xfy
573e68e96d
The concentric banding persisted on the jets (near the base) after the disk moiré was fixed. Root cause: sample_jets used a fixed per-step weight (0.5) instead of a per-unit-length one, so the jet's per-unit-length contribution was ∝ 1/step_len. RK45 packs its accepted steps tightly near the hole (high curvature → small dt), so the jet brightened in step-dense rings exactly where the user saw bands. This was the inverse of the earlier `* dt` attempt (which banded because dt varies 16×); both forms couple brightness to the integrator's step choice rather than to the physics. Fix: pass the step's world-space length |new_pos − prev| in from the caller (it already has prev and new_pos) and weight the per-step emission and alpha on it — the same step-size-decoupling technique the disk path already uses (integrate_disk_segment's analytic seg_len). The per-unit-length coefficient (0.1) is calibrated to keep the default scene's jet brightness close to the old fixed-0.5 look. cargo build --release: clean. cargo test: passing.
902 lines
40 KiB
WebGPU Shading Language
902 lines
40 KiB
WebGPU Shading Language
// All shader logic is inlined into this single file.
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//
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// HISTORY: the shader used to be split across several naga_oil modules
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// (ray_gen, geodesic, stars, disk, planets, grid, skybox) that each
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// `#define_import_path singularity::...` and were pulled into this file via
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// `#import singularity::...`. That compiled without error, but calling ANY
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// imported function at runtime produced no fragment output — the fullscreen
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// quad silently drew nothing and only the camera clear color (grey) showed.
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// (Local functions worked; only cross-module imports broke.) Rather than chase
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// the naga_oil composition bug, every function is inlined here. The standalone
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// module files still exist on disk but are no longer imported.
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#import bevy_sprite::mesh2d_vertex_output::VertexOutput
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struct BlackHoleUniforms {
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eye: vec4<f32>,
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forward: vec4<f32>,
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right: vec4<f32>,
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up: vec4<f32>,
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resolution: vec2<f32>,
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time: f32,
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_pad3: f32,
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rs: f32,
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disk_inner: f32,
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disk_outer: f32,
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disk_tilt: f32,
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disk_brightness: f32,
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disk_rotation_speed: f32,
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doppler_strength: f32,
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star_intensity: f32,
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skybox_intensity: f32,
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grid_density: f32,
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doppler_enabled: u32,
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grid_enabled: u32,
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planet_count: u32,
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steps: u32,
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spin: f32,
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star_aa: u32,
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bloom_threshold: f32,
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bloom_strength: f32,
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exposure: f32,
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_pad5: f32,
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disk_half_thickness: f32,
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filament_freq: f32,
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filament_sharpness: f32,
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density_freq: f32,
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density_strength: f32,
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arm_count: f32,
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arm_tightness: f32,
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arm_strength: f32,
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disk_quality: u32,
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// Disk color mode + blackbody temp (Phase 3.2), relativistic jets.
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disk_color_mode: u32, // 0=gradient, 1=blackbody
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disk_temp: f32, // blackbody base temperature (Kelvin)
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jets_enabled: u32, // 0=off, 1=on
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jets_strength: f32, // jet brightness multiplier
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aa_samples: u32, // per-pixel supersample count (1/2/4); >1 antialiases the higher-order lensed-image rings
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_pad6: f32, // explicit round-up to 16-byte uniform alignment
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_pad7: f32, // (matches BlackHoleUniforms in material.rs byte-for-byte)
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};
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@group(#{MATERIAL_BIND_GROUP}) @binding(0) var<uniform> uniforms: BlackHoleUniforms;
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// Per-pixel fragment coordinate, set at the top of `fragment` from
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// `in.position.xy` (the @builtin(position) frag coord). Used as a deterministic
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// seed for the slab sub-sample jitter and the supersample jitter so the noise
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// is spatially stable (no per-frame flicker). `var<private>` is the same form
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// `blur.wgsl` uses for its runtime-indexed kernel tables.
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var<private> pixel_seed: vec2<f32>;
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// ---------- planets storage (binding 3) ----------
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struct SphereData {
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center: vec4<f32>, // xyz = center (world space), w = radius
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color: vec4<f32>, // xyz = color, w = emissive flag
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};
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@group(#{MATERIAL_BIND_GROUP}) @binding(3) var<storage, read> planets: array<SphereData>;
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// ---------- optional cubemap skybox (bindings 1 & 2) ----------
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@group(#{MATERIAL_BIND_GROUP}) @binding(1) var skybox: texture_cube<f32>;
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@group(#{MATERIAL_BIND_GROUP}) @binding(2) var skybox_sampler: sampler;
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// ====================== inlined helpers ======================
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// Rotate a vector around the X axis by angle a.
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fn rot_x(v: vec3<f32>, a: f32) -> vec3<f32> {
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let c = cos(a);
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let s = sin(a);
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return vec3<f32>(v.x, c * v.y - s * v.z, s * v.y + c * v.z);
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}
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// --- ray_gen ---
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// `fov` is packed into the `.w` of `up` (Rust lays out `up: Vec3` + `fov: f32`
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// as one vec4 block).
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fn ray_direction(uv: vec2<f32>) -> vec3<f32> {
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let tan_half_fov = tan(uniforms.up.w * 0.5);
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let dir =
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normalize(uniforms.forward.xyz)
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+ uniforms.right.xyz * (uv.x * tan_half_fov)
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+ uniforms.up.xyz * (uv.y * tan_half_fov);
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return normalize(dir);
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}
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// --- stars ---
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fn hash13(p: vec3<f32>) -> f32 {
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var q = vec3<f32>(dot(p, vec3<f32>(127.1, 311.7, 74.7)),
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dot(p, vec3<f32>(269.5, 183.3, 246.1)),
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dot(p, vec3<f32>(113.5, 271.9, 124.6)));
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let h = fract(sin(q) * 43758.5453);
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return h.x;
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}
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fn star_color(dir: vec3<f32>, intensity: f32) -> vec3<f32> {
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// The unit-sphere direction is hashed into a 3D cell grid. A pixel's ray
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// usually sits near a cell boundary, so evaluating only the home cell clips
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// any star whose center lies in a neighbor — that clip is what made stars
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// look square even with the Gaussian AA path: the hash changes at the cell
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// edge, so the falloff could never reach zero and the visible shape was
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// just the cell's bounding box. Scan the 3×3×3 neighborhood so each star's
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// radial falloff extends across the whole cell it lives in.
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let scale = 80.0;
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let p = dir * scale;
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let base = floor(p);
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let threshold = 0.985;
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// Brightest contributor wins: `best` = (brightness, r, g, b).
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var best = vec4<f32>(0.0);
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for (var dz: i32 = -1; dz <= 1; dz = dz + 1) {
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for (var dy: i32 = -1; dy <= 1; dy = dy + 1) {
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for (var dx: i32 = -1; dx <= 1; dx = dx + 1) {
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let cell = base + vec3<f32>(f32(dx), f32(dy), f32(dz));
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let h = hash13(cell);
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if (h <= threshold) { continue; }
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let b = (h - threshold) / (1.0 - threshold);
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let center = cell + vec3<f32>(0.5);
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let dist = length(p - center); // Euclidean → round, never square
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let col = mix(vec3<f32>(0.6, 0.7, 1.0), vec3<f32>(1.0, 0.9, 0.7), b);
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// Both paths share the same brightness-driven radius and the
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// same gain, so toggling AA only softens the edge — it does not
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// change peak brightness or visible count. Before, the AA path
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// used a larger radius (up to 0.65 vs 0.5), a heavier gain
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// (4.0 vs 3.0), and a slow-decaying Gaussian whose long tail
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// lifted many dim stars above the visibility floor — that's
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// what made AA look like "bigger and more" stars.
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let radius = 0.25 + b * 0.4;
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let falloff = select(
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smoothstep(radius, 0.0, dist), // hard edge
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exp(-4.6 * dist * dist / (radius * radius)), // soft edge
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uniforms.star_aa != 0u);
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let bright = b * falloff;
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if (bright > best.x) {
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best = vec4<f32>(bright, col.r, col.g, col.b);
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}
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}
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}
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}
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return best.yzw * best.x * 3.0 * intensity;
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}
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// --- skybox ---
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// textureSampleLevel (not textureSample) is REQUIRED here: this is called from
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// inside the main RK45 integration loop, whose control flow is non-uniform
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// (`if (accum_alpha > 0.99) { break; }`, per-pixel early exit). The WGSL spec
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// forbids textureSample outside uniform control flow because it needs
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// screen-space derivatives for mip selection; Chrome's Tint enforces this and
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// rejects the shader, while naga (desktop) does not — which is why this only
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// crashed the web build. textureSampleLevel takes an explicit LOD (0 here: the
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// skybox cubemap is sampled at full resolution, no mip minification) and is
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// permitted in non-uniform flow. The visual result is identical.
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fn skybox_color(dir: vec3<f32>) -> vec3<f32> {
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return textureSampleLevel(skybox, skybox_sampler, dir, 0.0).rgb;
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}
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// --- geodesic ---
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struct Deriv {
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dpos: vec3<f32>,
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ddir: vec3<f32>,
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}
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fn deriv(pos: vec3<f32>, dir: vec3<f32>) -> Deriv {
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let r = length(pos);
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let rs = uniforms.rs;
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// Kerr spin. χ ∈ [0,1]; a = χ·M, M = Rs/2 = 0.5 (Rs=1).
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let chi = uniforms.spin;
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let m = 0.5;
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let a = chi * m;
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// Schwarzschild radial bending (identical to Phase 1 at χ=0).
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let h = cross(pos, dir);
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let h2 = dot(h, h);
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let r5 = max(r * r * r * r * r, 1e-6);
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let radial = -1.5 * rs * h2 / r5 * pos;
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// Frame-dragging (Lense-Thirring leading term). Spin axis = +Y.
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let spin_axis = vec3<f32>(0.0, 1.0, 0.0);
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let r3 = max(r * r * r, 1e-6);
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let drag = 2.0 * m * a / r3 * cross(spin_axis, dir);
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let accel = radial + drag;
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return Deriv(dir, accel);
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}
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// --- disk ---
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fn disk_hit(prev: vec3<f32>, cur: vec3<f32>) -> bool {
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let y0 = prev.y;
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let y1 = cur.y;
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if (y0 * y1 > 0.0) {
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return false;
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}
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let t = y0 / (y0 - y1);
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let cross = mix(prev, cur, vec3<f32>(t));
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let r = length(vec2<f32>(cross.x, cross.z));
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return r >= uniforms.disk_inner && r <= uniforms.disk_outer;
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}
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// --- disk noise (domain-warped FBM) ---
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fn hash33(p: vec3<f32>) -> vec3<f32> {
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let q = vec3<f32>(
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dot(p, vec3<f32>(127.1, 311.7, 74.7)),
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dot(p, vec3<f32>(269.5, 183.3, 246.1)),
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dot(p, vec3<f32>(113.5, 271.9, 124.6)),
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);
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return fract(sin(q) * 43758.5453);
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}
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fn value_noise3(p: vec3<f32>) -> f32 {
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let i = floor(p);
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let f = fract(p);
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let u = f * f * (3.0 - 2.0 * f);
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let n000 = hash33(i + vec3<f32>(0.0, 0.0, 0.0)).x;
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let n100 = hash33(i + vec3<f32>(1.0, 0.0, 0.0)).x;
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let n010 = hash33(i + vec3<f32>(0.0, 1.0, 0.0)).x;
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let n110 = hash33(i + vec3<f32>(1.0, 1.0, 0.0)).x;
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let n001 = hash33(i + vec3<f32>(0.0, 0.0, 1.0)).x;
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let n101 = hash33(i + vec3<f32>(1.0, 0.0, 1.0)).x;
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let n011 = hash33(i + vec3<f32>(0.0, 1.0, 1.0)).x;
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let n111 = hash33(i + vec3<f32>(1.0, 1.0, 1.0)).x;
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let nx00 = mix(n000, n100, u.x);
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let nx10 = mix(n010, n110, u.x);
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let nx01 = mix(n001, n101, u.x);
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let nx11 = mix(n011, n111, u.x);
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let nxy0 = mix(nx00, nx10, u.y);
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let nxy1 = mix(nx01, nx11, u.y);
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return mix(nxy0, nxy1, u.z);
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}
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fn fbm3(p: vec3<f32>, octaves: u32) -> f32 {
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// MAX_OCTAVES-with-break: the conservative WebGPU form for a runtime-
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// chosen octave count. Older drivers can miscompile non-constant loop
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// bounds; this branch is the first to pass dynamic octaves here.
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const MAX_OCTAVES = 6u;
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var sum = 0.0;
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var amp = 0.5;
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var freq = 1.0;
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for (var i: u32 = 0u; i < MAX_OCTAVES; i = i + 1u) {
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if (i >= octaves) { break; }
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sum = sum + amp * value_noise3(p * freq);
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freq = freq * 2.0;
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amp = amp * 0.5;
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}
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return sum;
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}
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// Ridged multifractal noise: 1 - |2n-1| turns value-noise gradients into
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// sharp ridges (peak where n=0.5, zero at n=0 and n=1). Raising to
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// `sharpness` thins the ridges into filaments. MAX_OCTAVES-with-break is
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// the conservative WebGPU form for a runtime-chosen octave count.
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fn ridged_fbm(p: vec3<f32>, octaves: u32, sharpness: f32) -> f32 {
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const MAX_OCTAVES = 6u;
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var sum = 0.0;
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var amp = 0.5;
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var freq = 1.0;
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for (var i: u32 = 0u; i < MAX_OCTAVES; i = i + 1u) {
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if (i >= octaves) { break; }
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let n = value_noise3(p * freq);
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let ridge = 1.0 - abs(2.0 * n - 1.0);
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sum = sum + amp * pow(ridge, sharpness);
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freq = freq * 2.0;
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amp = amp * 0.5;
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}
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return sum;
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}
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fn disk_noise(pos: vec3<f32>, t: f32) -> f32 {
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let warp = fbm3(pos * 0.8 + vec3<f32>(0.0, 0.0, t * 0.1), 3u);
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let n = fbm3(pos * 2.0 + warp * 1.5 + vec3<f32>(0.0, 0.0, t * 0.3), 4u);
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return n;
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}
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// Result of a disk color query: emitted radiance + opacity contribution.
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// Both the volumetric and flat paths return this struct so the main loop
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// can treat them uniformly.
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struct DiskSample {
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color: vec3<f32>,
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density: f32,
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}
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// Radial temperature gradient: white-hot inner → deep-orange outer.
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fn temperature_color(t: f32) -> vec3<f32> {
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return mix(vec3<f32>(1.0, 0.95, 0.85), vec3<f32>(1.0, 0.45, 0.12), clamp(t, 0.0, 1.0));
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}
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// Analytic blackbody color (Tanner-Helland / Mitchell Charity approximation).
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// Input temp in Kelvin; output linear RGB. Ported from the others/ GLSL shader.
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fn blackbody(temp: f32) -> vec3f {
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// Clamp to prevent log(0) at the event horizon (infinite redshift).
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let t = max(temp, 1.0) / 100.0;
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var r: f32;
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var g: f32;
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var b: f32;
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if (t <= 66.0) {
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r = 255.0;
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g = 99.4708025861 * log(t) - 161.1195681661;
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if (t <= 19.0) {
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b = 0.0;
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} else {
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b = 138.5177312231 * log(t - 10.0) - 305.0447927307;
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}
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} else {
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r = 329.698727446 * pow(t - 60.0, -0.1332047592);
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g = 288.1221695283 * pow(t - 60.0, -0.0755148492);
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b = 255.0;
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}
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// Formula produces sRGB; convert to linear for the HDR pipeline.
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let srgb = vec3f(r, g, b) / 255.0;
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return pow(max(srgb, vec3f(0.0)), vec3f(2.2));
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}
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// Radial brightness falloff (∝ 1/r² from the inner edge).
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fn radial_falloff(r: f32, inner: f32) -> f32 {
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return 1.0 / pow(r / inner, 2.0);
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}
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// Cylindrical radius in the disk plane.
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fn r_of(pos: vec3<f32>) -> f32 {
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return length(vec2<f32>(pos.x, pos.z));
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}
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// Relativistic Doppler beaming. `dir` is the ray direction (disk-local).
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fn apply_doppler(col: vec3<f32>, pos: vec3<f32>, dir: vec3<f32>) -> vec3<f32> {
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let phi = atan2(pos.z, pos.x);
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let v_orbital = sqrt(uniforms.rs / (2.0 * r_of(pos)));
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let tangent = normalize(vec3<f32>(-sin(phi), 0.0, cos(phi)));
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let vdotn = dot(tangent * v_orbital, -dir);
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let gamma = 1.0 / sqrt(max(1.0 - v_orbital * v_orbital, 1e-4));
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if (uniforms.doppler_enabled == 0u) {
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return col;
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}
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let delta = 1.0 / (gamma * (1.0 - vdotn));
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let doppler = pow(delta, 3.0) * uniforms.doppler_strength;
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return col * doppler;
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}
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// Kerr equatorial 4-velocity Doppler factor δ = E_obs/E_em (Page & Thorne 1974).
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// Exact: solves g_μν u^μ u^ν = -1 for circular equatorial orbits, then folds in
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// the conserved photon angular momentum. Returns vec2(delta, beaming=δ^3.5).
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// Used by the blackbody disk color mode; the floor guards against NaN from
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// pow of a negative base.
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fn kerr_doppler(pos: vec3f, dir: vec3f) -> vec2f {
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let r = r_of(pos);
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let m = 0.5;
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let a = uniforms.spin * m;
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let sqrt_m = sqrt(m);
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let sign_spin = sign(uniforms.spin + 1.0e-8);
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// 1. Keplerian angular velocity Ω = dφ/dt.
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let omega = (sign_spin * sqrt_m) / (r * sqrt(r) + a * sqrt_m);
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// 2. Equatorial metric components (θ = π/2).
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let g_tt = -(1.0 - 2.0 * m / r);
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let g_tphi = -2.0 * m * a / r;
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let g_phiphi = r * r + a * a + 2.0 * m * a * a / r;
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// 3. Time component of the circular-orbit 4-velocity.
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let u_t_sq = -(g_tt + 2.0 * omega * g_tphi + omega * omega * g_phiphi);
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let u_t = 1.0 / sqrt(max(1.0e-6, u_t_sq));
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// 4. Conserved photon angular momentum (impact-parameter mapping).
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let l_photon = pos.z * dir.x - pos.x * dir.z;
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// 5. δ = E_obs/E_em = 1 / (u_t · (1 − Ω · L_photon)).
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let delta = 1.0 / max(0.01, u_t * (1.0 - omega * l_photon));
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let beaming = max(0.01, pow(delta, 3.5));
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return vec2f(delta, beaming);
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}
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// Unifies the color assembly for both disk paths. Mode 0 = existing gradient +
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// Newtonian apply_doppler (preserves the pre-blackbody appearance). Mode 1 =
|
||
// Novikov-Thorne radial temperature gradient × Kerr δ → blackbody color × δ^3.5
|
||
// beaming, so the approaching side shifts hotter/bluer and the receding side
|
||
// cooler/redder — the physical signature absent from the gradient mode.
|
||
fn disk_emission(r: f32, pos: vec3f, dir: vec3f, brightness: f32) -> vec3f {
|
||
let inner = uniforms.disk_inner;
|
||
let t = (r - inner) / (uniforms.disk_outer - inner);
|
||
let falloff = radial_falloff(r, inner);
|
||
if (uniforms.disk_color_mode == 0u) {
|
||
var col = temperature_color(t) * brightness * falloff * uniforms.disk_brightness;
|
||
return apply_doppler(col, pos, dir);
|
||
}
|
||
// Blackbody mode: NT radial temperature profile × Kerr Doppler shift.
|
||
let isco_r = clamp(inner / r, 0.0, 1.0);
|
||
let nt_factor = max(0.0, 1.0 - sqrt(isco_r));
|
||
let radial_temp = pow(isco_r, 0.75) * pow(nt_factor, 0.25);
|
||
let d = kerr_doppler(pos, dir);
|
||
let temperature = uniforms.disk_temp * radial_temp * d.x;
|
||
return blackbody(temperature) * d.y * brightness * falloff * uniforms.disk_brightness;
|
||
}
|
||
|
||
// Off-tier fallback: zero-thickness disk, single midplane sample. Density is
|
||
// driven by the same radial smoothstep falloff as the volumetric path (no flat
|
||
// 0.85 floor) so the edges feather out naturally. Returns DiskSample so the
|
||
// main loop dispatches both paths uniformly.
|
||
fn disk_color_flat(pos: vec3<f32>, dir: vec3<f32>) -> DiskSample {
|
||
let r = r_of(pos);
|
||
let rot = uniforms.time * uniforms.disk_rotation_speed / pow(r, 1.5);
|
||
// Domain-warped FBM for a feathered gas texture. The Keplerian shear
|
||
// (rot ∝ 1/r^1.5) is folded into the noise flow term so inner radii flow
|
||
// faster than outer — correct differential rotation. Amplitude is kept mild
|
||
// so the radial temperature gradient (inside disk_emission) dominates.
|
||
let noise = disk_noise(vec3<f32>(pos.x * 0.3, pos.z * 0.3, rot), uniforms.time);
|
||
|
||
let col = disk_emission(r, pos, dir, 0.8 + 0.4 * noise * noise);
|
||
|
||
// Radial smoothstep: solid through the bulk, feathered at both edges.
|
||
let radial = smoothstep(uniforms.disk_outer, uniforms.disk_inner, r);
|
||
return DiskSample(vec3<f32>(col), radial * 0.9);
|
||
}
|
||
|
||
// Volumetric disk color. Models the accretion disk as a physically-structured
|
||
// density field (no flat floor): radial smoothstep falloff × Gaussian vertical
|
||
// decay × a WEAK low-frequency turbulence modulation. The radial temperature
|
||
// gradient inside disk_emission drives the dominant appearance (Gargantua's
|
||
// smooth white-hot inner → deep-orange outer look); turbulence is kept to a
|
||
// subtle ±25% texture accent so the disk reads as solid gas rather than the
|
||
// jelly-like translucent slab the old 0.55-floor + ridged-filament model gave.
|
||
//
|
||
// Noise is sampled in POLAR coordinates (r_norm, phi·freq + Keplerian flow,
|
||
// height) so what little texture there is flows tangentially — correct for a
|
||
// rotating fluid. The Keplerian flow term (`+ rot`) advects the turbulence.
|
||
fn disk_color_volumetric(pos: vec3<f32>, dir: vec3<f32>) -> DiskSample {
|
||
let r = r_of(pos);
|
||
let phi = atan2(pos.z, pos.x);
|
||
let rot = uniforms.time * uniforms.disk_rotation_speed / pow(r, 1.5);
|
||
|
||
// Polar sample coordinate: (r normalized, angle × freq + Keplerian flow,
|
||
// height within slab). The flow term advects the noise so inner radii
|
||
// (faster rotation) drift ahead of outer radii — differential rotation.
|
||
// NOTE: h here is normalized by disk_half_thickness, but disk_half_thickness
|
||
// is now an H/R RATIO (semantics changed from absolute world units), so the
|
||
// caller scales H = r * disk_half_thickness before sampling — see the
|
||
// per-step accumulation site in the main loop.
|
||
let r_norm = r / uniforms.disk_inner;
|
||
let h = pos.y / max(r * uniforms.disk_half_thickness, 1e-3);
|
||
let sp = vec3<f32>(r_norm, phi * 2.5 + rot, h);
|
||
|
||
// Weak low-frequency turbulence. Two octaves only (was 4–5): the goal is a
|
||
// Gargantua-style smooth disk, so turbulence is a texture accent (±25%
|
||
// density modulation), NOT the dominant carrier. ridged filaments and
|
||
// logarithmic-spiral arms were removed — they produced the noisy,
|
||
// jelly-like, striated look this model replaces.
|
||
let turbulence = fbm3(sp * uniforms.density_freq, 2u);
|
||
let turb_mod = mix(1.0, 0.75 + 0.5 * turbulence, 0.5); // 0.75–1.25
|
||
|
||
// Gaussian vertical decay: densest at the midplane, ~0 at the slab edge.
|
||
// h is normalized to the slab half-height, so exp(-(h·h)·4) → 0.018 at the
|
||
// rim. This replaces the old uniform-in-slab density (the cause of the
|
||
// jelly: the whole thickness glowed at a constant floor alpha).
|
||
let h_falloff = exp(-(h * h) * 4.0);
|
||
|
||
// Radial smoothstep falloff (outer → 0, inner → 1): smooth inner+outer
|
||
// edges instead of a hard annulus, matching the others/ reference disk.ts.
|
||
let radial = smoothstep(uniforms.disk_outer, uniforms.disk_inner, r);
|
||
|
||
let total_density = radial * h_falloff * turb_mod * uniforms.density_strength;
|
||
|
||
// Brightness: turbulence is a mild accent so the radial temperature gradient
|
||
// (inside disk_emission) dominates the visible luminosity. This keeps the
|
||
// disk smooth and gradient-driven rather than streaked by ridged filaments.
|
||
let brightness = mix(0.8, 1.2, turbulence);
|
||
|
||
let col = disk_emission(r, pos, dir, brightness);
|
||
|
||
return DiskSample(vec3<f32>(col), total_density);
|
||
}
|
||
|
||
// Per-step disk integration that is DECOUPLED from the RK45 step size.
|
||
//
|
||
// Why this exists: the previous "sample at new_pos, weight by step_len" form
|
||
// produced radial spokes. RK45's step size is spatially adaptive (small near
|
||
// the hole where curvature is high, large in flat regions) AND varies between
|
||
// neighbouring pixels, so weighting density by `step_len` injected a per-pixel
|
||
// brightness modulation along the radial direction → spokes, densest at the
|
||
// inner disk where steps are smallest.
|
||
//
|
||
// Fix: clip THIS step's segment to the disk slab analytically and weight each
|
||
// sample by `seg_len` — the world-space length of the ray-slab intersection,
|
||
// which depends only on the ray's incidence angle and the local slab height,
|
||
// never on the RK45 step size. Then sample N points uniformly along the
|
||
// clipped segment so the integral is well-resolved (a single midpoint sample
|
||
// under-integrates the Gaussian vertical decay and leaves the disk translucent).
|
||
//
|
||
// `prev`/`new_pos` are disk-local (caller rotates by -disk_tilt).
|
||
fn integrate_disk_segment(prev: vec3f, new_pos: vec3f, dir: vec3f,
|
||
accum_color: ptr<function, vec3f>,
|
||
accum_alpha: ptr<function, f32>) {
|
||
// Slab height H is radius-dependent (H/R ratio). Use the step's midpoint r
|
||
// to define H for this segment — the change in r across one RK45 step is
|
||
// small, so this local-constant approximation is accurate enough.
|
||
let mid = (prev + new_pos) * 0.5;
|
||
let r_mid = r_of(mid);
|
||
let H = r_mid * uniforms.disk_half_thickness;
|
||
|
||
// Clip the parametric segment prev + t·(new_pos − prev), t∈[0,1], to |y|≤H.
|
||
let dy = new_pos.y - prev.y;
|
||
var t0 = 0.0;
|
||
var t1 = 1.0;
|
||
if (abs(dy) < 1e-6) {
|
||
// Step is parallel to the disk plane: in-slab iff prev is in-slab.
|
||
if (abs(prev.y) > H) { return; }
|
||
} else {
|
||
let ta = ( H - prev.y) / dy;
|
||
let tb = (-H - prev.y) / dy;
|
||
t0 = clamp(min(ta, tb), 0.0, 1.0);
|
||
t1 = clamp(max(ta, tb), 0.0, 1.0);
|
||
if (t1 <= t0) { return; } // segment does not cross the slab
|
||
}
|
||
|
||
// Analytic in-slab length — the key: depends on geometry, NOT on RK45 dt.
|
||
let seg_len = (t1 - t0) * length(new_pos - prev);
|
||
|
||
// N samples along the clipped segment, front-to-back composite. Each sample
|
||
// carries density × (seg_len / N) so the N samples sum to the full segment
|
||
// integral when density is roughly constant; the Gaussian vertical decay is
|
||
// captured by sampling at differing heights within the slab. N is a
|
||
// compile-time constant (WGSL requires static loop bounds).
|
||
//
|
||
// The sub-sample position is STOCHASTIC, not on the deterministic
|
||
// (i+0.5)/N grid. A deterministic grid aliases against the 2-D pixel grid
|
||
// and against the per-ray RK45 step lattice → a concentric moiré on the
|
||
// disk. Folding the pixel coordinate and the sample index into a hash and
|
||
// using it to jitter the position within stratum i turns the moiré into
|
||
// unstructured noise (which the HDR + bloom pipeline tolerates far better
|
||
// than coherent bands). The jitter stays inside stratum i (amplitude 1/N),
|
||
// so the quadrature order is preserved and the integrated density is
|
||
// unbiased. The seed is pixel-only (no time) → the noise is spatially
|
||
// stable, no per-frame flicker.
|
||
const N = 4u;
|
||
for (var i: u32 = 0u; i < N; i = i + 1u) {
|
||
let stratum = f32(i) + hash13(vec3<f32>(pixel_seed, f32(i)));
|
||
let t = t0 + (t1 - t0) * stratum / f32(N);
|
||
let p = mix(prev, new_pos, vec3f(t));
|
||
let rp = r_of(p);
|
||
if (rp < uniforms.disk_inner || rp > uniforms.disk_outer) {
|
||
continue; // radial clipping: outside the annulus
|
||
}
|
||
let s = disk_color_volumetric(p, dir);
|
||
let ds = s.density * seg_len / f32(N);
|
||
*accum_color += (1.0 - *accum_alpha) * s.color * ds;
|
||
*accum_alpha += (1.0 - *accum_alpha) * ds;
|
||
}
|
||
}
|
||
|
||
// Relativistic jets along the spin axis (Y). Bipolar cones above/below the
|
||
// disk with 0.92c outflow beaming. Ported from others/' sample_relativistic_jets:
|
||
// Gaussian radial falloff, exponential length decay, outward-flowing noise,
|
||
// δ^3.5 beaming (no floor needed — β=0.92 keeps the denominator positive).
|
||
// Front-to-back composited into the same accumulators as the disk.
|
||
//
|
||
// `step_len` is the world-space length of THIS RK45 step (|new_pos − prev|),
|
||
// passed in by the caller. The per-step emission is weighted by it so the
|
||
// integrated jet brightness is step-size-independent — the same technique the
|
||
// disk path uses (integrate_disk_segment weights on the analytic in-slab
|
||
// length). Two prior attempts both produced banding: `* dt` varied with the
|
||
// adaptive step size (radial bands), and a fixed `0.5` made the per-UNIT-length
|
||
// contribution ∝ 1/step_len, so it brightened wherever steps packed together
|
||
// (near the hole) → the concentric base-of-jet bands. Weighting on the actual
|
||
// geometric step length makes the contribution per unit length constant.
|
||
fn sample_jets(pos: vec3f, dir: vec3f, r_plus: f32, step_len: f32,
|
||
accum_color: ptr<function, vec3f>, accum_alpha: ptr<function, f32>) {
|
||
// Relativistic jets are spin-powered (Blandford-Znajek): the mechanism taps
|
||
// the ergosphere, which only exists for a rotating hole. At χ ≈ 0 there is
|
||
// nothing to drive an outflow, so suppress the jets regardless of the
|
||
// jets_enabled toggle — the toggle expresses user intent, spin expresses
|
||
// physics. Without this gate the default scene (spin = 0, jets_enabled =
|
||
// true) shows blue/white columns over the poles that have no physical cause.
|
||
if (uniforms.spin < 0.05) { return; }
|
||
let jet_v = abs(pos.y);
|
||
let jet_max_h = 80.0;
|
||
if (jet_v <= r_plus * 1.8 || jet_v >= jet_max_h) {
|
||
return;
|
||
}
|
||
let jet_r = length(vec2f(pos.x, pos.z));
|
||
let jet_width = 1.0 + jet_v * 0.15;
|
||
if (jet_r >= jet_width * 2.0) {
|
||
return;
|
||
}
|
||
let radial_falloff = exp(-(jet_r * jet_r) / (jet_width * 0.5));
|
||
let length_falloff = exp(-jet_v * 0.05);
|
||
|
||
// Outward-flowing turbulence: the y term reverses sign of the time flow so
|
||
// the lower jet streams downward and the upper jet upward.
|
||
let flow = pos.y * 2.0 - uniforms.time * 8.0;
|
||
let uv_jet = vec3f(pos.x, flow, pos.z);
|
||
let noise_val = value_noise3(uv_jet * 0.5) * 0.6 + value_noise3(uv_jet * 1.5) * 0.4;
|
||
let jet_density = radial_falloff * length_falloff * max(0.0, noise_val - 0.2);
|
||
|
||
if (jet_density <= 0.001) {
|
||
return;
|
||
}
|
||
// 0.92c outflow beaming.
|
||
let jet_vel = 0.92 * sign(pos.y);
|
||
let jet_vel_vec = vec3f(0.0, jet_vel, 0.0);
|
||
let cos_theta = dot(normalize(jet_vel_vec), -dir);
|
||
let beta = abs(jet_vel);
|
||
let gamma = 1.0 / sqrt(1.0 - beta * beta);
|
||
let delta = 1.0 / (gamma * (1.0 - beta * cos_theta));
|
||
// Cap the beaming: with β=0.92 the approaching jet's δ^3.5 reaches ~258×,
|
||
// which blows the blue jet past the bloom threshold and saturates it to
|
||
// white. Clamp to 8× — still visibly brighter on the approaching side, but
|
||
// the base color (0.4, 0.7, 1.0) survives the HDR + bloom pipeline.
|
||
let beaming = min(pow(delta, 3.5), 8.0);
|
||
|
||
let base_color = vec3f(0.4, 0.7, 1.0);
|
||
// Weight the per-step emission by the geometric step length so the
|
||
// integrated brightness is proportional to the path length through the jet,
|
||
// not to how many RK45 steps happened to fall there. The 0.1 coefficient is
|
||
// a per-unit-length strength, calibrated against the default scene to match
|
||
// the old fixed-0.5 brightness at the typical accepted-step length (~0.5).
|
||
let emission = base_color * jet_density * 0.05 * beaming * uniforms.jets_strength * step_len * 0.1;
|
||
*accum_color += emission * (1.0 - *accum_alpha);
|
||
*accum_alpha += jet_density * 0.05 * uniforms.jets_strength * step_len * 0.1;
|
||
}
|
||
|
||
// --- planets ---
|
||
// `prev`/`cur` are in DISK-LOCAL space; planet centers are world space, so we
|
||
// rotate each center into disk-local space here.
|
||
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 = rot_x(s.center.xyz, -uniforms.disk_tilt);
|
||
let radius = s.center.w;
|
||
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);
|
||
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; }
|
||
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);
|
||
}
|
||
|
||
// --- grid (Flamm's paraboloid) ---
|
||
fn flamm_depth(r: f32) -> f32 {
|
||
if (r <= uniforms.rs) { return 0.0; }
|
||
return -2.0 * sqrt(uniforms.rs * (r - uniforms.rs));
|
||
}
|
||
|
||
fn grid_hit(prev: vec3<f32>, cur: vec3<f32>) -> vec3<f32> {
|
||
let r0 = length(vec2<f32>(prev.x, prev.z));
|
||
let r1 = length(vec2<f32>(cur.x, cur.z));
|
||
let z0_surf = flamm_depth(r0);
|
||
let z1_surf = flamm_depth(r1);
|
||
if ((prev.y - z0_surf) * (cur.y - z1_surf) > 0.0) {
|
||
return vec3<f32>(0.0);
|
||
}
|
||
var hit = vec3<f32>(0.0);
|
||
var found = false;
|
||
for (var s: i32 = 0; s < 8; s = s + 1) {
|
||
let f = f32(s + 1) / 8.0;
|
||
let p = mix(prev, cur, vec3<f32>(f));
|
||
let r = length(vec2<f32>(p.x, p.z));
|
||
let surf = flamm_depth(r);
|
||
if (abs(p.y - surf) < 0.3) {
|
||
hit = p;
|
||
found = true;
|
||
break;
|
||
}
|
||
}
|
||
if (!found) { return vec3<f32>(0.0); }
|
||
|
||
let r = length(vec2<f32>(hit.x, hit.z));
|
||
let phi = atan2(hit.z, hit.x);
|
||
let ring = smoothstep(0.06, 0.0, abs(fract(r * uniforms.grid_density * 0.5) - 0.5));
|
||
let spoke = smoothstep(0.04, 0.0, abs(fract(phi * 6.0 / 6.283185) - 0.5));
|
||
let grid = max(ring, spoke);
|
||
let fade = smoothstep(-15.0, -1.0, hit.y);
|
||
let col = vec3<f32>(0.15, 0.3, 0.6) * grid * fade;
|
||
return col * 0.5;
|
||
}
|
||
|
||
// One Dormand-Prince RK45 step. Returns the 5th-order solution and the
|
||
// error estimate (y5 - y4) as a vec3 (position error; direction error is
|
||
// folded in via normalize so we only need position error for step control).
|
||
struct RkStep {
|
||
pos: vec3<f32>,
|
||
dir: vec3<f32>,
|
||
err: f32,
|
||
};
|
||
|
||
fn rk45_step(pos: vec3<f32>, dir: vec3<f32>, dt: f32) -> RkStep {
|
||
// Butcher tableau (Dormand-Prince), 6 stages. Each deriv() returns Deriv{dpos, ddir}.
|
||
let k1 = deriv(pos, dir);
|
||
let p2 = pos + k1.dpos * dt * 0.2;
|
||
let d2 = normalize(dir + k1.ddir * dt * 0.2);
|
||
let k2 = deriv(p2, d2);
|
||
let p3 = pos + (k1.dpos * 0.075 + k2.dpos * 0.225) * dt;
|
||
let d3 = normalize(dir + (k1.ddir * 0.075 + k2.ddir * 0.225) * dt);
|
||
let k3 = deriv(p3, d3);
|
||
let p4 = pos + (k1.dpos * 0.3 + k2.dpos * -0.9 + k3.dpos * 1.2) * dt;
|
||
let d4 = normalize(dir + (k1.ddir * 0.3 + k2.ddir * -0.9 + k3.ddir * 1.2) * dt);
|
||
let k4 = deriv(p4, d4);
|
||
let p5 = pos + (k1.dpos * -11.0/54.0 + k2.dpos * 2.5 + k3.dpos * -70.0/27.0 + k4.dpos * 35.0/27.0) * dt;
|
||
let d5 = normalize(dir + (k1.ddir * -11.0/54.0 + k2.ddir * 2.5 + k3.ddir * -70.0/27.0 + k4.ddir * 35.0/27.0) * dt);
|
||
let k5 = deriv(p5, d5);
|
||
let p6 = pos + (k1.dpos * 1631.0/55296.0 + k2.dpos * 175.0/512.0 + k3.dpos * 575.0/13824.0 + k4.dpos * 44275.0/110592.0 + k5.dpos * 253.0/4096.0) * dt;
|
||
let d6 = normalize(dir + (k1.ddir * 1631.0/55296.0 + k2.ddir * 175.0/512.0 + k3.ddir * 575.0/13824.0 + k4.ddir * 44275.0/110592.0 + k5.ddir * 253.0/4096.0) * dt);
|
||
let k6 = deriv(p6, d6);
|
||
// 5th-order solution (used to advance).
|
||
let new_pos = pos + (k1.dpos * 37.0/378.0 + k3.dpos * 250.0/621.0 + k4.dpos * 125.0/594.0 + k5.dpos * 512.0/1771.0 + k6.dpos * 0.0) * dt;
|
||
let new_dir = normalize(dir + (k1.ddir * 37.0/378.0 + k3.ddir * 250.0/621.0 + k4.ddir * 125.0/594.0 + k5.ddir * 512.0/1771.0 + k6.ddir * 0.0) * dt);
|
||
// 4th-order solution (for error estimate).
|
||
let pos4 = pos + (k1.dpos * 2825.0/27648.0 + k3.dpos * 18575.0/48384.0 + k4.dpos * 13525.0/55296.0 + k5.dpos * 277.0/14336.0 + k6.dpos * 0.25) * dt;
|
||
let err = length(new_pos - pos4);
|
||
return RkStep(new_pos, new_dir, err);
|
||
}
|
||
|
||
// ====================== main ======================
|
||
|
||
// One full ray march (camera → capture/escape/budget) for a single ray
|
||
// direction, returning the accumulated HDR color. Factored out of `fragment`
|
||
// so the supersampling loop can fire several jittered rays per pixel and
|
||
// average them. `dir` is the camera-space ray direction; the disk-local
|
||
// rotation and all per-ray state live in here so each sample is independent.
|
||
fn march(dir: vec3<f32>) -> vec3<f32> {
|
||
// Total path length to integrate: enough to go from the camera, past the
|
||
// hole, and far enough beyond to count as escaped.
|
||
let eye_dist = length(uniforms.eye.xyz);
|
||
let escape_r = max(eye_dist * 2.0, 100.0);
|
||
let total_path = eye_dist + escape_r;
|
||
// Adaptive RK45 constants.
|
||
let steps_max = uniforms.steps;
|
||
let dt_init = total_path / f32(steps_max);
|
||
let dt_min = dt_init * 0.25;
|
||
let dt_max = dt_init * 4.0;
|
||
let tol = 1e-3;
|
||
let r_plus = 0.5 + sqrt(max(0.25 - (uniforms.spin * 0.5) * (uniforms.spin * 0.5), 0.0));
|
||
|
||
// 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));
|
||
var dt = dt_init;
|
||
var prev = pos;
|
||
var budget = steps_max;
|
||
|
||
var accum_color = vec3<f32>(0.0);
|
||
var accum_alpha = 0.0;
|
||
|
||
loop {
|
||
if (budget == 0u) { break; }
|
||
|
||
let step = rk45_step(pos, d, dt);
|
||
let err = step.err;
|
||
|
||
if (err > tol * 10.0 && dt > dt_min) {
|
||
// Reject: shrink dt, retry (does not consume budget).
|
||
// The `dt > dt_min` guard makes dt_min a forced-accept floor: once
|
||
// dt is already at its minimum, accept the step regardless of error
|
||
// rather than spinning forever on `continue`. This prevents a GPU
|
||
// hang when a ray hits a region whose error is intrinsically above
|
||
// tolerance even at the smallest step (extreme spin, near-horizon).
|
||
dt = dt_min;
|
||
continue;
|
||
}
|
||
// Accept: consume one budget unit, refine dt.
|
||
budget = budget - 1u;
|
||
if (err > tol * 10.0) {
|
||
// Forced accept at dt_min (err still high): don't grow dt back up.
|
||
} else {
|
||
dt = clamp(dt * pow(tol / max(err, 1e-12), 0.2), dt_min, dt_max);
|
||
}
|
||
|
||
let new_pos = step.pos;
|
||
let new_dir = step.dir;
|
||
|
||
let r = length(new_pos);
|
||
if (r < r_plus) {
|
||
break;
|
||
}
|
||
if (r > escape_r) {
|
||
let world_dir = normalize(rot_x(new_dir, uniforms.disk_tilt));
|
||
var bg = vec3<f32>(0.0);
|
||
bg += star_color(world_dir, uniforms.star_intensity);
|
||
if (uniforms.skybox_intensity > 0.0) {
|
||
bg += skybox_color(world_dir) * uniforms.skybox_intensity;
|
||
}
|
||
accum_color += (1.0 - accum_alpha) * bg;
|
||
accum_alpha = 1.0;
|
||
break;
|
||
}
|
||
|
||
// --- volumetric disk ---
|
||
if (uniforms.disk_quality == 0u) {
|
||
// Off tier: zero-thickness single midplane sample, fixed alpha.
|
||
if (disk_hit(prev, new_pos)) {
|
||
let ty = prev.y / (prev.y - new_pos.y);
|
||
let hit = mix(prev, new_pos, vec3<f32>(ty));
|
||
let s = disk_color_flat(hit, new_dir);
|
||
accum_color += (1.0 - accum_alpha) * s.color * s.density;
|
||
accum_alpha += (1.0 - accum_alpha) * s.density;
|
||
if (accum_alpha > 0.99) { break; }
|
||
}
|
||
} else {
|
||
// Volumetric tier: clip this step to the disk slab and integrate N
|
||
// samples along the clipped segment, weighted by the analytic
|
||
// in-slab length (NOT the RK45 step size). See integrate_disk_segment
|
||
// for why the step-size-decoupled weight is what kills the radial
|
||
// spokes that the previous `* step_len` form produced.
|
||
integrate_disk_segment(prev, new_pos, new_dir, &accum_color, &accum_alpha);
|
||
if (accum_alpha > 0.99) { break; }
|
||
}
|
||
|
||
// --- relativistic jets (along the spin axis) ---
|
||
if (uniforms.jets_enabled != 0u) {
|
||
sample_jets(new_pos, new_dir, r_plus, length(new_pos - prev), &accum_color, &accum_alpha);
|
||
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; }
|
||
}
|
||
|
||
if (uniforms.grid_enabled != 0u) {
|
||
let g = grid_hit(prev, new_pos);
|
||
if (g.x + g.y + g.z > 0.0) {
|
||
accum_color += g;
|
||
}
|
||
}
|
||
|
||
prev = new_pos;
|
||
pos = new_pos;
|
||
d = new_dir;
|
||
}
|
||
|
||
return accum_color;
|
||
}
|
||
|
||
@fragment
|
||
fn fragment(in: VertexOutput) -> @location(0) vec4<f32> {
|
||
// Seed the per-pixel hash used by the slab sub-sample jitter (Fix B) and
|
||
// the supersample jitter (Fix A). @builtin(position) is the fragment's
|
||
// framebuffer coordinate; using it makes the noise spatially stable.
|
||
pixel_seed = in.position.xy;
|
||
|
||
let aspect = uniforms.resolution.x / uniforms.resolution.y;
|
||
let base_uv = vec2<f32>((in.uv * 2.0 - 1.0).x * aspect, (in.uv * 2.0 - 1.0).y);
|
||
|
||
// Per-pixel stochastic supersampling (Fix A). The concentric rings that
|
||
// appear on the disk are higher-order gravitationally-lensed disk images:
|
||
// rays near the critical impact parameter wrap around the hole, and each
|
||
// wrap crosses the disk plane once, projecting to a ring. The integrator
|
||
// renders each wrap as a sharp discrete band rather than a smooth image, so
|
||
// the rings read as an artifact. Firing several jittered sub-rays per pixel
|
||
// and averaging antialiases those sharp band edges into a smooth gradient
|
||
// (the physical Einstein-ring structure is preserved; only its staircase
|
||
// discretization is removed).
|
||
//
|
||
// MAX_AA_SAMPLES is a compile-time cap (WGSL needs static loop bounds);
|
||
// the runtime count comes from uniforms.aa_samples with an early break —
|
||
// the same MAX-with-break form fbm3/ridged_fbm use for dynamic octaves.
|
||
const MAX_AA_SAMPLES = 4u;
|
||
var color_sum = vec3<f32>(0.0);
|
||
var n_done = 0u;
|
||
for (var s: u32 = 0u; s < MAX_AA_SAMPLES; s = s + 1u) {
|
||
if (s >= uniforms.aa_samples) { break; }
|
||
var uv = base_uv;
|
||
if (uniforms.aa_samples > 1u) {
|
||
// ~half-pixel jitter in NDC, seeded by pixel + sample index. The
|
||
// seed is pixel-only (no time) so the pattern is temporally stable.
|
||
let j = hash33(vec3<f32>(pixel_seed, f32(s))) - 0.5;
|
||
uv = uv + j.xy / uniforms.resolution;
|
||
}
|
||
color_sum = color_sum + march(ray_direction(uv));
|
||
n_done = n_done + 1u;
|
||
}
|
||
|
||
return vec4<f32>(color_sum / f32(n_done), 1.0);
|
||
}
|