1#define_import_path bevy_pbr::atmosphere::functions
2
3#import bevy_render::maths::{PI, HALF_PI, PI_2, fast_acos, fast_acos_4, fast_atan2, ray_sphere_intersect}
4
5#import bevy_pbr::atmosphere::{
6    types::Atmosphere,
7    bindings::{
8        atmosphere, settings, view, lights, transmittance_lut, atmosphere_lut_sampler,
9        multiscattering_lut, sky_view_lut, aerial_view_lut, atmosphere_transforms,
10        medium_density_lut, medium_scattering_lut, medium_sampler,
11    },
12    bruneton_functions::{
13        transmittance_lut_r_mu_to_uv, ray_intersects_ground,
14        distance_to_top_atmosphere_boundary, distance_to_bottom_atmosphere_boundary
15    },
16}
17
18// NOTE FOR CONVENTIONS: 
19// r:
20//   radius, or distance from planet center 
21//
22// altitude:
23//   distance from planet **surface**
24//
25// mu:
26//   cosine of the zenith angle of a ray with
27//   respect to the planet normal
28//
29// atmosphere space:
30//   abbreviated as "as" (contrast with vs, cs, ws), this space is similar
31//   to view space, but with the camera positioned horizontally on the planet
32//   surface, so the horizon is a horizontal line centered vertically in the
33//   frame. This enables the non-linear latitude parametrization the paper uses 
34//   to concentrate detail near the horizon 
35
36
37// CONSTANTS
38const FRAC_PI: f32 = 0.3183098862; // 1 / π
39const FRAC_2_PI: f32 = 0.15915494309;  // 1 / (2π)
40const FRAC_3_16_PI: f32 = 0.0596831036594607509; // 3 / (16π)
41const FRAC_4_PI: f32 = 0.07957747154594767; // 1 / (4π)
42const ROOT_2: f32 = 1.41421356; // √2
43const EPSILON: f32 = 1.0; // 1 meter
44const MIN_EXTINCTION: vec3<f32> = vec3(1e-12);
45
46// During raymarching, each segment is sampled at a single point. This constant determines
47// where in the segment that sample is taken (0.0 = start, 0.5 = middle, 1.0 = end).
48// We use 0.3 to sample closer to the start of each segment, which better approximates
49// the exponential falloff of atmospheric density.
50const MIDPOINT_RATIO: f32 = 0.3;
51
52// LUT UV PARAMETERIZATIONS
53
54fn unit_to_sub_uvs(val: vec2<f32>, resolution: vec2<f32>) -> vec2<f32> {
55    return (val + 0.5f / resolution) * (resolution / (resolution + 1.0f));
56}
57
58fn sub_uvs_to_unit(val: vec2<f32>, resolution: vec2<f32>) -> vec2<f32> {
59    return (val - 0.5f / resolution) * (resolution / (resolution - 1.0f));
60}
61
62fn multiscattering_lut_r_mu_to_uv(r: f32, mu: f32) -> vec2<f32> {
63    let u = 0.5 + 0.5 * mu;
64    let v = saturate((r - atmosphere.inner_radius) / (atmosphere.outer_radius - atmosphere.inner_radius)); //TODO
65    return unit_to_sub_uvs(vec2(u, v), vec2<f32>(settings.multiscattering_lut_size));
66}
67
68fn multiscattering_lut_uv_to_r_mu(uv: vec2<f32>) -> vec2<f32> {
69    let adj_uv = sub_uvs_to_unit(uv, vec2<f32>(settings.multiscattering_lut_size));
70    let r = mix(atmosphere.inner_radius, atmosphere.outer_radius, adj_uv.y);
71    let mu = adj_uv.x * 2 - 1;
72    return vec2(r, mu);
73}
74
75fn sky_view_lut_r_mu_azimuth_to_uv(r: f32, mu: f32, azimuth: f32) -> vec2<f32> {
76    let u = (azimuth * FRAC_2_PI) + 0.5;
77
78    let v_horizon = sqrt(r * r - atmosphere.inner_radius * atmosphere.inner_radius);
79    let cos_beta = v_horizon / r;
80    // Using fast_acos_4 for better precision at small angles
81    // to avoid artifacts at the horizon
82    let beta = fast_acos_4(cos_beta);
83    let horizon_zenith = PI - beta;
84    let view_zenith = fast_acos_4(mu);
85
86    // Apply non-linear transformation to compress more texels 
87    // near the horizon where high-frequency details matter most
88    // l is latitude in [-π/2, π/2] and v is texture coordinate in [0,1]
89    let l = view_zenith - horizon_zenith;
90    let abs_l = abs(l);
91
92    let v = 0.5 + 0.5 * sign(l) * sqrt(abs_l / HALF_PI);
93
94    return unit_to_sub_uvs(vec2(u, v), vec2<f32>(settings.sky_view_lut_size));
95}
96
97fn sky_view_lut_uv_to_zenith_azimuth(r: f32, uv: vec2<f32>) -> vec2<f32> {
98    let adj_uv = sub_uvs_to_unit(vec2(uv.x, 1.0 - uv.y), vec2<f32>(settings.sky_view_lut_size));
99    let azimuth = (adj_uv.x - 0.5) * PI_2;
100
101    // Horizon parameters
102    let v_horizon = sqrt(r * r - atmosphere.inner_radius * atmosphere.inner_radius);
103    let cos_beta = v_horizon / r;
104    let beta = fast_acos_4(cos_beta);
105    let horizon_zenith = PI - beta;
106
107    // Inverse of horizon-detail mapping to recover original latitude from texture coordinate
108    let t = abs(2.0 * (adj_uv.y - 0.5));
109    let l = sign(adj_uv.y - 0.5) * HALF_PI * t * t;
110
111    return vec2(horizon_zenith - l, azimuth);
112}
113
114// LUT SAMPLING
115
116fn sample_transmittance_lut(r: f32, mu: f32) -> vec3<f32> {
117    let uv = transmittance_lut_r_mu_to_uv(atmosphere, r, mu);
118    return textureSampleLevel(transmittance_lut, atmosphere_lut_sampler, uv, 0.0).rgb;
119}
120
121// NOTICE: This function is copyrighted by Eric Bruneton and INRIA, and falls
122// under the license reproduced in bruneton_functions.wgsl (variant of MIT license)
123//
124// FIXME: this function should be in bruneton_functions.wgsl, but because naga_oil doesn't 
125// support cyclic imports it's stuck here
126fn sample_transmittance_lut_segment(r: f32, mu: f32, t: f32) -> vec3<f32> {
127    let r_t = get_local_r(r, mu, t);
128    let mu_t = clamp((r * mu + t) / r_t, -1.0, 1.0);
129
130    if ray_intersects_ground(r, mu) {
131        return min(
132            sample_transmittance_lut(r_t, -mu_t) / sample_transmittance_lut(r, -mu),
133            vec3(1.0)
134        );
135    } else {
136        return min(
137            sample_transmittance_lut(r, mu) / sample_transmittance_lut(r_t, mu_t), vec3(1.0)
138        );
139    }
140}
141
142fn sample_multiscattering_lut(r: f32, mu: f32) -> vec3<f32> {
143    let uv = multiscattering_lut_r_mu_to_uv(r, mu);
144    return textureSampleLevel(multiscattering_lut, atmosphere_lut_sampler, uv, 0.0).rgb;
145}
146
147fn sample_sky_view_lut(r: f32, ray_dir_as: vec3<f32>) -> vec3<f32> {
148    let mu = ray_dir_as.y;
149    let azimuth = fast_atan2(ray_dir_as.x, -ray_dir_as.z);
150    let uv = sky_view_lut_r_mu_azimuth_to_uv(r, mu, azimuth);
151    return textureSampleLevel(sky_view_lut, atmosphere_lut_sampler, uv, 0.0).rgb;
152}
153
154fn ndc_to_camera_dist(ndc: vec3<f32>) -> f32 {
155    let view_pos = view.view_from_clip * vec4(ndc, 1.0);
156    let p_view = view_pos.xyz / view_pos.w;
157    let p_world = (view.world_from_view * vec4(p_view, 1.0)).xyz;
158    let p_atmo = (atmosphere.world_to_atmosphere * vec4(p_world, 1.0)).xyz;
159    let cam_atmo = (atmosphere.world_to_atmosphere * vec4(view.world_position, 1.0)).xyz;
160    return length(p_atmo - cam_atmo);
161}
162
163// RGB channels: total inscattered light along the camera ray to the current sample.
164// A channel: average transmittance across all wavelengths to the current sample.
165fn sample_aerial_view_lut(uv: vec2<f32>, t: f32) -> vec3<f32> {
166    let t_max = settings.aerial_view_lut_max_distance;
167    let num_slices = f32(settings.aerial_view_lut_size.z);
168    // Each texel stores the value of the scattering integral over the whole slice,
169    // which requires us to offset the w coordinate by half a slice. For
170    // example, if we wanted the value of the integral at the boundary between slices,
171    // we'd need to sample at the center of the previous slice, and vice-versa for
172    // sampling in the center of a slice.
173    let uvw = vec3(uv, saturate(t / t_max - 0.5 / num_slices));
174    let sample = textureSampleLevel(aerial_view_lut, atmosphere_lut_sampler, uvw, 0.0);
175    // Since sampling anywhere between w=0 and w=t_slice will clamp to the first slice,
176    // we need to do a linear step over the first slice towards zero at the camera's
177    // position to recover the correct integral value.
178    let t_slice = t_max / num_slices;
179    let fade = saturate(t / t_slice);
180    // Recover the values from log space
181    return exp(sample.rgb) * fade;
182}
183
184// ATMOSPHERE SAMPLING
185
186const ABSORPTION_DENSITY: f32 = 0.0;
187const SCATTERING_DENSITY: f32 = 1.0;
188
189// samples from the atmosphere density LUT.
190//
191// calling with `component = 0.0` will return the atmosphere's absorption density,
192// while calling with `component = 1.0` will return the atmosphere's scattering density.
193fn sample_density_lut(r: f32, component: f32) -> vec3<f32> {
194    // sampler clamps to [0, 1] anyways, no need to clamp the altitude
195    let normalized_altitude = (r - atmosphere.inner_radius) / (atmosphere.outer_radius - atmosphere.inner_radius);
196    let uv = vec2(1.0 - normalized_altitude, component);
197    return textureSampleLevel(medium_density_lut, medium_sampler, uv, 0.0).xyz;
198}
199
200// samples from the atmosphere scattering LUT. `neg_LdotV` is the dot product
201// of the light direction and the incoming view vector.
202// Nonlinear phase mapping to mitigate banding in low-resolution LUTs.
203const PHASE_MAPPING_N: f32 = 0.5;
204fn sample_scattering_lut(r: f32, neg_LdotV: f32) -> vec3<f32> {
205    let normalized_altitude = (r - atmosphere.inner_radius) / (atmosphere.outer_radius - atmosphere.inner_radius);
206    let phase_uv = 0.5 + 0.5 * sign(neg_LdotV) * (1.0 - pow(1.0 - abs(neg_LdotV), PHASE_MAPPING_N));
207    let uv = vec2(1.0 - normalized_altitude, phase_uv);
208    return textureSampleLevel(medium_scattering_lut, medium_sampler, uv, 0.0).xyz;
209}
210
211/// evaluates L_scat, equation 3 in the paper, which gives the total single-order scattering towards the view at a single point
212fn sample_local_inscattering(local_scattering: vec3<f32>, ray_dir: vec3<f32>, world_pos: vec3<f32>) -> vec3<f32> {
213    let local_r = length(world_pos);
214    let local_up = normalize(world_pos);
215    var inscattering = vec3(0.0);
216    for (var light_i: u32 = 0u; light_i < lights.n_directional_lights; light_i++) {
217        let light = &lights.directional_lights[light_i];
218
219        let mu_light = dot((*light).direction_to_light, local_up);
220
221        // -(L . V) == (L . -V). -V here is our ray direction, which points away from the view
222        // instead of towards it (as is the convention for V)
223        let neg_LdotV = dot((*light).direction_to_light, ray_dir);
224
225        let transmittance_to_light = sample_transmittance_lut(local_r, mu_light);
226        let shadow_factor = transmittance_to_light * f32(!ray_intersects_ground(local_r, mu_light));
227        let scattering_coeff = sample_scattering_lut(local_r, neg_LdotV);
228
229        // Transmittance from scattering event to light source
230        let scattering_factor = shadow_factor * scattering_coeff;
231
232        // Additive factor from the multiscattering LUT
233        let psi_ms = sample_multiscattering_lut(local_r, mu_light);
234        let multiscattering_factor = psi_ms * local_scattering;
235
236        inscattering += (*light).color.rgb * (scattering_factor + multiscattering_factor);
237    }
238    return inscattering;
239}
240
241fn sample_sun_radiance(ray_dir_ws: vec3<f32>) -> vec3<f32> {
242    let view_pos = get_view_position();
243    let r = length(view_pos);
244    let up = normalize(view_pos);
245    let mu_view = dot(ray_dir_ws, up);
246    let shadow_factor = f32(!ray_intersects_ground(r, mu_view));
247    var sun_radiance = vec3(0.0);
248    for (var light_i: u32 = 0u; light_i < lights.n_directional_lights; light_i++) {
249        let light = &lights.directional_lights[light_i];
250        let neg_LdotV = dot((*light).direction_to_light, ray_dir_ws);
251        let angle_to_sun = fast_acos(clamp(neg_LdotV, -1.0, 1.0));
252        let w = max(0.5 * fwidth(angle_to_sun), 1e-6);
253        let sun_angular_size = (*light).sun_disk_angular_size;
254        let sun_intensity = (*light).sun_disk_intensity;
255        if sun_angular_size > 0.0 && sun_intensity > 0.0 {
256            let factor = 1 - smoothstep(sun_angular_size * 0.5 - w, sun_angular_size * 0.5 + w, angle_to_sun);
257            let sun_solid_angle = (sun_angular_size * sun_angular_size) * 0.25 * PI;
258            sun_radiance += ((*light).color.rgb / sun_solid_angle) * sun_intensity * factor * shadow_factor;
259        }
260    }
261    return sun_radiance;
262}
263
264fn calculate_visible_sun_ratio(atmosphere: Atmosphere, r: f32, mu: f32, sun_angular_size: f32) -> f32 {
265    let inner_radius = atmosphere.inner_radius;
266    // Calculate the angle between horizon and sun center
267    // Invert the horizon angle calculation to fix shading direction
268    let horizon_cos = -sqrt(1.0 - (inner_radius * inner_radius) / (r * r));
269    let horizon_angle = fast_acos_4(horizon_cos);
270    let sun_zenith_angle = fast_acos_4(mu);
271    
272    // If sun is completely above horizon
273    if sun_zenith_angle + sun_angular_size * 0.5 <= horizon_angle {
274        return 1.0;
275    }
276    
277    // If sun is completely below horizon
278    if sun_zenith_angle - sun_angular_size * 0.5 >= horizon_angle {
279        return 0.0;
280    }
281    
282    // Calculate partial visibility using circular segment area formula
283    let d = (horizon_angle - sun_zenith_angle) / (sun_angular_size * 0.5);
284    let visible_ratio = 0.5 + d * 0.5;
285    return clamp(visible_ratio, 0.0, 1.0);
286}
287
288// TRANSFORM UTILITIES
289
290/// Clamp a position to the planet surface (with a small epsilon) to avoid underground artifacts.
291fn clamp_to_surface(atmosphere: Atmosphere, position: vec3<f32>) -> vec3<f32> {
292    let min_radius = atmosphere.inner_radius + EPSILON;
293    let r = length(position);
294    if r < min_radius {
295        let up = normalize(position);
296        return up * min_radius;
297    }
298    return position;
299}
300
301fn max_atmosphere_distance(r: f32, mu: f32) -> f32 {
302    let t_top = distance_to_top_atmosphere_boundary(atmosphere, r, mu);
303    let t_bottom = distance_to_bottom_atmosphere_boundary(r, mu);
304    let hits = ray_intersects_ground(r, mu);
305    return mix(t_top, t_bottom, f32(hits));
306}
307
308/// Returns the observer's position in the atmosphere
309fn get_view_position() -> vec3<f32> {
310    let atmo_pos = (atmosphere.world_to_atmosphere * vec4(view.world_position, 1.0)).xyz;
311    return clamp_to_surface(atmosphere, atmo_pos);
312}
313
314// We assume the `up` vector at the view position is the y axis, since the world is locally flat/level.
315// t = distance along view ray in atmosphere space
316// NOTE: this means that if your world is actually spherical, this will be wrong.
317fn get_local_up(r: f32, t: f32, ray_dir: vec3<f32>) -> vec3<f32> {
318    return normalize(vec3(0.0, r, 0.0) + t * ray_dir);
319}
320
321// Given a ray starting at radius r, with mu = cos(zenith angle),
322// and a t = distance along the ray, gives the new radius at point t
323fn get_local_r(r: f32, mu: f32, t: f32) -> f32 {
324    return sqrt(t * t + 2.0 * r * mu * t + r * r);
325}
326
327// Convert uv [0.0 .. 1.0] coordinate to ndc space xy [-1.0 .. 1.0]
328fn uv_to_ndc(uv: vec2<f32>) -> vec2<f32> {
329    return uv * vec2(2.0, -2.0) + vec2(-1.0, 1.0);
330}
331
332/// Convert ndc space xy coordinate [-1.0 .. 1.0] to uv [0.0 .. 1.0]
333fn ndc_to_uv(ndc: vec2<f32>) -> vec2<f32> {
334    return ndc * vec2(0.5, -0.5) + vec2(0.5);
335}
336
337/// Converts a direction in world space to atmosphere space
338fn direction_world_to_atmosphere(dir_ws: vec3<f32>) -> vec3<f32> {
339    let dir_as = atmosphere_transforms.atmosphere_from_world * vec4(dir_ws, 0.0);
340    return dir_as.xyz;
341}
342
343/// Converts a direction in atmosphere space to world space
344fn direction_atmosphere_to_world(dir_as: vec3<f32>) -> vec3<f32> {
345    let dir_ws = atmosphere_transforms.world_from_atmosphere * vec4(dir_as, 0.0);
346    return dir_ws.xyz;
347}
348
349// Modified from skybox.wgsl. For this pass we don't need to apply a separate sky transform or consider camera viewport.
350// Returns a normalized ray direction in world space.
351fn uv_to_ray_direction(uv: vec2<f32>) -> vec3<f32> {
352    // Using world positions of the fragment and camera to calculate a ray direction
353    // breaks down at large translations. This code only needs to know the ray direction.
354    // The ray direction is along the direction from the camera to the fragment position.
355    // In view space, the camera is at the origin, so the view space ray direction is
356    // along the direction of the fragment position - (0,0,0) which is just the
357    // fragment position.
358    // Use the position on the near clipping plane to avoid -inf world position
359    // because the far plane of an infinite reverse projection is at infinity.
360    let view_position_homogeneous = view.view_from_clip * vec4(
361        uv_to_ndc(uv),
362        1.0,
363        1.0,
364    );
365
366    let view_ray_direction = view_position_homogeneous.xyz / view_position_homogeneous.w;
367    // Transforming the view space ray direction by the inverse view matrix, transforms the
368    // direction to world space. Note that the w element is set to 0.0, as this is a
369    // vector direction, not a position, That causes the matrix multiplication to ignore
370    // the translations from the view matrix.
371    let ray_direction = (view.world_from_view * vec4(view_ray_direction, 0.0)).xyz;
372
373    return normalize(ray_direction);
374}
375
376fn zenith_azimuth_to_ray_dir(zenith: f32, azimuth: f32) -> vec3<f32> {
377    let sin_zenith = sin(zenith);
378    let mu = cos(zenith);
379    let sin_azimuth = sin(azimuth);
380    let cos_azimuth = cos(azimuth);
381    return vec3(sin_azimuth * sin_zenith, mu, -cos_azimuth * sin_zenith);
382}
383
384struct RaymarchSegment {
385    start: f32,
386    end: f32,
387}
388
389fn get_raymarch_segment(r: f32, mu: f32) -> RaymarchSegment {
390    // Get both intersection points with atmosphere
391    let atmosphere_intersections = ray_sphere_intersect(r, mu, atmosphere.outer_radius);
392    let ground_intersections = ray_sphere_intersect(r, mu, atmosphere.inner_radius);
393
394    var segment: RaymarchSegment;
395
396    if r < atmosphere.inner_radius {
397        // Inside planet - start from bottom of atmosphere
398        segment.start = ground_intersections.y; // Use second intersection point with ground
399        segment.end = atmosphere_intersections.y;
400    } else if r < atmosphere.outer_radius {
401        // Inside atmosphere
402        segment.start = 0.0;
403        segment.end = select(atmosphere_intersections.y, ground_intersections.x, ray_intersects_ground(r, mu));
404    } else {
405        // Outside atmosphere
406        if atmosphere_intersections.x < 0.0 {
407            // No intersection with atmosphere
408            return segment;
409        }
410        // Start at atmosphere entry, end at exit or ground
411        segment.start = atmosphere_intersections.x;
412        segment.end = select(atmosphere_intersections.y, ground_intersections.x, ray_intersects_ground(r, mu));
413    }
414
415    return segment;
416}
417
418struct RaymarchResult {
419    inscattering: vec3<f32>,
420    transmittance: vec3<f32>,
421}
422
423fn raymarch_atmosphere(
424    pos: vec3<f32>,
425    ray_dir: vec3<f32>,
426    t_max: f32,
427    max_samples: u32,
428    uv: vec2<f32>,
429    ground: bool
430) -> RaymarchResult {
431    let r = length(pos);
432    let up = normalize(pos);
433    let mu = dot(ray_dir, up);
434
435    // Optimization: Reduce sample count at close proximity to the scene
436    let sample_count = mix(1.0, f32(max_samples), saturate(t_max * 0.01));
437
438    let segment = get_raymarch_segment(r, mu);
439    let t_start = segment.start;
440    var t_end = segment.end;
441
442    t_end = min(t_end, t_max);
443    let t_total = t_end - t_start;
444
445    var result: RaymarchResult;
446    result.inscattering = vec3(0.0);
447    result.transmittance = vec3(1.0);
448
449    // Skip if invalid segment
450    if t_total <= 0.0 {
451        return result;
452    }
453
454    var prev_t = t_start;
455    var optical_depth = vec3(0.0);
456    for (var s = 0.0; s < sample_count; s += 1.0) {
457        // Linear distribution from atmosphere entry to exit/ground
458        let t_i = t_start + t_total * (s + MIDPOINT_RATIO) / sample_count;
459        let dt_i = (t_i - prev_t);
460        prev_t = t_i;
461
462        let sample_pos = pos + ray_dir * t_i;
463        let local_r = length(sample_pos);
464        let local_up = normalize(sample_pos);
465
466        let absorption = sample_density_lut(local_r, ABSORPTION_DENSITY);
467        let scattering = sample_density_lut(local_r, SCATTERING_DENSITY);
468        let extinction = absorption + scattering;
469
470        let sample_optical_depth = extinction * dt_i;
471        optical_depth += sample_optical_depth;
472        let sample_transmittance = exp(-sample_optical_depth);
473
474        let inscattering = sample_local_inscattering(
475            scattering,
476            ray_dir,
477            sample_pos
478        );
479
480        let s_int = (inscattering - inscattering * sample_transmittance) / max(extinction, MIN_EXTINCTION);
481        result.inscattering += result.transmittance * s_int;
482
483        result.transmittance *= sample_transmittance;
484        if all(result.transmittance < vec3(0.001)) {
485            break;
486        }
487    }
488
489    // include reflected luminance from planet ground 
490    if ground && ray_intersects_ground(r, mu) {
491        for (var light_i: u32 = 0u; light_i < lights.n_directional_lights; light_i++) {
492            let light = &lights.directional_lights[light_i];
493            let light_dir = (*light).direction_to_light;
494            let light_color = (*light).color.rgb;
495            let transmittance_to_ground = exp(-optical_depth);
496            // position on the sphere and get the sphere normal (up)
497            let sphere_point = pos + ray_dir * t_end;
498            let sphere_normal = normalize(sphere_point);
499            let mu_light = dot(light_dir, sphere_normal);
500            let transmittance_to_light = sample_transmittance_lut(0.0, mu_light);
501            let light_luminance = transmittance_to_light * max(mu_light, 0.0) * light_color;
502            // Normalized Lambert BRDF
503            let ground_luminance = transmittance_to_ground * atmosphere.ground_albedo / PI;
504            result.inscattering += ground_luminance * light_luminance;
505        }
506    }
507
508    return result;
509}