feat(shaders): Add optimized 4-sample SDF normal estimation

Adds get_normal_fast() variant using tetrahedral gradient approximation.

Performance improvement:
- 4 SDF evaluations (vs 6 in get_normal_basic)
- ~33% fewer distance field samples
- Tetrahedron pattern: k.xyy, k.yyx, k.yxy, k.xxx where k=(1,-1)

Trade-off:
- Slightly less accurate than central differences method
- Good for real-time rendering where performance matters
- Same sphere optimization (analytical normal for obj_type == 1.0)

Parameters:
- epsilon: 0.0001 (vs 0.001 in basic method)
- Same interface: takes position and object params

Use case: Fast lighting calculations, performance-critical shaders

1 files changed, 16 insertions, 0 deletions

diff --git a/assets/final/shaders/math/sdf_utils.wgsl b/assets/final/shaders/math/sdf_utils.wgsl
index c2e49cf..3b06b93 100644
--- a/assets/final/shaders/math/sdf_utils.wgsl
+++ b/assets/final/shaders/math/sdf_utils.wgsl
@@ -9,6 +9,22 @@ fn get_normal_basic(p: vec3<f32>, obj_params: vec4<f32>) -> vec3<f32> {
     ));
 }
 
+// Optimized normal estimation using tetrahedron pattern (4 SDF evals instead of 6).
+// Slightly less accurate than central differences but faster.
+// Uses tetrahedral gradient approximation with corners at (±1, ±1, ±1).
+fn get_normal_fast(p: vec3<f32>, obj_params: vec4<f32>) -> vec3<f32> {
+    let obj_type = obj_params.x;
+    if (obj_type == 1.0) { return normalize(p); }
+    let eps = 0.0001;
+    let k = vec2<f32>(1.0, -1.0);
+    return normalize(
+        k.xyy * get_dist(p + k.xyy * eps, obj_params) +
+        k.yyx * get_dist(p + k.yyx * eps, obj_params) +
+        k.yxy * get_dist(p + k.yxy * eps, obj_params) +
+        k.xxx * get_dist(p + k.xxx * eps, obj_params)
+    );
+}
+
 // Distance to an Axis-Aligned Bounding Box
 fn aabb_sdf(p: vec3<f32>, min_p: vec3<f32>, max_p: vec3<f32>) -> f32 {
     let center = (min_p + max_p) * 0.5;