mandelbulb

assets/shaders/material.wgsl

@@ -9,13 +9,51 @@ struct VoluMaterial {
     mesh_translation: vec3<f32>,
     sphere_radius: f32,
     color: vec4<f32>,
+    model_inverse: mat4x4<f32>,
+    power: f32,
+    iterations: i32,
 }
 
 @group(2) @binding(100)
 var<storage, read> volu_material: VoluMaterial;
 
-fn sphere_sdf(p: vec3<f32>, center: vec3<f32>, radius: f32) -> f32 {
+fn mandelbulb_sdf(p: vec3<f32>) -> f32 {
-    return length(p - center) - radius;
+    var z = p;
+    var dr = 1.0;
+    var r = 0.0;
+    let power = volu_material.power;
+    let iterations = volu_material.iterations;
+
+    for (var i = 0; i < iterations; i++) {
+        r = length(z);
+        if r > 2.0 {
+            break;
+        }
+
+        let theta = acos(clamp(z.z / r, -1.0, 1.0));
+        let phi = atan2(z.y, z.x);
+        dr = pow(r, power - 1.0) * power * dr + 1.0;
+
+        let zr = pow(r, power);
+        let new_theta = theta * power;
+        let new_phi = phi * power;
+
+        z = zr * vec3<f32>(
+            sin(new_theta) * cos(new_phi),
+            sin(new_theta) * sin(new_phi),
+            cos(new_theta)
+        ) + p;
+    }
+
+    return 0.5 * log(max(r, 0.001)) * r / dr;
+}
+
+fn mandelbulb_normal(p: vec3<f32>) -> vec3<f32> {
+    let e = 0.001;
+    let dx = mandelbulb_sdf(p + vec3<f32>(e, 0.0, 0.0)) - mandelbulb_sdf(p - vec3<f32>(e, 0.0, 0.0));
+    let dy = mandelbulb_sdf(p + vec3<f32>(0.0, e, 0.0)) - mandelbulb_sdf(p - vec3<f32>(0.0, e, 0.0));
+    let dz = mandelbulb_sdf(p + vec3<f32>(0.0, 0.0, e)) - mandelbulb_sdf(p - vec3<f32>(0.0, 0.0, e));
+    return normalize(vec3<f32>(dx, dy, dz));
 }
 
 fn raymarch(ray_origin: vec3<f32>, ray_direction: vec3<f32>) -> f32 {
@@ -26,7 +64,7 @@ fn raymarch(ray_origin: vec3<f32>, ray_direction: vec3<f32>) -> f32 {
 
     for (var i = 0; i < max_steps; i++) {
         let current_pos = ray_origin + t * ray_direction;
-        let distance = sphere_sdf(current_pos, volu_material.mesh_translation, volu_material.sphere_radius);
+        let distance = mandelbulb_sdf(current_pos);
 
         if distance < epsilon {
             return t;
@@ -42,20 +80,6 @@ fn raymarch(ray_origin: vec3<f32>, ray_direction: vec3<f32>) -> f32 {
     return -1.0;
 }
 
-fn sphere_normal(p: vec3<f32>) -> vec3<f32> {
-    let epsilon = 0.001;
-    let center = volu_material.mesh_translation;
-    let radius = volu_material.sphere_radius;
-
-    let gradient = vec3<f32>(
-        sphere_sdf(p + vec3<f32>(epsilon, 0.0, 0.0), center, radius) - sphere_sdf(p - vec3<f32>(epsilon, 0.0, 0.0), center, radius),
-        sphere_sdf(p + vec3<f32>(0.0, epsilon, 0.0), center, radius) - sphere_sdf(p - vec3<f32>(0.0, epsilon, 0.0), center, radius),
-        sphere_sdf(p + vec3<f32>(0.0, 0.0, epsilon), center, radius) - sphere_sdf(p - vec3<f32>(0.0, 0.0, epsilon), center, radius)
-    );
-
-    return normalize(gradient);
-}
-
 @fragment
 fn fragment(
     vertex_output: VertexOutput,
@@ -66,20 +90,27 @@ fn fragment(
     let ray_origin = view.world_position;
     let ray_direction = normalize(in.world_position.xyz - view.world_position);
 
-    let t = raymarch(ray_origin, ray_direction);
+    let local_origin = (volu_material.model_inverse * vec4<f32>(ray_origin, 1.0)).xyz;
+    let local_direction = normalize((volu_material.model_inverse * vec4<f32>(ray_direction, 0.0)).xyz);
+
+    let t = raymarch(local_origin, local_direction);
 
     var out: FragmentOutput;
 
     if t > 0.0 {
-        let hit_point = ray_origin + t * ray_direction;
+        let local_hit_point = ray_origin + t * ray_direction;
-        let normal = sphere_normal(hit_point);
+        let local_normal = mandelbulb_normal(local_hit_point);
 
-        in.world_position = vec4<f32>(hit_point, 1.0);
+        let world_hit_point = (transpose(volu_material.model_inverse) * vec4<f32>(local_hit_point, 1.0)).xyz;
-        in.world_normal = normal;
+        let world_normal = normalize((transpose(volu_material.model_inverse) * vec4<f32>(local_normal, 0.0)).xyz);
+
+        in.world_position = vec4<f32>(world_hit_point, 1.0);
+        in.world_normal = world_normal;
 
         var pbr_input = pbr_input_from_standard_material(in, is_front);
 
-        pbr_input.material.base_color = alpha_discard(pbr_input.material, pbr_input.material.base_color);
+        let n = world_normal * 0.5 + 0.5;
+        pbr_input.material.base_color = alpha_discard(pbr_input.material, vec4<f32>(n, 1.0));
 
         out.color = apply_pbr_lighting(pbr_input);
 

src/main.rs

@@ -30,6 +30,9 @@ fn setup(
         mesh_translation: transform.translation,
         sphere_radius: 1.0,
         color: Vec4::default(),
+        model_inverse: transform.compute_matrix().inverse(),
+        power: 8.0,
+        iterations: 32,
     }));
 
     commands.spawn((
@@ -49,6 +52,7 @@ fn setup(
     commands.spawn((
         DirectionalLight::default(),
         Transform::from_xyz(1.0, 1.0, 1.0).looking_at(Vec3::ZERO, Vec3::Y),
+        Rotate,
     ));
 
     commands.spawn((
@@ -67,14 +71,12 @@ fn rotate_things(mut q: Query<&mut Transform, With<Rotate>>, time: Res<Time>) {
 }
 
 fn update_volu_material(
-    mut q: Query<(&mut Transform, &MeshMaterial3d<VoluMaterial>), Changed<Transform>>,
+    q: Query<(&Transform, &MeshMaterial3d<VoluMaterial>), Changed<Transform>>,
     mut volu_materials: ResMut<Assets<VoluMaterial>>,
     mut buffers: ResMut<Assets<ShaderStorageBuffer>>,
     time: Res<Time>,
 ) {
-    for (mut transform, material) in q.iter_mut() {
+    for (transform, material) in q.iter() {
-        transform.translation.y = time.elapsed_secs().sin();
-
         let volu_material = volu_materials.get_mut(material.0.id()).unwrap();
 
         let buffer = buffers
@@ -87,6 +89,9 @@ fn update_volu_material(
             mesh_translation: transform.translation,
             sphere_radius: (elapsed.sin() + 3.) / 4.,
             color: vec4((elapsed.sin() + 1.) / 2., 0.0, 0.0, 1.0),
+            model_inverse: transform.compute_matrix(),
+            power: 8.0,
+            iterations: 32,
         };
 
         buffer.set_data(volu_storage);
@@ -110,4 +115,7 @@ pub struct VoluStorage {
     mesh_translation: Vec3,
     sphere_radius: f32,
     color: Vec4,
+    model_inverse: Mat4,
+    power: f32,
+    iterations: i32,
 }