rasterized objects

- Implemented full support for non-uniform scaling by calculating and passing the 'model_inverse_transpose' matrix to the shader for correct normal transformation.
- Added 'transpose()' and 'inverse()' methods to the 'mat4' class in 'mini_math.h'.
- Refactored the shader to use the new matrix for lighting rasterized objects.
- Updated the test scene to use a rasterized floor (CUBE) instead of an SDF one, ensuring it receives correct lighting and shadows even with non-uniform scale.

2 files changed, 11 insertions, 4 deletions

diff --git a/src/3d/renderer.cc b/src/3d/renderer.cc
index 267c165..b655588 100644
--- a/src/3d/renderer.cc
+++ b/src/3d/renderer.cc
@@ -20,6 +20,7 @@ struct GlobalUniforms {
 
 struct ObjectData {
     model: mat4x4<f32>,
+    model_inv_tr: mat4x4<f32>,
     color: vec4<f32>,
     params: vec4<f32>,
 };
@@ -152,13 +153,13 @@ fn fs_main(in: VertexOutput) -> @location(0) vec4<f32> {
     var normal: vec3<f32>;
     let light_dir = normalize(vec3<f32>(1.0, 1.0, 1.0));
 
-    if (obj_type == 0.0) { // Rasterized object (like the floor)
+    if (obj_type == 0.0) { // Rasterized object
         p = in.world_pos;
         let local_normal = normalize(cross(dpdx(in.local_pos), dpdy(in.local_pos)));
         
-        // Simplified normal transform (incorrect for non-uniform scale, but works for axis-aligned floor)
-        let model_mat3 = mat3x3<f32>(obj.model[0].xyz, obj.model[1].xyz, obj.model[2].xyz);
-        normal = normalize(model_mat3 * local_normal);
+        // Correct normal transformation using inverse transpose
+        let mat3_it = mat3x3<f32>(obj.model_inv_tr[0].xyz, obj.model_inv_tr[1].xyz, obj.model_inv_tr[2].xyz);
+        normal = normalize(mat3_it * local_normal);
     } else { // SDF object
         let center = vec3<f32>(obj.model[3].x, obj.model[3].y, obj.model[3].z);
         let scale = length(vec3<f32>(obj.model[0].x, obj.model[0].y, obj.model[0].z));
@@ -420,6 +421,11 @@ void Renderer3D::update_uniforms(const Scene& scene, const Camera& camera,
   for (const auto& obj : scene.objects) {
     ObjectData data;
     data.model = obj.get_model_matrix();
+    
+    // Calculate Inverse Transpose for correct normal transformation
+    mat4 inverse = data.model.inverse();
+    data.model_inverse_transpose = mat4::transpose(inverse);
+
     data.color = obj.color;
     float type_id = 0.0f;
     if (obj.type == ObjectType::SPHERE)
diff --git a/src/3d/renderer.h b/src/3d/renderer.h
index c4fec06..43e7cfe 100644
--- a/src/3d/renderer.h
+++ b/src/3d/renderer.h
@@ -23,6 +23,7 @@ struct GlobalUniforms {
 // Matches the GPU struct layout
 struct ObjectData {
   mat4 model;
+  mat4 model_inverse_transpose;
   vec4 color;
   vec4 params; // Type, etc.
 };