feat: procedural lensed starfield background

assets/shaders/black_hole.wgsl

@@ -1,6 +1,7 @@
 #import bevy_sprite::mesh2d_vertex_output::VertexOutput
 #import "shaders/ray_gen.wgsl"
 #import "shaders/geodesic_schwarzschild.wgsl"
+#import "shaders/stars.wgsl"
 
 struct BlackHoleUniforms {
     eye: vec4<f32>,
@@ -36,13 +37,13 @@ fn fragment(in: VertexOutput) -> @location(0) vec4<f32> {
     var uv = (in.uv * 2.0 - 1.0);
     uv.x *= aspect;
     let dir = ray_direction(uv);
-    // Step size scales with how far we need to travel (~ distance/ steps).
     let dt = max(length(uniforms.eye.xyz), 20.0) / f32(uniforms.steps);
     let res = classify_ray(uniforms.eye.xyz, dir, uniforms.steps, dt);
     if (res.status == 1u) {
         // Captured = shadow.
         return vec4<f32>(0.0, 0.0, 0.0, 1.0);
     }
-    // Escaped: dim grey for now (stars come in Task 11).
+    // Escaped: sample procedural stars along the bent final direction.
-    return vec4<f32>(0.02, 0.02, 0.02, 1.0);
+    let star = star_color(normalize(res.final_dir), uniforms.star_intensity);
+    return vec4<f32>(star, 1.0);
 }

assets/shaders/stars.wgsl

@@ -0,0 +1,27 @@
+// Hash-based procedural stars on the unit sphere. Returns RGB radiance.
+fn hash13(p: vec3<f32>) -> f32 {
+    var q = vec3<f32>(dot(p, vec3<f32>(127.1, 311.7, 74.7)),
+                      dot(p, vec3<f32>(269.5, 183.3, 246.1)),
+                      dot(p, vec3<f32>(113.5, 271.9, 124.6)));
+    let h = fract(sin(q) * 43758.5453);
+    return h.x;
+}
+
+fn star_color(dir: vec3<f32>, intensity: f32) -> vec3<f32> {
+    // Divide the sphere into cells; a cell gets a star if its hash passes a threshold.
+    let scale = 80.0;
+    let cell = floor(dir * scale);
+    let h = hash13(cell);
+    let threshold = 0.985; // ~1.5% of cells hold a star
+    if (h > threshold) {
+        // Brightness from the hash remainder.
+        let b = (h - threshold) / (1.0 - threshold);
+        let col = mix(vec3<f32>(0.6, 0.7, 1.0), vec3<f32>(1.0, 0.9, 0.7), b);
+        // Soften the star with the fractional position inside the cell.
+        let f = abs(dir * scale - cell);
+        let d = max(f.x, max(f.y, f.z));
+        let falloff = smoothstep(0.5, 0.0, d);
+        return col * b * falloff * 3.0 * intensity;
+    }
+    return vec3<f32>(0.0);
+}