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,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, clusterable_objects, 24 atmosphere_data, 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 ClusterableObject32}33#import bevy_pbr::shadow_sampling::{34 sample_shadow_map_hardware,35 sample_shadow_cubemap,36 sample_shadow_map,37 SPOT_SHADOW_TEXEL_SIZE38}39#import bevy_pbr::shadows::{get_cascade_index, world_to_directional_light_local}40#import bevy_pbr::utils::interleaved_gradient_noise41#import bevy_pbr::view_transformations::{42 depth_ndc_to_view_z,43 frag_coord_to_ndc,44 position_ndc_to_view,45 position_ndc_to_world,46 position_view_to_world47}48#import bevy_pbr::clustered_forward as clustering49#import bevy_pbr::lighting::getDistanceAttenuation;51// The GPU version of [`VolumetricFog`]. See the comments in52// `volumetric_fog/mod.rs` for descriptions of the fields here.53struct VolumetricFog {54 clip_from_local: mat4x4<f32>,55 uvw_from_world: mat4x4<f32>,56 far_planes: array<vec4<f32>, 3>,57 fog_color: vec3<f32>,58 light_tint: vec3<f32>,59 ambient_color: vec3<f32>,60 ambient_intensity: f32,61 step_count: u32,62 bounding_radius: f32,63 absorption: f32,64 scattering: f32,65 density_factor: f32,66 density_texture_offset: vec3<f32>,67 scattering_asymmetry: f32,68 light_intensity: f32,69 jitter_strength: f32,70}72@group(1) @binding(0) var<uniform> volumetric_fog: VolumetricFog;74#ifdef MULTISAMPLED75@group(1) @binding(1) var depth_texture: texture_depth_multisampled_2d;76#else77@group(1) @binding(1) var depth_texture: texture_depth_2d;78#endif80#ifdef DENSITY_TEXTURE81@group(1) @binding(2) var density_texture: texture_3d<f32>;82@group(1) @binding(3) var density_sampler: sampler;83#endif // DENSITY_TEXTURE85// 1 / (4π)86const FRAC_4_PI: f32 = 0.07957747154594767;88struct Vertex {89 @builtin(instance_index) instance_index: u32,90 @location(0) position: vec3<f32>,91}93@vertex94fn vertex(vertex: Vertex) -> @builtin(position) vec4<f32> {95 return volumetric_fog.clip_from_local * vec4<f32>(vertex.position, 1.0);96}98// The common Henyey-Greenstein asymmetric phase function [1] [2].99//100// This determines how much light goes toward the viewer as opposed to away from101// the viewer. From a visual point of view, it controls how the light shafts102// appear and disappear as the camera looks at the light source.103//104// [1]: https://www.scratchapixel.com/lessons/3d-basic-rendering/volume-rendering-for-developers/ray-marching-get-it-right.html105//106// [2]: https://www.pbr-book.org/4ed/Volume_Scattering/Phase_Functions#TheHenyeyndashGreensteinPhaseFunction107fn henyey_greenstein(neg_LdotV: f32) -> f32 {108 let g = volumetric_fog.scattering_asymmetry;109 let denom = 1.0 + g * g - 2.0 * g * neg_LdotV;110 return FRAC_4_PI * (1.0 - g * g) / (denom * sqrt(denom));111}113@fragment114fn fragment(@builtin(position) position: vec4<f32>) -> @location(0) vec4<f32> {115 // Unpack the `volumetric_fog` settings.116 let uvw_from_world = volumetric_fog.uvw_from_world;117 let fog_color = volumetric_fog.fog_color;118 let ambient_color = volumetric_fog.ambient_color;119 let ambient_intensity = volumetric_fog.ambient_intensity;120 let step_count = volumetric_fog.step_count;121 let bounding_radius = volumetric_fog.bounding_radius;122 let absorption = volumetric_fog.absorption;123 let scattering = volumetric_fog.scattering;124 let density_factor = volumetric_fog.density_factor;125 let density_texture_offset = volumetric_fog.density_texture_offset;126 let light_tint = volumetric_fog.light_tint;127 let light_intensity = volumetric_fog.light_intensity;128 let jitter_strength = volumetric_fog.jitter_strength;130 // Unpack the view.131 let exposure = view.exposure;133 // Sample the depth to put an upper bound on the length of the ray (as we134 // shouldn't trace through solid objects). If this is multisample, just use135 // sample 0; this is approximate but good enough.136 let frag_coord = position;137 let ndc_end_depth_from_buffer = textureLoad(depth_texture, vec2<i32>(frag_coord.xy), 0);138 let view_end_depth_from_buffer = -position_ndc_to_view(139 frag_coord_to_ndc(vec4(position.xy, ndc_end_depth_from_buffer, 1.0))).z;141 // Calculate the start position of the ray. Since we're only rendering front142 // faces of the AABB, this is the current fragment's depth.143 let view_start_pos = position_ndc_to_view(frag_coord_to_ndc(frag_coord));145 // Calculate the end position of the ray. This requires us to raytrace the146 // three back faces of the AABB to find the one that our ray intersects.147 var end_depth_view = 0.0;148 for (var plane_index = 0; plane_index < 3; plane_index += 1) {149 let plane = volumetric_fog.far_planes[plane_index];150 let other_plane_a = volumetric_fog.far_planes[(plane_index + 1) % 3];151 let other_plane_b = volumetric_fog.far_planes[(plane_index + 2) % 3];153 // Calculate the intersection of the ray and the plane. The ray must154 // intersect in front of us (t > 0).155 let t = -plane.w / dot(plane.xyz, view_start_pos.xyz);156 if (t < 0.0) {157 continue;158 }159 let hit_pos = view_start_pos.xyz * t;161 // The intersection point must be in front of the other backfaces.162 let other_sides = vec2(163 dot(vec4(hit_pos, 1.0), other_plane_a) >= 0.0,164 dot(vec4(hit_pos, 1.0), other_plane_b) >= 0.0165 );167 // If those tests pass, we found our backface.168 if (all(other_sides)) {169 end_depth_view = -hit_pos.z;170 break;171 }172 }174 // Starting at the end depth, which we got above, figure out how long the175 // ray we want to trace is and the length of each increment.176 end_depth_view = min(end_depth_view, view_end_depth_from_buffer);178 // We assume world and view have the same scale here.179 let start_depth_view = -depth_ndc_to_view_z(frag_coord.z);180 let ray_length_view = abs(end_depth_view - start_depth_view);181 let inv_step_count = 1.0 / f32(step_count);182 let step_size_world = ray_length_view * inv_step_count;184 let directional_light_count = lights.n_directional_lights;186 // Calculate the ray origin (`Ro`) and the ray direction (`Rd`) in NDC,187 // view, and world coordinates.188 let Rd_ndc = vec3(frag_coord_to_ndc(position).xy, 1.0);189 let Rd_view = normalize(position_ndc_to_view(Rd_ndc));190 var Ro_world = position_view_to_world(view_start_pos.xyz);191 let Rd_world = normalize(position_ndc_to_world(Rd_ndc) - view.world_position);193 // Offset by jitter.194 let jitter = interleaved_gradient_noise(position.xy, globals.frame_count) * jitter_strength;195 Ro_world += Rd_world * jitter;197 // Use Beer's law [1] [2] to calculate the maximum amount of light that each198 // directional light could contribute, and modulate that value by the light199 // tint and fog color. (The actual value will in turn be modulated by the200 // phase according to the Henyey-Greenstein formula.)201 //202 // [1]: https://www.scratchapixel.com/lessons/3d-basic-rendering/volume-rendering-for-developers/intro-volume-rendering.html203 //204 // [2]: https://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law206 // Use Beer's law again to accumulate the ambient light all along the path.207 var accumulated_color = exp(-ray_length_view * (absorption + scattering)) * ambient_color *208 ambient_intensity;210 // This is the amount of the background that shows through. We're actually211 // going to recompute this over and over again for each directional light,212 // coming up with the same values each time.213 var background_alpha = 1.0;215 // If we have a density texture, transform to its local space.216#ifdef DENSITY_TEXTURE217 let Ro_uvw = (uvw_from_world * vec4(Ro_world, 1.0)).xyz;218 let Rd_step_uvw = mat3x3(uvw_from_world[0].xyz, uvw_from_world[1].xyz, uvw_from_world[2].xyz) *219 (Rd_world * step_size_world);220#endif // DENSITY_TEXTURE222 for (var light_index = 0u; light_index < directional_light_count; light_index += 1u) {223 // Volumetric lights are all sorted first, so the first time we come to224 // a non-volumetric light, we know we've seen them all.225 let light = &lights.directional_lights[light_index];226 if (((*light).flags & DIRECTIONAL_LIGHT_FLAGS_VOLUMETRIC_BIT) == 0) {227 break;228 }230 let L = (*light).direction_to_light.xyz;232 // Offset the depth value by the bias.233 let depth_offset = (*light).shadow_depth_bias * L;235 // Compute phase, which determines the fraction of light that's236 // scattered toward the camera instead of away from it.237 let neg_LdotV = dot(normalize(L), Rd_world);238 let phase = henyey_greenstein(neg_LdotV);240 // Reset `background_alpha` for a new raymarch.241 background_alpha = 1.0;243 // Start raymarching.244 for (var step = 0u; step < step_count; step += 1u) {245 // As an optimization, break if we've gotten too dark.246 if (background_alpha < 0.001) {247 break;248 }250 // Calculate where we are in the ray.251 let P_world = Ro_world + Rd_world * f32(step) * step_size_world;252 let P_view = Rd_view * f32(step) * step_size_world;254 var density = density_factor;255#ifdef DENSITY_TEXTURE256 // Take the density texture into account, if there is one.257 //258 // The uvs should never go outside the (0, 0, 0) to (1, 1, 1) box,259 // but sometimes due to floating point error they can. Handle this260 // case.261 let P_uvw = Ro_uvw + Rd_step_uvw * f32(step);262 if (all(P_uvw >= vec3(0.0)) && all(P_uvw <= vec3(1.0))) {263 density *= textureSampleLevel(density_texture, density_sampler, P_uvw + density_texture_offset, 0.0).r;264 } else {265 density = 0.0;266 }267#endif // DENSITY_TEXTURE269 // Calculate absorption (amount of light absorbed by the fog) and270 // out-scattering (amount of light the fog scattered away).271 let sample_attenuation = exp(-step_size_world * density * (absorption + scattering));273 // Process absorption and out-scattering.274 background_alpha *= sample_attenuation;276 // Compute in-scattering (amount of light other fog particles277 // scattered into this ray). This is where any directional light is278 // scattered in.280 // Prepare to sample the shadow map.281 let cascade_index = get_cascade_index(light_index, P_view.z);282 let light_local = world_to_directional_light_local(283 light_index,284 cascade_index,285 vec4(P_world + depth_offset, 1.0)286 );288 // If we're outside the shadow map entirely, local light attenuation289 // is zero.290 var local_light_attenuation = f32(light_local.w != 0.0);292 // Otherwise, sample the shadow map to determine whether, and by how293 // much, this sample is in the light.294 if (local_light_attenuation != 0.0) {295 let cascade = &(*light).cascades[cascade_index];296 let array_index = i32((*light).depth_texture_base_index + cascade_index);297 local_light_attenuation =298 sample_shadow_map_hardware(light_local.xy, light_local.z, array_index);299 }301 if (local_light_attenuation != 0.0) {302 let light_attenuation = exp(-density * bounding_radius * (absorption + scattering));303 var light_factors_per_step = fog_color * light_tint * light_attenuation *304 scattering * density * step_size_world * light_intensity * exposure;306#ifdef ATMOSPHERE307 // attenuate by atmospheric scattering308 let P = P_world + depth_offset;309 let P_scaled = P * vec3(atmosphere_data.settings.scene_units_to_m);310 let O = vec3(0.0, atmosphere_data.atmosphere.bottom_radius, 0.0);311 let P_as = P_scaled + O;312 let r = length(P_as);313 let local_up = normalize(P_as);314 let mu_light = dot(L, local_up);316 let transmittance = sample_transmittance_lut(r, mu_light);317 let sun_visibility = calculate_visible_sun_ratio(atmosphere_data.atmosphere, r, mu_light, (*light).sun_disk_angular_size);318 light_factors_per_step *= transmittance * sun_visibility;319#endif321 // Modulate the factor we calculated above by the phase, fog color,322 // light color, light tint.323 let light_color_per_step = (*light).color.rgb * phase * light_factors_per_step;325 // Accumulate the light.326 accumulated_color += light_color_per_step * local_light_attenuation *327 background_alpha;328 }329 }330 }332 // Point lights and Spot lights333 let view_z = view_start_pos.z;334 let is_orthographic = view.clip_from_view[3].w == 1.0;335 let cluster_index = clustering::fragment_cluster_index(frag_coord.xy, view_z, is_orthographic);336 var clusterable_object_index_ranges =337 clustering::unpack_clusterable_object_index_ranges(cluster_index);338 for (var i: u32 = clusterable_object_index_ranges.first_point_light_index_offset;339 i < clusterable_object_index_ranges.first_reflection_probe_index_offset;340 i = i + 1u) {341 let light_id = clustering::get_clusterable_object_id(i);342 let light = &clusterable_objects.data[light_id];343 if (((*light).flags & POINT_LIGHT_FLAGS_VOLUMETRIC_BIT) == 0) {344 continue;345 }347 // Reset `background_alpha` for a new raymarch.348 background_alpha = 1.0;350 // Start raymarching.351 for (var step = 0u; step < step_count; step += 1u) {352 // As an optimization, break if we've gotten too dark.353 if (background_alpha < 0.001) {354 break;355 }357 // Calculate where we are in the ray.358 let P_world = Ro_world + Rd_world * f32(step) * step_size_world;359 let P_view = Rd_view * f32(step) * step_size_world;361 var density = density_factor;363 let light_to_frag = (*light).position_radius.xyz - P_world;364 let V = Rd_world;365 let L = normalize(light_to_frag);366 let distance_square = dot(light_to_frag, light_to_frag);367 let distance_atten = getDistanceAttenuation(distance_square, (*light).color_inverse_square_range.w);368 var local_light_attenuation = distance_atten;369 if (i < clusterable_object_index_ranges.first_spot_light_index_offset) {370 var shadow: f32 = 1.0;371 if (((*light).flags & POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT) != 0u) {372 shadow = fetch_point_shadow_without_normal(light_id, vec4(P_world, 1.0));373 }374 local_light_attenuation *= shadow;375 } else {376 // spot light attenuation377 // reconstruct spot dir from x/z and y-direction flag378 var spot_dir = vec3<f32>((*light).light_custom_data.x, 0.0, (*light).light_custom_data.y);379 spot_dir.y = sqrt(max(0.0, 1.0 - spot_dir.x * spot_dir.x - spot_dir.z * spot_dir.z));380 if ((*light).flags & POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE) != 0u {381 spot_dir.y = -spot_dir.y;382 }383 let light_to_frag = (*light).position_radius.xyz - P_world;385 // calculate attenuation based on filament formula https://google.github.io/filament/Filament.html#listing_glslpunctuallight386 // spot_scale and spot_offset have been precomputed387 // note we normalize here to get "l" from the filament listing. spot_dir is already normalized388 let cd = dot(-spot_dir, normalize(light_to_frag));389 let attenuation = saturate(cd * (*light).light_custom_data.z + (*light).light_custom_data.w);390 let spot_attenuation = attenuation * attenuation;392 var shadow: f32 = 1.0;393 if (((*light).flags & POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT) != 0u) {394 shadow = fetch_spot_shadow_without_normal(light_id, vec4(P_world, 1.0));395 }396 local_light_attenuation *= spot_attenuation * shadow;397 }399 // Calculate absorption (amount of light absorbed by the fog) and400 // out-scattering (amount of light the fog scattered away).401 let sample_attenuation = exp(-step_size_world * density * (absorption + scattering));403 // Process absorption and out-scattering.404 background_alpha *= sample_attenuation;406 let light_attenuation = exp(-density * bounding_radius * (absorption + scattering));407 let light_factors_per_step = fog_color * light_tint * light_attenuation *408 scattering * density * step_size_world * light_intensity * exposure;410 // Modulate the factor we calculated above by the phase, fog color,411 // light color, light tint.412 let light_color_per_step = (*light).color_inverse_square_range.rgb * light_factors_per_step;414 // Accumulate the light.415 accumulated_color += light_color_per_step * local_light_attenuation *416 background_alpha;417 }418 }420 // We're done! Return the color with alpha so it can be blended onto the421 // render target.422 return vec4(accumulated_color, 1.0 - background_alpha);423}425fn fetch_point_shadow_without_normal(light_id: u32, frag_position: vec4<f32>) -> f32 {426 let light = &clusterable_objects.data[light_id];428 // because the shadow maps align with the axes and the frustum planes are at 45 degrees429 // we can get the worldspace depth by taking the largest absolute axis430 let surface_to_light = (*light).position_radius.xyz - frag_position.xyz;431 let surface_to_light_abs = abs(surface_to_light);432 let distance_to_light = max(surface_to_light_abs.x, max(surface_to_light_abs.y, surface_to_light_abs.z));434 // The normal bias here is already scaled by the texel size at 1 world unit from the light.435 // The texel size increases proportionally with distance from the light so multiplying by436 // distance to light scales the normal bias to the texel size at the fragment distance.437 let depth_offset = (*light).shadow_depth_bias * normalize(surface_to_light.xyz);438 let offset_position = frag_position.xyz + depth_offset;440 // similar largest-absolute-axis trick as above, but now with the offset fragment position441 let frag_ls = offset_position.xyz - (*light).position_radius.xyz ;442 let abs_position_ls = abs(frag_ls);443 let major_axis_magnitude = max(abs_position_ls.x, max(abs_position_ls.y, abs_position_ls.z));445 // NOTE: These simplifications come from multiplying:446 // projection * vec4(0, 0, -major_axis_magnitude, 1.0)447 // and keeping only the terms that have any impact on the depth.448 // Projection-agnostic approach:449 let zw = -major_axis_magnitude * (*light).light_custom_data.xy + (*light).light_custom_data.zw;450 let depth = zw.x / zw.y;452 // Do the lookup, using HW PCF and comparison. Cubemaps assume a left-handed coordinate space,453 // so we have to flip the z-axis when sampling.454 let flip_z = vec3(1.0, 1.0, -1.0);455 return sample_shadow_cubemap(frag_ls * flip_z, distance_to_light, depth, light_id);456}458fn fetch_spot_shadow_without_normal(light_id: u32, frag_position: vec4<f32>) -> f32 {459 let light = &clusterable_objects.data[light_id];461 let surface_to_light = (*light).position_radius.xyz - frag_position.xyz;463 // construct the light view matrix464 var spot_dir = vec3<f32>((*light).light_custom_data.x, 0.0, (*light).light_custom_data.y);465 // reconstruct spot dir from x/z and y-direction flag466 spot_dir.y = sqrt(max(0.0, 1.0 - spot_dir.x * spot_dir.x - spot_dir.z * spot_dir.z));467 if (((*light).flags & POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE) != 0u) {468 spot_dir.y = -spot_dir.y;469 }471 // view matrix z_axis is the reverse of transform.forward()472 let fwd = -spot_dir;473 let offset_position =474 -surface_to_light475 + ((*light).shadow_depth_bias * normalize(surface_to_light));477 // the construction of the up and right vectors needs to precisely mirror the code478 // in render/light.rs:spot_light_view_matrix479 var sign = -1.0;480 if (fwd.z >= 0.0) {481 sign = 1.0;482 }483 let a = -1.0 / (fwd.z + sign);484 let b = fwd.x * fwd.y * a;485 let up_dir = vec3<f32>(1.0 + sign * fwd.x * fwd.x * a, sign * b, -sign * fwd.x);486 let right_dir = vec3<f32>(-b, -sign - fwd.y * fwd.y * a, fwd.y);487 let light_inv_rot = mat3x3<f32>(right_dir, up_dir, fwd);489 // because the matrix is a pure rotation matrix, the inverse is just the transpose, and to calculate490 // the product of the transpose with a vector we can just post-multiply instead of pre-multiplying.491 // this allows us to keep the matrix construction code identical between CPU and GPU.492 let projected_position = offset_position * light_inv_rot;494 // divide xy by perspective matrix "f" and by -projected.z (projected.z is -projection matrix's w)495 // to get ndc coordinates496 let f_div_minus_z = 1.0 / ((*light).spot_light_tan_angle * -projected_position.z);497 let shadow_xy_ndc = projected_position.xy * f_div_minus_z;498 // convert to uv coordinates499 let shadow_uv = shadow_xy_ndc * vec2<f32>(0.5, -0.5) + vec2<f32>(0.5, 0.5);501 // 0.1 must match POINT_LIGHT_NEAR_Z502 let depth = 0.1 / -projected_position.z;504 return sample_shadow_map(505 shadow_uv,506 depth,507 i32(light_id) + lights.spot_light_shadowmap_offset,508 SPOT_SHADOW_TEXEL_SIZE509 );510}512#ifdef ATMOSPHERE513fn sample_transmittance_lut(r: f32, mu: f32) -> vec3<f32> {514 let uv = transmittance_lut_r_mu_to_uv(atmosphere_data.atmosphere, r, mu);515 return textureSampleLevel(516 atmosphere_transmittance_texture, 517 atmosphere_transmittance_sampler, uv, 0.0).rgb;518}519#endif // ATMOSPHERE
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