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);181 let ray_length_view = max(0.0, end_depth_view - start_depth_view);182 // If the end is behind the start of the first opaque pixel, then we know it183 // is occluded, and we don't need to render it184 if (ray_length_view == 0.0) {185 return vec4(0.0, 0.0, 0.0, 0.0);186 }187 let inv_step_count = 1.0 / f32(step_count);188 let step_size_world = ray_length_view * inv_step_count;190 let directional_light_count = lights.n_directional_lights;192 // Calculate the ray origin (`Ro`) and the ray direction (`Rd`) in NDC,193 // view, and world coordinates.194 let Rd_ndc = vec3(frag_coord_to_ndc(position).xy, 1.0);195 let Rd_view = normalize(position_ndc_to_view(Rd_ndc));196 var Ro_world = position_view_to_world(view_start_pos.xyz);197 let Rd_world = normalize(position_ndc_to_world(Rd_ndc) - view.world_position);199 // Offset by jitter.200 let jitter = interleaved_gradient_noise(position.xy, globals.frame_count) * jitter_strength;201 Ro_world += Rd_world * jitter;203 // Use Beer's law [1] [2] to calculate the maximum amount of light that each204 // directional light could contribute, and modulate that value by the light205 // tint and fog color. (The actual value will in turn be modulated by the206 // phase according to the Henyey-Greenstein formula.)207 //208 // [1]: https://www.scratchapixel.com/lessons/3d-basic-rendering/volume-rendering-for-developers/intro-volume-rendering.html209 //210 // [2]: https://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law212 // Use Beer's law again to accumulate the ambient light all along the path.213 var accumulated_color = exp(-ray_length_view * (absorption + scattering)) * ambient_color *214 ambient_intensity;216 // This is the amount of the background that shows through. We're actually217 // going to recompute this over and over again for each directional light,218 // coming up with the same values each time.219 var background_alpha = 1.0;221 // If we have a density texture, transform to its local space.222#ifdef DENSITY_TEXTURE223 let Ro_uvw = (uvw_from_world * vec4(Ro_world, 1.0)).xyz;224 let Rd_step_uvw = mat3x3(uvw_from_world[0].xyz, uvw_from_world[1].xyz, uvw_from_world[2].xyz) *225 (Rd_world * step_size_world);226#endif // DENSITY_TEXTURE228 for (var light_index = 0u; light_index < directional_light_count; light_index += 1u) {229 // Volumetric lights are all sorted first, so the first time we come to230 // a non-volumetric light, we know we've seen them all.231 let light = &lights.directional_lights[light_index];232 if (((*light).flags & DIRECTIONAL_LIGHT_FLAGS_VOLUMETRIC_BIT) == 0) {233 break;234 }236 let L = (*light).direction_to_light.xyz;238 // Offset the depth value by the bias.239 let depth_offset = (*light).shadow_depth_bias * L;241 // Compute phase, which determines the fraction of light that's242 // scattered toward the camera instead of away from it.243 let neg_LdotV = dot(normalize(L), Rd_world);244 let phase = henyey_greenstein(neg_LdotV);246 // Reset `background_alpha` for a new raymarch.247 background_alpha = 1.0;249 // Start raymarching.250 for (var step = 0u; step < step_count; step += 1u) {251 // As an optimization, break if we've gotten too dark.252 if (background_alpha < 0.001) {253 break;254 }256 // Calculate where we are in the ray.257 let P_world = Ro_world + Rd_world * f32(step) * step_size_world;258 let P_view = Rd_view * f32(step) * step_size_world;260 var density = density_factor;261#ifdef DENSITY_TEXTURE262 // Take the density texture into account, if there is one.263 //264 // The uvs should never go outside the (0, 0, 0) to (1, 1, 1) box,265 // but sometimes due to floating point error they can. Handle this266 // case.267 let P_uvw = Ro_uvw + Rd_step_uvw * f32(step);268 if (all(P_uvw >= vec3(0.0)) && all(P_uvw <= vec3(1.0))) {269 density *= textureSampleLevel(density_texture, density_sampler, P_uvw + density_texture_offset, 0.0).r;270 } else {271 density = 0.0;272 }273#endif // DENSITY_TEXTURE275 // Calculate absorption (amount of light absorbed by the fog) and276 // out-scattering (amount of light the fog scattered away).277 let sample_attenuation = exp(-step_size_world * density * (absorption + scattering));279 // Process absorption and out-scattering.280 background_alpha *= sample_attenuation;282 // Compute in-scattering (amount of light other fog particles283 // scattered into this ray). This is where any directional light is284 // scattered in.286 // Prepare to sample the shadow map.287 let cascade_index = get_cascade_index(light_index, P_view.z);288 let light_local = world_to_directional_light_local(289 light_index,290 cascade_index,291 vec4(P_world + depth_offset, 1.0)292 );294 // If we're outside the shadow map entirely, local light attenuation295 // is zero.296 var local_light_attenuation = f32(light_local.w != 0.0);298 // Otherwise, sample the shadow map to determine whether, and by how299 // much, this sample is in the light.300 if (local_light_attenuation != 0.0) {301 let cascade = &(*light).cascades[cascade_index];302 let array_index = i32((*light).depth_texture_base_index + cascade_index);303 local_light_attenuation =304 sample_shadow_map_hardware(light_local.xy, light_local.z, array_index);305 }307 if (local_light_attenuation != 0.0) {308 let light_attenuation = exp(-density * bounding_radius * (absorption + scattering));309 var light_factors_per_step = fog_color * light_tint * light_attenuation *310 scattering * density * step_size_world * light_intensity * exposure;312#ifdef ATMOSPHERE313 // attenuate by atmospheric scattering314 let P = P_world + depth_offset;315 let P_scaled = P * vec3(atmosphere_data.settings.scene_units_to_m);316 let O = vec3(0.0, atmosphere_data.atmosphere.bottom_radius, 0.0);317 let P_as = P_scaled + O;318 let r = length(P_as);319 let local_up = normalize(P_as);320 let mu_light = dot(L, local_up);322 let transmittance = sample_transmittance_lut(r, mu_light);323 let sun_visibility = calculate_visible_sun_ratio(atmosphere_data.atmosphere, r, mu_light, (*light).sun_disk_angular_size);324 light_factors_per_step *= transmittance * sun_visibility;325#endif327 // Modulate the factor we calculated above by the phase, fog color,328 // light color, light tint.329 let light_color_per_step = (*light).color.rgb * phase * light_factors_per_step;331 // Accumulate the light.332 accumulated_color += light_color_per_step * local_light_attenuation *333 background_alpha;334 }335 }336 }338 // Point lights and Spot lights339 let view_z = view_start_pos.z;340 let is_orthographic = view.clip_from_view[3].w == 1.0;341 let cluster_index = clustering::fragment_cluster_index(frag_coord.xy, view_z, is_orthographic);342 var clusterable_object_index_ranges =343 clustering::unpack_clusterable_object_index_ranges(cluster_index);344 for (var i: u32 = clusterable_object_index_ranges.first_point_light_index_offset;345 i < clusterable_object_index_ranges.first_reflection_probe_index_offset;346 i = i + 1u) {347 let light_id = clustering::get_clusterable_object_id(i);348 let light = &clusterable_objects.data[light_id];349 if (((*light).flags & POINT_LIGHT_FLAGS_VOLUMETRIC_BIT) == 0) {350 continue;351 }353 // Reset `background_alpha` for a new raymarch.354 background_alpha = 1.0;356 // Start raymarching.357 for (var step = 0u; step < step_count; step += 1u) {358 // As an optimization, break if we've gotten too dark.359 if (background_alpha < 0.001) {360 break;361 }363 // Calculate where we are in the ray.364 let P_world = Ro_world + Rd_world * f32(step) * step_size_world;365 let P_view = Rd_view * f32(step) * step_size_world;367 var density = density_factor;369 let light_to_frag = (*light).position_radius.xyz - P_world;370 let V = Rd_world;371 let L = normalize(light_to_frag);372 let distance_square = dot(light_to_frag, light_to_frag);373 let distance_atten = getDistanceAttenuation(distance_square, (*light).color_inverse_square_range.w);374 var local_light_attenuation = distance_atten;375 if (i < clusterable_object_index_ranges.first_spot_light_index_offset) {376 var shadow: f32 = 1.0;377 if (((*light).flags & POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT) != 0u) {378 shadow = fetch_point_shadow_without_normal(light_id, vec4(P_world, 1.0));379 }380 local_light_attenuation *= shadow;381 } else {382 // spot light attenuation383 // reconstruct spot dir from x/z and y-direction flag384 var spot_dir = vec3<f32>((*light).light_custom_data.x, 0.0, (*light).light_custom_data.y);385 spot_dir.y = sqrt(max(0.0, 1.0 - spot_dir.x * spot_dir.x - spot_dir.z * spot_dir.z));386 if ((*light).flags & POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE) != 0u {387 spot_dir.y = -spot_dir.y;388 }389 let light_to_frag = (*light).position_radius.xyz - P_world;391 // calculate attenuation based on filament formula https://google.github.io/filament/Filament.html#listing_glslpunctuallight392 // spot_scale and spot_offset have been precomputed393 // note we normalize here to get "l" from the filament listing. spot_dir is already normalized394 let cd = dot(-spot_dir, normalize(light_to_frag));395 let attenuation = saturate(cd * (*light).light_custom_data.z + (*light).light_custom_data.w);396 let spot_attenuation = attenuation * attenuation;398 var shadow: f32 = 1.0;399 if (((*light).flags & POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT) != 0u) {400 shadow = fetch_spot_shadow_without_normal(light_id, vec4(P_world, 1.0));401 }402 local_light_attenuation *= spot_attenuation * shadow;403 }405 // Calculate absorption (amount of light absorbed by the fog) and406 // out-scattering (amount of light the fog scattered away).407 let sample_attenuation = exp(-step_size_world * density * (absorption + scattering));409 // Process absorption and out-scattering.410 background_alpha *= sample_attenuation;412 let light_attenuation = exp(-density * bounding_radius * (absorption + scattering));413 let light_factors_per_step = fog_color * light_tint * light_attenuation *414 scattering * density * step_size_world * light_intensity * exposure;416 // Modulate the factor we calculated above by the phase, fog color,417 // light color, light tint.418 let light_color_per_step = (*light).color_inverse_square_range.rgb * light_factors_per_step;420 // Accumulate the light.421 accumulated_color += light_color_per_step * local_light_attenuation *422 background_alpha;423 }424 }426 // We're done! Return the color with alpha so it can be blended onto the427 // render target.428 return vec4(accumulated_color, 1.0 - background_alpha);429}431fn fetch_point_shadow_without_normal(light_id: u32, frag_position: vec4<f32>) -> f32 {432 let light = &clusterable_objects.data[light_id];434 // because the shadow maps align with the axes and the frustum planes are at 45 degrees435 // we can get the worldspace depth by taking the largest absolute axis436 let surface_to_light = (*light).position_radius.xyz - frag_position.xyz;437 let surface_to_light_abs = abs(surface_to_light);438 let distance_to_light = max(surface_to_light_abs.x, max(surface_to_light_abs.y, surface_to_light_abs.z));440 // The normal bias here is already scaled by the texel size at 1 world unit from the light.441 // The texel size increases proportionally with distance from the light so multiplying by442 // distance to light scales the normal bias to the texel size at the fragment distance.443 let depth_offset = (*light).shadow_depth_bias * normalize(surface_to_light.xyz);444 let offset_position = frag_position.xyz + depth_offset;446 // similar largest-absolute-axis trick as above, but now with the offset fragment position447 let frag_ls = offset_position.xyz - (*light).position_radius.xyz ;448 let abs_position_ls = abs(frag_ls);449 let major_axis_magnitude = max(abs_position_ls.x, max(abs_position_ls.y, abs_position_ls.z));451 // NOTE: These simplifications come from multiplying:452 // projection * vec4(0, 0, -major_axis_magnitude, 1.0)453 // and keeping only the terms that have any impact on the depth.454 // Projection-agnostic approach:455 let zw = -major_axis_magnitude * (*light).light_custom_data.xy + (*light).light_custom_data.zw;456 let depth = zw.x / zw.y;458 // Do the lookup, using HW PCF and comparison. Cubemaps assume a left-handed coordinate space,459 // so we have to flip the z-axis when sampling.460 let flip_z = vec3(1.0, 1.0, -1.0);461 return sample_shadow_cubemap(frag_ls * flip_z, distance_to_light, depth, light_id);462}464fn fetch_spot_shadow_without_normal(light_id: u32, frag_position: vec4<f32>) -> f32 {465 let light = &clusterable_objects.data[light_id];467 let surface_to_light = (*light).position_radius.xyz - frag_position.xyz;469 // construct the light view matrix470 var spot_dir = vec3<f32>((*light).light_custom_data.x, 0.0, (*light).light_custom_data.y);471 // reconstruct spot dir from x/z and y-direction flag472 spot_dir.y = sqrt(max(0.0, 1.0 - spot_dir.x * spot_dir.x - spot_dir.z * spot_dir.z));473 if (((*light).flags & POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE) != 0u) {474 spot_dir.y = -spot_dir.y;475 }477 // view matrix z_axis is the reverse of transform.forward()478 let fwd = -spot_dir;479 let offset_position =480 -surface_to_light481 + ((*light).shadow_depth_bias * normalize(surface_to_light));483 // the construction of the up and right vectors needs to precisely mirror the code484 // in render/light.rs:spot_light_view_matrix485 var sign = -1.0;486 if (fwd.z >= 0.0) {487 sign = 1.0;488 }489 let a = -1.0 / (fwd.z + sign);490 let b = fwd.x * fwd.y * a;491 let up_dir = vec3<f32>(1.0 + sign * fwd.x * fwd.x * a, sign * b, -sign * fwd.x);492 let right_dir = vec3<f32>(-b, -sign - fwd.y * fwd.y * a, fwd.y);493 let light_inv_rot = mat3x3<f32>(right_dir, up_dir, fwd);495 // because the matrix is a pure rotation matrix, the inverse is just the transpose, and to calculate496 // the product of the transpose with a vector we can just post-multiply instead of pre-multiplying.497 // this allows us to keep the matrix construction code identical between CPU and GPU.498 let projected_position = offset_position * light_inv_rot;500 // divide xy by perspective matrix "f" and by -projected.z (projected.z is -projection matrix's w)501 // to get ndc coordinates502 let f_div_minus_z = 1.0 / ((*light).spot_light_tan_angle * -projected_position.z);503 let shadow_xy_ndc = projected_position.xy * f_div_minus_z;504 // convert to uv coordinates505 let shadow_uv = shadow_xy_ndc * vec2<f32>(0.5, -0.5) + vec2<f32>(0.5, 0.5);507 // 0.1 must match POINT_LIGHT_NEAR_Z508 let depth = 0.1 / -projected_position.z;510 return sample_shadow_map(511 shadow_uv,512 depth,513 i32(light_id) + lights.spot_light_shadowmap_offset,514 SPOT_SHADOW_TEXEL_SIZE515 );516}518#ifdef ATMOSPHERE519fn sample_transmittance_lut(r: f32, mu: f32) -> vec3<f32> {520 let uv = transmittance_lut_r_mu_to_uv(atmosphere_data.atmosphere, r, mu);521 return textureSampleLevel(522 atmosphere_transmittance_texture, 523 atmosphere_transmittance_sampler, uv, 0.0).rgb;524}525#endif // ATMOSPHERE
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