1// A postprocessing shader that implements volumetric fog via raymarching and2// sampling directional light shadow maps.3//4// The overall approach is a combination of the volumetric rendering in [1] and5// the shadow map raymarching in [2]. First, we raytrace the AABB of the fog6// volume in order to determine how long our ray is. Then we do a raymarch, with7// physically-based calculations at each step to determine how much light was8// absorbed, scattered out, and scattered in. To determine in-scattering, we9// sample the shadow map for the light to determine whether the point was in10// shadow or not.11//12// [1]: https://www.scratchapixel.com/lessons/3d-basic-rendering/volume-rendering-for-developers/intro-volume-rendering.html13//14// [2]: http://www.alexandre-pestana.com/volumetric-lights/16#import bevy_core_pipeline::fullscreen_vertex_shader::FullscreenVertexOutput17#import bevy_pbr::atmosphere::{18 functions::{calculate_visible_sun_ratio, clamp_to_surface},19 bruneton_functions::transmittance_lut_r_mu_to_uv,20}21#import bevy_pbr::mesh_functions::{get_world_from_local, mesh_position_local_to_clip}22#import bevy_pbr::mesh_view_bindings::{23 globals, lights, view, clustered_lights,24 atmosphere, atmosphere_transmittance_texture, atmosphere_transmittance_sampler25}26#import bevy_pbr::mesh_view_types::{27 DIRECTIONAL_LIGHT_FLAGS_VOLUMETRIC_BIT,28 POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT,29 POINT_LIGHT_FLAGS_VOLUMETRIC_BIT,30 POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE,31}32#import bevy_pbr::shadow_sampling::{33 sample_shadow_map_hardware,34 sample_shadow_cubemap,35 sample_shadow_map,36 SPOT_SHADOW_TEXEL_SIZE37}38#import bevy_pbr::shadows::{get_cascade_index, world_to_directional_light_local}39#import bevy_pbr::utils::interleaved_gradient_noise40#import bevy_pbr::view_transformations::{41 depth_ndc_to_view_z,42 frag_coord_to_ndc,43 position_ndc_to_view,44 position_ndc_to_world,45 position_view_to_world46}47#import bevy_pbr::clustered_forward as clustering48#import bevy_pbr::lighting::getDistanceAttenuation;50// The GPU version of [`VolumetricFog`]. See the comments in51// `volumetric_fog/mod.rs` for descriptions of the fields here.52struct VolumetricFog {53 clip_from_local: mat4x4<f32>,54 uvw_from_world: mat4x4<f32>,55 far_planes: array<vec4<f32>, 3>,56 fog_color: vec3<f32>,57 light_tint: vec3<f32>,58 ambient_color: vec3<f32>,59 ambient_intensity: f32,60 step_count: u32,61 bounding_radius: f32,62 absorption: f32,63 scattering: f32,64 density_factor: f32,65 density_texture_offset: vec3<f32>,66 scattering_asymmetry: f32,67 light_intensity: f32,68 jitter_strength: f32,69}71@group(1) @binding(0) var<uniform> volumetric_fog: VolumetricFog;73#ifdef MULTISAMPLED74@group(1) @binding(1) var depth_texture: texture_depth_multisampled_2d;75#else76@group(1) @binding(1) var depth_texture: texture_depth_2d;77#endif79#ifdef DENSITY_TEXTURE80@group(1) @binding(2) var density_texture: texture_3d<f32>;81@group(1) @binding(3) var density_sampler: sampler;82#endif // DENSITY_TEXTURE84// 1 / (4π)85const FRAC_4_PI: f32 = 0.07957747154594767;87struct Vertex {88 @builtin(instance_index) instance_index: u32,89 @location(0) position: vec3<f32>,90}92@vertex93fn vertex(vertex: Vertex) -> @builtin(position) vec4<f32> {94 return volumetric_fog.clip_from_local * vec4<f32>(vertex.position, 1.0);95}97// The common Henyey-Greenstein asymmetric phase function [1] [2].98//99// This determines how much light goes toward the viewer as opposed to away from100// the viewer. From a visual point of view, it controls how the light shafts101// appear and disappear as the camera looks at the light source.102//103// [1]: https://www.scratchapixel.com/lessons/3d-basic-rendering/volume-rendering-for-developers/ray-marching-get-it-right.html104//105// [2]: https://www.pbr-book.org/4ed/Volume_Scattering/Phase_Functions#TheHenyeyndashGreensteinPhaseFunction106fn henyey_greenstein(neg_LdotV: f32) -> f32 {107 let g = volumetric_fog.scattering_asymmetry;108 let denom = 1.0 + g * g - 2.0 * g * neg_LdotV;109 return FRAC_4_PI * (1.0 - g * g) / (denom * sqrt(denom));110}112@fragment113fn fragment(@builtin(position) position: vec4<f32>) -> @location(0) vec4<f32> {114 // Unpack the `volumetric_fog` settings.115 let uvw_from_world = volumetric_fog.uvw_from_world;116 let fog_color = volumetric_fog.fog_color;117 let ambient_color = volumetric_fog.ambient_color;118 let ambient_intensity = volumetric_fog.ambient_intensity;119 let step_count = volumetric_fog.step_count;120 let bounding_radius = volumetric_fog.bounding_radius;121 let absorption = volumetric_fog.absorption;122 let scattering = volumetric_fog.scattering;123 let density_factor = volumetric_fog.density_factor;124 let density_texture_offset = volumetric_fog.density_texture_offset;125 let light_tint = volumetric_fog.light_tint;126 let light_intensity = volumetric_fog.light_intensity;127 let jitter_strength = volumetric_fog.jitter_strength;129 // Unpack the view.130 let exposure = view.exposure;132 // Sample the depth to put an upper bound on the length of the ray (as we133 // shouldn't trace through solid objects). If this is multisample, just use134 // sample 0; this is approximate but good enough.135 let frag_coord = position;136 let ndc_end_depth_from_buffer = textureLoad(depth_texture, vec2<i32>(frag_coord.xy), 0);137 let view_end_depth_from_buffer = -position_ndc_to_view(138 frag_coord_to_ndc(vec4(position.xy, ndc_end_depth_from_buffer, 1.0))).z;140 // Calculate the start position of the ray. Since we're only rendering front141 // faces of the AABB, this is the current fragment's depth.142 let view_start_pos = position_ndc_to_view(frag_coord_to_ndc(frag_coord));144 // Calculate the end position of the ray. This requires us to raytrace the145 // three back faces of the AABB to find the one that our ray intersects.146 var end_depth_view = 0.0;147 for (var plane_index = 0; plane_index < 3; plane_index += 1) {148 let plane = volumetric_fog.far_planes[plane_index];149 let other_plane_a = volumetric_fog.far_planes[(plane_index + 1) % 3];150 let other_plane_b = volumetric_fog.far_planes[(plane_index + 2) % 3];152 // Calculate the intersection of the ray and the plane. The ray must153 // intersect in front of us (t > 0).154 let t = -plane.w / dot(plane.xyz, view_start_pos.xyz);155 if (t < 0.0) {156 continue;157 }158 let hit_pos = view_start_pos.xyz * t;160 // The intersection point must be in front of the other backfaces.161 let other_sides = vec2(162 dot(vec4(hit_pos, 1.0), other_plane_a) >= 0.0,163 dot(vec4(hit_pos, 1.0), other_plane_b) >= 0.0164 );166 // If those tests pass, we found our backface.167 if (all(other_sides)) {168 end_depth_view = -hit_pos.z;169 break;170 }171 }173 // Starting at the end depth, which we got above, figure out how long the174 // ray we want to trace is and the length of each increment.175 end_depth_view = min(end_depth_view, view_end_depth_from_buffer);177 // We assume world and view have the same scale here.178 let start_depth_view = -depth_ndc_to_view_z(frag_coord.z);180 let ray_length_view = max(0.0, end_depth_view - start_depth_view);181 // If the end is behind the start of the first opaque pixel, then we know it182 // is occluded, and we don't need to render it183 if (ray_length_view == 0.0) {184 return vec4(0.0, 0.0, 0.0, 0.0);185 }186 let inv_step_count = 1.0 / f32(step_count);187 let step_size_world = ray_length_view * inv_step_count;189 let directional_light_count = lights.n_directional_lights;191 // Calculate the ray origin (`Ro`) and the ray direction (`Rd`) in NDC,192 // view, and world coordinates.193 let Rd_ndc = vec3(frag_coord_to_ndc(position).xy, 1.0);194 let Rd_view = normalize(position_ndc_to_view(Rd_ndc));195 var Ro_world = position_view_to_world(view_start_pos.xyz);196 let Rd_world = normalize(position_ndc_to_world(Rd_ndc) - view.world_position);198 // Offset by jitter.199 let jitter = interleaved_gradient_noise(position.xy, globals.frame_count) * jitter_strength;200 Ro_world += Rd_world * jitter;202 // Use Beer's law [1] [2] to calculate the maximum amount of light that each203 // directional light could contribute, and modulate that value by the light204 // tint and fog color. (The actual value will in turn be modulated by the205 // phase according to the Henyey-Greenstein formula.)206 //207 // [1]: https://www.scratchapixel.com/lessons/3d-basic-rendering/volume-rendering-for-developers/intro-volume-rendering.html208 //209 // [2]: https://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law211 // Use Beer's law again to accumulate the ambient light all along the path.212 var accumulated_color = exp(-ray_length_view * (absorption + scattering)) * ambient_color *213 ambient_intensity;215 // This is the amount of the background that shows through. We're actually216 // going to recompute this over and over again for each directional light,217 // coming up with the same values each time.218 var background_alpha = 1.0;220 // If we have a density texture, transform to its local space.221#ifdef DENSITY_TEXTURE222 let Ro_uvw = (uvw_from_world * vec4(Ro_world, 1.0)).xyz;223 let Rd_step_uvw = mat3x3(uvw_from_world[0].xyz, uvw_from_world[1].xyz, uvw_from_world[2].xyz) *224 (Rd_world * step_size_world);225#endif // DENSITY_TEXTURE227 for (var light_index = 0u; light_index < directional_light_count; light_index += 1u) {228 // Volumetric lights are all sorted first, so the first time we come to229 // a non-volumetric light, we know we've seen them all.230 let light = &lights.directional_lights[light_index];231 if (((*light).flags & DIRECTIONAL_LIGHT_FLAGS_VOLUMETRIC_BIT) == 0) {232 break;233 }235 let L = (*light).direction_to_light.xyz;237 // Offset the depth value by the bias.238 let depth_offset = (*light).shadow_depth_bias * L;240 // Compute phase, which determines the fraction of light that's241 // scattered toward the camera instead of away from it.242 let neg_LdotV = dot(normalize(L), Rd_world);243 let phase = henyey_greenstein(neg_LdotV);245 // Reset `background_alpha` for a new raymarch.246 background_alpha = 1.0;248 // Start raymarching.249 for (var step = 0u; step < step_count; step += 1u) {250 // As an optimization, break if we've gotten too dark.251 if (background_alpha < 0.001) {252 break;253 }255 // Calculate where we are in the ray.256 let P_world = Ro_world + Rd_world * f32(step) * step_size_world;257 let P_view = view_start_pos + Rd_view * f32(step) * step_size_world;259 var density = density_factor;260#ifdef DENSITY_TEXTURE261 // Take the density texture into account, if there is one.262 //263 // The uvs should never go outside the (0, 0, 0) to (1, 1, 1) box,264 // but sometimes due to floating point error they can. Handle this265 // case.266 let P_uvw = Ro_uvw + Rd_step_uvw * f32(step);267 if (all(P_uvw >= vec3(0.0)) && all(P_uvw <= vec3(1.0))) {268 density *= textureSampleLevel(density_texture, density_sampler, P_uvw + density_texture_offset, 0.0).r;269 } else {270 density = 0.0;271 }272#endif // DENSITY_TEXTURE274 // Calculate absorption (amount of light absorbed by the fog) and275 // out-scattering (amount of light the fog scattered away).276 let sample_attenuation = exp(-step_size_world * density * (absorption + scattering));278 // Process absorption and out-scattering.279 background_alpha *= sample_attenuation;281 // Compute in-scattering (amount of light other fog particles282 // scattered into this ray). This is where any directional light is283 // scattered in.285 // Prepare to sample the shadow map.286 let cascade_index = get_cascade_index(light_index, P_view.z);287 let light_local = world_to_directional_light_local(288 light_index,289 cascade_index,290 vec4(P_world + depth_offset, 1.0)291 );293 // If we're outside the shadow map entirely, local light attenuation294 // is zero.295 var local_light_attenuation = f32(light_local.w != 0.0);297 // Otherwise, sample the shadow map to determine whether, and by how298 // much, this sample is in the light.299 if (local_light_attenuation != 0.0) {300 let cascade = &(*light).cascades[cascade_index];301 let array_index = i32((*light).depth_texture_base_index + cascade_index);302 local_light_attenuation =303 sample_shadow_map_hardware(light_local.xy, light_local.z, array_index);304 }306 if (local_light_attenuation != 0.0) {307 let light_attenuation = exp(-density * bounding_radius * (absorption + scattering));308 var light_factors_per_step = fog_color * light_tint * light_attenuation *309 scattering * density * step_size_world * light_intensity * exposure;311#ifdef ATMOSPHERE312 // attenuate by atmospheric scattering313 let P = P_world + depth_offset;314 let P_as = (atmosphere.world_to_atmosphere * vec4(P, 1.0)).xyz;315 let P_clamped = clamp_to_surface(atmosphere, P_as);316 let r = length(P_clamped);317 let local_up = normalize(P_clamped);318 let mu_light = dot(L, local_up);320 let transmittance = sample_transmittance_lut(r, mu_light);321 let sun_visibility = calculate_visible_sun_ratio(atmosphere, r, mu_light, (*light).sun_disk_angular_size);322 light_factors_per_step *= transmittance * sun_visibility;323#endif325 // Modulate the factor we calculated above by the phase, fog color,326 // light color, light tint.327 let light_color_per_step = (*light).color.rgb * phase * light_factors_per_step;329 // Accumulate the light.330 accumulated_color += light_color_per_step * local_light_attenuation *331 background_alpha;332 }333 }334 }336 // Point lights and Spot lights337 let is_orthographic = view.clip_from_view[3].w == 1.0;339 // Reset `background_alpha` for a new raymarch.340 background_alpha = 1.0;342 // Start raymarching.343 for (var step = 0u; step < step_count; step += 1u) {344 // As an optimization, break if we've gotten too dark.345 if (background_alpha < 0.001) {346 break;347 }349 // Calculate where we are in the ray.350 let P_world = Ro_world + Rd_world * f32(step) * step_size_world;351 let P_view = view_start_pos + Rd_view * f32(step) * step_size_world;353 var density = density_factor;354#ifdef DENSITY_TEXTURE355 // Take the density texture into account, if there is one.356 //357 // The uvs should never go outside the (0, 0, 0) to (1, 1, 1) box,358 // but sometimes due to floating point error they can. Handle this359 // case.360 let P_uvw = Ro_uvw + Rd_step_uvw * f32(step);361 if (all(P_uvw >= vec3(0.0)) && all(P_uvw <= vec3(1.0))) {362 density *= textureSampleLevel(density_texture, density_sampler, P_uvw + density_texture_offset, 0.0).r;363 } else {364 density = 0.0;365 }366#endif // DENSITY_TEXTURE368 var sample_color = vec3(0.0);370 let cluster_index = clustering::view_fragment_cluster_index(frag_coord.xy, P_view.z, is_orthographic);371 var clusterable_object_index_ranges = clustering::unpack_clusterable_object_index_ranges(cluster_index);372 for (var i: u32 = clusterable_object_index_ranges.first_point_light_index_offset;373 i < clusterable_object_index_ranges.first_reflection_probe_index_offset;374 i = i + 1u)375 {376 let light_id = clustering::get_clusterable_object_id(i);377 let light = &clustered_lights.data[light_id];378 if (((*light).flags & POINT_LIGHT_FLAGS_VOLUMETRIC_BIT) == 0) {379 continue;380 }382 let light_to_frag = (*light).position_radius.xyz - P_world;383 let V = Rd_world;384 let L = normalize(light_to_frag);385 let distance_square = dot(light_to_frag, light_to_frag);386 let distance_atten = getDistanceAttenuation(distance_square, (*light).color_inverse_square_range.w);387 var local_light_attenuation = distance_atten;388 if (i < clusterable_object_index_ranges.first_spot_light_index_offset) {389 var shadow: f32 = 1.0;390 if (((*light).flags & POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT) != 0u) {391 shadow = fetch_point_shadow_without_normal(light_id, vec4(P_world, 1.0), position.xy);392 }393 local_light_attenuation *= shadow;394 } else {395 // spot light attenuation396 // reconstruct spot dir from x/z and y-direction flag397 var spot_dir = vec3<f32>((*light).light_custom_data.x, 0.0, (*light).light_custom_data.y);398 spot_dir.y = sqrt(max(0.0, 1.0 - spot_dir.x * spot_dir.x - spot_dir.z * spot_dir.z));399 if ((*light).flags & POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE) != 0u {400 spot_dir.y = -spot_dir.y;401 }403 // calculate attenuation based on filament formula https://google.github.io/filament/Filament.md.html#listing_glslpunctuallight404 // spot_scale and spot_offset have been precomputed405 // note we normalize here to get "l" from the filament listing. spot_dir is already normalized406 let cd = dot(-spot_dir, normalize(light_to_frag));407 let attenuation = saturate(cd * (*light).light_custom_data.z + (*light).light_custom_data.w);408 let spot_attenuation = attenuation * attenuation;410 var shadow: f32 = 1.0;411 if (((*light).flags & POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT) != 0u) {412 shadow = fetch_spot_shadow_without_normal(light_id, vec4(P_world, 1.0), position.xy);413 }414 local_light_attenuation *= spot_attenuation * shadow;415 }417 let light_attenuation = exp(-density * bounding_radius * (absorption + scattering));418 let light_factors_per_step = fog_color * light_tint * light_attenuation *419 scattering * density * step_size_world * light_intensity * exposure;421 // Modulate the factor we calculated above by the phase, fog color,422 // light color, light tint.423 let light_color_per_step = (*light).color_inverse_square_range.rgb * light_factors_per_step;425 // Accumulate the light.426 sample_color += light_color_per_step * local_light_attenuation;427 }429 // Calculate absorption (amount of light absorbed by the fog) and430 // out-scattering (amount of light the fog scattered away).431 let sample_attenuation = exp(-step_size_world * density * (absorption + scattering));433 // Process absorption and out-scattering.434 background_alpha *= sample_attenuation;435 accumulated_color += sample_color * background_alpha;436 }438 // We're done! Return the color with alpha so it can be blended onto the439 // render target.440 return vec4(accumulated_color, 1.0 - background_alpha);441}443fn fetch_point_shadow_without_normal(light_id: u32, frag_position: vec4<f32>, frag_coord_xy: vec2<f32>) -> f32 {444 let light = &clustered_lights.data[light_id];446 // because the shadow maps align with the axes and the frustum planes are at 45 degrees447 // we can get the worldspace depth by taking the largest absolute axis448 let surface_to_light = (*light).position_radius.xyz - frag_position.xyz;449 let surface_to_light_abs = abs(surface_to_light);450 let distance_to_light = max(surface_to_light_abs.x, max(surface_to_light_abs.y, surface_to_light_abs.z));452 // The normal bias here is already scaled by the texel size at 1 world unit from the light.453 // The texel size increases proportionally with distance from the light so multiplying by454 // distance to light scales the normal bias to the texel size at the fragment distance.455 let depth_offset = (*light).shadow_depth_bias * normalize(surface_to_light.xyz);456 let offset_position = frag_position.xyz + depth_offset;458 // similar largest-absolute-axis trick as above, but now with the offset fragment position459 let frag_ls = offset_position.xyz - (*light).position_radius.xyz;460 let abs_position_ls = abs(frag_ls);461 let major_axis_magnitude = max(abs_position_ls.x, max(abs_position_ls.y, abs_position_ls.z));463 // NOTE: These simplifications come from multiplying:464 // projection * vec4(0, 0, -major_axis_magnitude, 1.0)465 // and keeping only the terms that have any impact on the depth.466 // Projection-agnostic approach:467 let zw = -major_axis_magnitude * (*light).light_custom_data.xy + (*light).light_custom_data.zw;468 let depth = zw.x / zw.y;470 // Do the lookup, using HW PCF and comparison. Cubemaps assume a left-handed coordinate space,471 // so we have to flip the z-axis when sampling.472 let flip_z = vec3(1.0, 1.0, -1.0);473 return sample_shadow_cubemap(frag_ls * flip_z, distance_to_light, depth, light_id, frag_coord_xy);474}476fn fetch_spot_shadow_without_normal(light_id: u32, frag_position: vec4<f32>, frag_coord_xy: vec2<f32>) -> f32 {477 let light = &clustered_lights.data[light_id];479 let surface_to_light = (*light).position_radius.xyz - frag_position.xyz;481 // construct the light view matrix482 var spot_dir = vec3<f32>((*light).light_custom_data.x, 0.0, (*light).light_custom_data.y);483 // reconstruct spot dir from x/z and y-direction flag484 spot_dir.y = sqrt(max(0.0, 1.0 - spot_dir.x * spot_dir.x - spot_dir.z * spot_dir.z));485 if (((*light).flags & POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE) != 0u) {486 spot_dir.y = -spot_dir.y;487 }489 // view matrix z_axis is the reverse of transform.forward()490 let fwd = -spot_dir;491 let offset_position =492 -surface_to_light493 + ((*light).shadow_depth_bias * normalize(surface_to_light));495 // the construction of the up and right vectors needs to precisely mirror the code496 // in render/light.rs:spot_light_view_matrix497 var sign = -1.0;498 if (fwd.z >= 0.0) {499 sign = 1.0;500 }501 let a = -1.0 / (fwd.z + sign);502 let b = fwd.x * fwd.y * a;503 let up_dir = vec3<f32>(1.0 + sign * fwd.x * fwd.x * a, sign * b, -sign * fwd.x);504 let right_dir = vec3<f32>(-b, -sign - fwd.y * fwd.y * a, fwd.y);505 let light_inv_rot = mat3x3<f32>(right_dir, up_dir, fwd);507 // because the matrix is a pure rotation matrix, the inverse is just the transpose, and to calculate508 // the product of the transpose with a vector we can just post-multiply instead of pre-multiplying.509 // this allows us to keep the matrix construction code identical between CPU and GPU.510 let projected_position = offset_position * light_inv_rot;512 // divide xy by perspective matrix "f" and by -projected.z (projected.z is -projection matrix's w)513 // to get ndc coordinates514 let f_div_minus_z = 1.0 / ((*light).spot_light_tan_angle * -projected_position.z);515 let shadow_xy_ndc = projected_position.xy * f_div_minus_z;516 // convert to uv coordinates517 let shadow_uv = shadow_xy_ndc * vec2<f32>(0.5, -0.5) + vec2<f32>(0.5, 0.5);519 // 0.1 must match POINT_LIGHT_NEAR_Z520 let depth = 0.1 / -projected_position.z;522 return sample_shadow_map(523 shadow_uv,524 depth,525 i32(light_id) + lights.spot_light_shadowmap_offset,526 frag_coord_xy,527 SPOT_SHADOW_TEXEL_SIZE528 );529}531#ifdef ATMOSPHERE532fn sample_transmittance_lut(r: f32, mu: f32) -> vec3<f32> {533 let uv = transmittance_lut_r_mu_to_uv(atmosphere, r, mu);534 return textureSampleLevel(535 atmosphere_transmittance_texture,536 atmosphere_transmittance_sampler, uv, 0.0).rgb;537}538#endif // ATMOSPHERE
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