feat: lensed planet ray-sphere intersection in geodesic tracer

Add planets as ray-traced spheres inside the RK4 geodesic loop. A new
planets.wgsl shader tests each integrator segment against a storage
buffer of SphereData (center/radius/color/emissive) and composites hits
front-to-back alongside the accretion disk. Lambert shading with a fixed
light direction; emissive flag bypasses shading.

- assets/shaders/planets.wgsl: segment-sphere intersection + shading
- src/scene/: Planet component, upload_planets system, default planet
- black_hole.wgsl: wire planet_hit into the compositing loop
- geodesic_schwarzschild.wgsl: replace tuple return with Deriv struct

assets/shaders/black_hole.wgsl

@@ -3,6 +3,7 @@
 #import "shaders/geodesic_schwarzschild.wgsl"
 #import "shaders/stars.wgsl"
 #import "shaders/disk.wgsl"
+#import "shaders/planets.wgsl"
 
 struct BlackHoleUniforms {
     eye: vec4<f32>,
@@ -39,15 +40,12 @@ fn fragment(in: VertexOutput) -> @location(0) vec4<f32> {
     uv.x *= aspect;
     let dir = ray_direction(uv);
 
-    // Work in disk-local space: rotate eye + dir by -disk_tilt around X so the
-    // disk lies on y=0. (disk_hit/disk_color assume disk-local coords.)
     var pos = rot_x(uniforms.eye.xyz, -uniforms.disk_tilt);
     var d   = normalize(rot_x(dir, -uniforms.disk_tilt));
 
     let dt = max(length(uniforms.eye.xyz), 20.0) / f32(uniforms.steps);
     let steps = uniforms.steps;
 
-    // Front-to-back compositing.
     var accum_color = vec3<f32>(0.0);
     var accum_alpha = 0.0;
 
@@ -55,12 +53,9 @@ fn fragment(in: VertexOutput) -> @location(0) vec4<f32> {
     for (var i: u32 = 0u; i < steps; i = i + 1u) {
         let r = length(pos);
         if (r < uniforms.rs) {
-            // Captured: whatever we've composited so far is the result.
             break;
         }
         if (r > 1000.0) {
-            // Escaped: add background stars along the (disk-local) final dir.
-            // Rotate back to world for the star sample.
             let world_dir = normalize(rot_x(d, uniforms.disk_tilt));
             let star = star_color(world_dir, uniforms.star_intensity);
             accum_color += (1.0 - accum_alpha) * star;
@@ -68,25 +63,30 @@ fn fragment(in: VertexOutput) -> @location(0) vec4<f32> {
             break;
         }
 
-        // RK4 step (single step), then test disk crossing on the segment.
-        let (k1p, k1d) = deriv(pos, d);
-        let (k2p, k2d) = deriv(pos + k1p * dt * 0.5, normalize(d + k1d * dt * 0.5));
-        let (k3p, k3d) = deriv(pos + k2p * dt * 0.5, normalize(d + k2d * dt * 0.5));
-        let (k4p, k4d) = deriv(pos + k3p * dt, normalize(d + k3d * dt));
-        let new_pos = pos + (k1p + 2.0*k2p + 2.0*k3p + k4p) * dt / 6.0;
-        let new_dir = normalize(d + (k1d + 2.0*k2d + 2.0*k3d + k4d) * dt / 6.0);
+        let k1 = deriv(pos, d);
+        let k2 = deriv(pos + k1.dpos * dt * 0.5, normalize(d + k1.ddir * dt * 0.5));
+        let k3 = deriv(pos + k2.dpos * dt * 0.5, normalize(d + k2.ddir * dt * 0.5));
+        let k4 = deriv(pos + k3.dpos * dt, normalize(d + k3.ddir * dt));
+        let new_pos = pos + (k1.dpos + 2.0*k2.dpos + 2.0*k3.dpos + k4.dpos) * dt / 6.0;
+        let new_dir = normalize(d + (k1.ddir + 2.0*k2.ddir + 2.0*k3.ddir + k4.ddir) * dt / 6.0);
 
         if (disk_hit(prev, new_pos)) {
-            // Approximate the crossing point by interpolating to y=0.
             let ty = prev.y / (prev.y - new_pos.y);
             let hit = mix(prev, new_pos, vec3<f32>(ty));
             let dc = disk_color(hit, new_dir);
-            let a = 0.85; // disk is nearly opaque
+            let a = 0.85;
             accum_color += (1.0 - accum_alpha) * dc * a;
             accum_alpha += (1.0 - accum_alpha) * a;
             if (accum_alpha > 0.99) { break; }
         }
 
+        let ph = planet_hit(prev, new_pos, new_dir);
+        if (ph.w > 0.0) {
+            accum_color += (1.0 - accum_alpha) * ph.xyz * ph.w;
+            accum_alpha += (1.0 - accum_alpha) * ph.w;
+            if (accum_alpha > 0.99) { break; }
+        }
+
         prev = new_pos;
         pos = new_pos;
         d = new_dir;

assets/shaders/geodesic_schwarzschild.wgsl

@@ -1,55 +1,40 @@
 const R_ESCAPE: f32 = 1000.0;
 
-// One RK4 sub-step derivative of (pos, dir) under the Schwarzschild
-// bending acceleration. Rs is uniforms.rs.
-fn deriv(pos: vec3<f32>, dir: vec3<f32>) -> (vec3<f32>, vec3<f32>) {
-    let r = length(pos);
-    let rs = uniforms.rs;
-    // Angular momentum squared: |cross(pos, dir)|^2
-    let h = cross(pos, dir);
-    let h2 = dot(h, h);
-    // Avoid division by zero.
-    let r5 = max(r * r * r * r * r, 1e-6);
-    // d(pos)/dt = dir
-    let dpos = dir;
-    // d(dir)/dt = bending acceleration (re-normalized each step in integrate)
-    let accel = -1.5 * rs * h2 / r5 * pos;
-    return (dpos, accel);
+struct Deriv {
+    dpos: vec3<f32>,
+    ddir: vec3<f32>,
+}
+
+fn deriv(pos: vec3<f32>, dir: vec3<f32>) -> Deriv {
+    let r = length(pos);
+    let rs = uniforms.rs;
+    let h = cross(pos, dir);
+    let h2 = dot(h, h);
+    let r5 = max(r * r * r * r * r, 1e-6);
+    let dpos = dir;
+    let accel = -1.5 * rs * h2 / r5 * pos;
+    return Deriv(dpos, accel);
 }
 
-// Integrate a ray from `pos` along `dir`. Returns:
-//   .status: 0 = escaped, 1 = captured (shadow)
-//   .final_pos, .final_dir: end state (used for sky sampling on escape)
 struct RayResult {
     status: u32,
     final_pos: vec3<f32>,
     final_dir: vec3<f32>,
 }
 
-// Accumulator callback pattern: the caller passes a function-style body via
-// a per-step check. Because WGSL has no first-class closures, we inline the
-// per-step intersection tests in black_hole.wgsl's integrate_and_trace().
-// This function returns ONLY the escape/capture classification, used as a
-// fallback when no scene object is hit.
 fn classify_ray(start_pos: vec3<f32>, start_dir: vec3<f32>, steps: u32, dt: f32) -> RayResult {
     var pos = start_pos;
     var dir = start_dir;
     for (var i: u32 = 0u; i < steps; i = i + 1u) {
         let r = length(pos);
-        if (r < uniforms.rs) {
-            return RayResult(1u, pos, dir);
-        }
-        if (r > R_ESCAPE) {
-            return RayResult(0u, pos, dir);
-        }
-        // RK4
-        let (k1p, k1d) = deriv(pos, dir);
-        let (k2p, k2d) = deriv(pos + k1p * dt * 0.5, normalize(dir + k1d * dt * 0.5));
-        let (k3p, k3d) = deriv(pos + k2p * dt * 0.5, normalize(dir + k2d * dt * 0.5));
-        let (k4p, k4d) = deriv(pos + k3p * dt,     normalize(dir + k3d * dt));
-        pos = pos + (k1p + 2.0 * k2p + 2.0 * k3p + k4p) * dt / 6.0;
-        dir = normalize(dir + (k1d + 2.0 * k2d + 2.0 * k3d + k4d) * dt / 6.0);
+        if (r < uniforms.rs) { return RayResult(1u, pos, dir); }
+        if (r > R_ESCAPE) { return RayResult(0u, pos, dir); }
+        let k1 = deriv(pos, dir);
+        let k2 = deriv(pos + k1.dpos * dt * 0.5, normalize(dir + k1.ddir * dt * 0.5));
+        let k3 = deriv(pos + k2.dpos * dt * 0.5, normalize(dir + k2.ddir * dt * 0.5));
+        let k4 = deriv(pos + k3.dpos * dt,     normalize(dir + k3.ddir * dt));
+        pos = pos + (k1.dpos + 2.0 * k2.dpos + 2.0 * k3.dpos + k4.dpos) * dt / 6.0;
+        dir = normalize(dir + (k1.ddir + 2.0 * k2.ddir + 2.0 * k3.ddir + k4.ddir) * dt / 6.0);
     }
-    // Ran out of steps without a clear verdict: treat as escaped.
     return RayResult(0u, pos, dir);
 }

assets/shaders/planets.wgsl

@@ -0,0 +1,46 @@
+struct SphereData {
+    center: vec4<f32>,   // xyz = center, w = radius
+    color: vec4<f32>,    // xyz = color, w = emissive flag (u32 reinterpreted; we just check > 0.5)
+};
+
+@group(#{MATERIAL_BIND_GROUP}) @binding(3) var<storage, read> planets: array<SphereData>;
+
+// Test the segment prev->cur against all planets. Returns hit color & alpha,
+// or (0,0,0,0) if no hit. `dir` is the ray direction (for shading).
+fn planet_hit(prev: vec3<f32>, cur: vec3<f32>, dir: vec3<f32>) -> vec4<f32> {
+    var nearest_t = 1e9;
+    var nearest_col = vec3<f32>(0.0);
+    var found = false;
+    for (var i: u32 = 0u; i < uniforms.planet_count; i = i + 1u) {
+        let s = planets[i];
+        let center = s.center.xyz;
+        let radius = s.center.w;
+        // Ray-sphere intersection for the segment.
+        let seg = cur - prev;
+        let oc = prev - center;
+        let a = dot(seg, seg);
+        let b = 2.0 * dot(oc, seg);
+        let c = dot(oc, oc) - radius * radius;
+        let disc = b * b - 4.0 * a * c;
+        if (disc < 0.0) { continue; }
+        let sq = sqrt(disc);
+        var t = (-b - sq) / (2.0 * a);
+        if (t < 0.0) { t = (-b + sq) / (2.0 * a); }
+        if (t >= 0.0 && t <= 1.0 && t < nearest_t) {
+            nearest_t = t;
+            let hit_pos = prev + seg * t;
+            let n = normalize(hit_pos - center);
+            // Lambert shading from a fixed light direction.
+            let light_dir = normalize(vec3<f32>(0.5, 0.8, 0.3));
+            let ndl = max(dot(n, light_dir), 0.0);
+            var col = s.color.xyz * (0.2 + 0.8 * ndl);
+            if (s.color.w > 0.5) { col = s.color.xyz; } // emissive
+            nearest_col = col;
+            found = true;
+        }
+    }
+    if (found) {
+        return vec4<f32>(nearest_col, 0.95);
+    }
+    return vec4<f32>(0.0, 0.0, 0.0, 0.0);
+}

src/main.rs

@@ -7,6 +7,7 @@ mod render;
 mod camera;
 mod params;
 mod ui;
+mod scene;
 
 fn main() {
     // On web, abort startup if WebGPU isn't available and show a message.

src/render/plugin.rs

@@ -12,10 +12,12 @@ impl Plugin for BlackHolePlugin {
             .add_plugins(Material2dPlugin::<BlackHoleMaterial>::default())
             .add_plugins(bevy_egui::EguiPlugin::default())
             .add_systems(Startup, spawn_fullscreen_quad)
+            .add_systems(Startup, crate::scene::planets::spawn_default_planet)
             .add_systems(
                 Update,
                 (crate::camera::orbit_controller, mirror_params),
             )
+            .add_systems(Update, crate::scene::planets::upload_planets)
             // bevy_egui 0.41 requires UI systems to run inside the egui context
             // pass (fonts/ctx are initialized there); placing them in Update panics.
             .add_systems(bevy_egui::EguiPrimaryContextPass, crate::ui::ui_system);

src/scene/mod.rs

@@ -0,0 +1 @@
+pub mod planets;

src/scene/planets.rs

@@ -0,0 +1,60 @@
+use bevy::prelude::*;
+use bevy::render::storage::ShaderBuffer;
+
+use crate::render::material::{SphereData, MAX_PLANETS};
+
+/// A planet rendered as a lensed sphere inside the geodesic shader.
+#[derive(Component, Clone, Copy)]
+pub struct Planet {
+    pub center: Vec3,
+    pub radius: f32,
+    pub color: Vec3,
+    pub emissive: bool,
+}
+
+/// Collects all Planet components, builds a fixed-size Vec<SphereData> (padded
+/// to MAX_PLANETS), wraps it in a ShaderBuffer, and ensures every BlackHoleMaterial
+/// points its `planets` handle at that buffer. Also updates planet_count in params.
+///
+/// NOTE: the material field is `Handle<ShaderBuffer>` (Bevy 0.19 AsBindGroup
+/// requirement). We create one ShaderBuffer asset and have all materials share it.
+pub fn upload_planets(
+    planets: Query<&Planet>,
+    mut params: ResMut<crate::params::BlackHoleParams>,
+    mut materials: ResMut<Assets<crate::render::material::BlackHoleMaterial>>,
+    mut buffers: ResMut<Assets<ShaderBuffer>>,
+) {
+    let mut data: Vec<SphereData> = planets
+        .iter()
+        .take(MAX_PLANETS)
+        .map(|p| SphereData {
+            center: p.center,
+            radius: p.radius,
+            color: p.color,
+            emissive: p.emissive as u32,
+            _pad0: 0.0,
+            _pad1: 0.0,
+            _pad2: 0.0,
+        })
+        .collect();
+    // Pad to MAX_PLANETS so the buffer size is constant (avoids reallocation churn).
+    data.resize(MAX_PLANETS, SphereData::default());
+    params.planet_count = planets.iter().count().min(MAX_PLANETS) as u32;
+
+    // Build (or rebuild) the ShaderBuffer and share its handle across materials.
+    let buffer = ShaderBuffer::from(data);
+    for (_, mat) in materials.iter_mut() {
+        // Replace the handle each frame (simple, correct; cheap for one material).
+        mat.planets = buffers.add(buffer.clone());
+    }
+}
+
+/// Spawns a default test planet behind/above the hole so lensing is visible.
+pub fn spawn_default_planet(mut commands: Commands) {
+    commands.spawn(Planet {
+        center: Vec3::new(0.0, 2.0, -25.0),
+        radius: 2.0,
+        color: Vec3::new(0.3, 0.5, 1.0),
+        emissive: false,
+    });
+}