even nicer rings

assets/shaders/jupiters_rings.wgsl

@@ -140,6 +140,53 @@ fn ring_density(radius: f32) -> f32 {
     return 0.0;
 }
 
+fn smooth_edge2(start: f32, end: f32, value: f32) -> f32 {
+    var x: f32 = (value - start) / (end - start);
+    return 4 * x * x * (1 - x * x);
+}
+
+fn ring_density2(radius: f32) -> f32 {
+    let halo_inner: f32 = 92.0;
+    let halo_outer: f32 = 122.5;
+    let main_inner: f32 = 122.5;
+    let main_outer: f32 = 129.0;
+    let amalthea_inner: f32 = 129.0;
+    let amalthea_outer: f32 = 182.0;
+    let thebe_inner: f32 = 129.0;
+    let thebe_outer: f32 = 229.0;
+    let metis_notch_center: f32 = 128.0;
+    let metis_notch_width: f32 = 0.6;
+
+    let halo_brightness: f32 = 0.3;
+    let main_brightness: f32 = 1.0;
+    let almathea_brightness: f32 = 0.2;
+    let thebe_brightness: f32 = 0.2;
+
+    let inner_smooth_factor: f32 = 2.0; // Smooth inner edges
+    let outer_smooth_factor: f32 = 1.5; // Rougher outer edges
+
+    var density: f32 = 0.0;
+
+    if (radius >= halo_inner && radius <= halo_outer) {
+        density = halo_brightness * smooth_edge2(halo_inner, halo_outer, radius);
+    } else if (radius >= main_inner && radius <= main_outer) {
+        var metis_notch_effect: f32 = 1.0;
+        if (radius > metis_notch_center - metis_notch_width * 0.5 && radius < metis_notch_center + metis_notch_width * 0.5) {
+            metis_notch_effect = 0.5 * (1.0 - smooth_edge2(metis_notch_center - metis_notch_width * 0.5, metis_notch_center + metis_notch_width * 0.5, radius));
+        }
+        density = main_brightness * metis_notch_effect * smooth_edge2(main_inner, main_outer, radius);
+    } else {
+        if (radius >= amalthea_inner && radius <= amalthea_outer) {
+            density = almathea_brightness * smooth_edge2(amalthea_inner, amalthea_outer, radius);
+        }
+        if (radius >= thebe_inner && radius <= thebe_outer) {
+            density += thebe_brightness * smooth_edge2(thebe_inner, thebe_outer, radius);
+        }
+    }
+
+    return density;
+}
+
 @fragment
 fn fragment(in: VertexOutput) -> @location(0) vec4<f32> {
     let jupiter_percent = jupiter_radius / ring_radius;
@@ -148,7 +195,7 @@ fn fragment(in: VertexOutput) -> @location(0) vec4<f32> {
     let r_uv = 2 * distance(in.uv, vec2<f32>(0.5));
     let r = r_uv * ring_radius / jupiter_radius * jupiter_radius_Mm;
 
-    alpha *= ring_density(r);
+    alpha *= ring_density2(r);
     if alpha <= 0.0 {
         return vec4<f32>(color, alpha);
     }