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::mesh_functions::{get_world_from_local, mesh_position_local_to_clip}18#import bevy_pbr::mesh_view_bindings::{globals, lights, view, clusterable_objects}19#import bevy_pbr::mesh_view_types::{20 DIRECTIONAL_LIGHT_FLAGS_VOLUMETRIC_BIT, 21 POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT, 22 POINT_LIGHT_FLAGS_VOLUMETRIC_BIT,23 POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE,24 ClusterableObject25}26#import bevy_pbr::shadow_sampling::{27 sample_shadow_map_hardware, 28 sample_shadow_cubemap,29 sample_shadow_map,30 SPOT_SHADOW_TEXEL_SIZE31}32#import bevy_pbr::shadows::{get_cascade_index, world_to_directional_light_local}33#import bevy_pbr::utils::interleaved_gradient_noise34#import bevy_pbr::view_transformations::{35 depth_ndc_to_view_z,36 frag_coord_to_ndc,37 position_ndc_to_view,38 position_ndc_to_world,39 position_view_to_world40}41#import bevy_pbr::clustered_forward as clustering42#import bevy_pbr::lighting::getDistanceAttenuation;44// The GPU version of [`VolumetricFog`]. See the comments in45// `volumetric_fog/mod.rs` for descriptions of the fields here.46struct VolumetricFog {47 clip_from_local: mat4x4<f32>,48 uvw_from_world: mat4x4<f32>,49 far_planes: array<vec4<f32>, 3>,50 fog_color: vec3<f32>,51 light_tint: vec3<f32>,52 ambient_color: vec3<f32>,53 ambient_intensity: f32,54 step_count: u32,55 bounding_radius: f32,56 absorption: f32,57 scattering: f32,58 density_factor: f32,59 density_texture_offset: vec3<f32>,60 scattering_asymmetry: f32,61 light_intensity: f32,62 jitter_strength: f32,63}65@group(1) @binding(0) var<uniform> volumetric_fog: VolumetricFog;67#ifdef MULTISAMPLED68@group(1) @binding(1) var depth_texture: texture_depth_multisampled_2d;69#else70@group(1) @binding(1) var depth_texture: texture_depth_2d;71#endif73#ifdef DENSITY_TEXTURE74@group(1) @binding(2) var density_texture: texture_3d<f32>;75@group(1) @binding(3) var density_sampler: sampler;76#endif // DENSITY_TEXTURE78// 1 / (4π)79const FRAC_4_PI: f32 = 0.07957747154594767;81struct Vertex {82 @builtin(instance_index) instance_index: u32,83 @location(0) position: vec3<f32>,84}86@vertex87fn vertex(vertex: Vertex) -> @builtin(position) vec4<f32> {88 return volumetric_fog.clip_from_local * vec4<f32>(vertex.position, 1.0);89}91// The common Henyey-Greenstein asymmetric phase function [1] [2].92//93// This determines how much light goes toward the viewer as opposed to away from94// the viewer. From a visual point of view, it controls how the light shafts95// appear and disappear as the camera looks at the light source.96//97// [1]: https://www.scratchapixel.com/lessons/3d-basic-rendering/volume-rendering-for-developers/ray-marching-get-it-right.html98//99// [2]: https://www.pbr-book.org/4ed/Volume_Scattering/Phase_Functions#TheHenyeyndashGreensteinPhaseFunction100fn henyey_greenstein(neg_LdotV: f32) -> f32 {101 let g = volumetric_fog.scattering_asymmetry;102 let denom = 1.0 + g * g - 2.0 * g * neg_LdotV;103 return FRAC_4_PI * (1.0 - g * g) / (denom * sqrt(denom));104}106@fragment107fn fragment(@builtin(position) position: vec4<f32>) -> @location(0) vec4<f32> {108 // Unpack the `volumetric_fog` settings.109 let uvw_from_world = volumetric_fog.uvw_from_world;110 let fog_color = volumetric_fog.fog_color;111 let ambient_color = volumetric_fog.ambient_color;112 let ambient_intensity = volumetric_fog.ambient_intensity;113 let step_count = volumetric_fog.step_count;114 let bounding_radius = volumetric_fog.bounding_radius;115 let absorption = volumetric_fog.absorption;116 let scattering = volumetric_fog.scattering;117 let density_factor = volumetric_fog.density_factor;118 let density_texture_offset = volumetric_fog.density_texture_offset;119 let light_tint = volumetric_fog.light_tint;120 let light_intensity = volumetric_fog.light_intensity;121 let jitter_strength = volumetric_fog.jitter_strength;123 // Unpack the view.124 let exposure = view.exposure;126 // Sample the depth to put an upper bound on the length of the ray (as we127 // shouldn't trace through solid objects). If this is multisample, just use128 // sample 0; this is approximate but good enough.129 let frag_coord = position;130 let ndc_end_depth_from_buffer = textureLoad(depth_texture, vec2<i32>(frag_coord.xy), 0);131 let view_end_depth_from_buffer = -position_ndc_to_view(132 frag_coord_to_ndc(vec4(position.xy, ndc_end_depth_from_buffer, 1.0))).z;134 // Calculate the start position of the ray. Since we're only rendering front135 // faces of the AABB, this is the current fragment's depth.136 let view_start_pos = position_ndc_to_view(frag_coord_to_ndc(frag_coord));138 // Calculate the end position of the ray. This requires us to raytrace the139 // three back faces of the AABB to find the one that our ray intersects.140 var end_depth_view = 0.0;141 for (var plane_index = 0; plane_index < 3; plane_index += 1) {142 let plane = volumetric_fog.far_planes[plane_index];143 let other_plane_a = volumetric_fog.far_planes[(plane_index + 1) % 3];144 let other_plane_b = volumetric_fog.far_planes[(plane_index + 2) % 3];146 // Calculate the intersection of the ray and the plane. The ray must147 // intersect in front of us (t > 0).148 let t = -plane.w / dot(plane.xyz, view_start_pos.xyz);149 if (t < 0.0) {150 continue;151 }152 let hit_pos = view_start_pos.xyz * t;154 // The intersection point must be in front of the other backfaces.155 let other_sides = vec2(156 dot(vec4(hit_pos, 1.0), other_plane_a) >= 0.0,157 dot(vec4(hit_pos, 1.0), other_plane_b) >= 0.0158 );160 // If those tests pass, we found our backface.161 if (all(other_sides)) {162 end_depth_view = -hit_pos.z;163 break;164 }165 }167 // Starting at the end depth, which we got above, figure out how long the168 // ray we want to trace is and the length of each increment.169 end_depth_view = min(end_depth_view, view_end_depth_from_buffer);171 // We assume world and view have the same scale here.172 let start_depth_view = -depth_ndc_to_view_z(frag_coord.z);173 let ray_length_view = abs(end_depth_view - start_depth_view);174 let inv_step_count = 1.0 / f32(step_count);175 let step_size_world = ray_length_view * inv_step_count;177 let directional_light_count = lights.n_directional_lights;179 // Calculate the ray origin (`Ro`) and the ray direction (`Rd`) in NDC,180 // view, and world coordinates.181 let Rd_ndc = vec3(frag_coord_to_ndc(position).xy, 1.0);182 let Rd_view = normalize(position_ndc_to_view(Rd_ndc));183 var Ro_world = position_view_to_world(view_start_pos.xyz);184 let Rd_world = normalize(position_ndc_to_world(Rd_ndc) - view.world_position);186 // Offset by jitter.187 let jitter = interleaved_gradient_noise(position.xy, globals.frame_count) * jitter_strength;188 Ro_world += Rd_world * jitter;190 // Use Beer's law [1] [2] to calculate the maximum amount of light that each191 // directional light could contribute, and modulate that value by the light192 // tint and fog color. (The actual value will in turn be modulated by the193 // phase according to the Henyey-Greenstein formula.)194 //195 // [1]: https://www.scratchapixel.com/lessons/3d-basic-rendering/volume-rendering-for-developers/intro-volume-rendering.html196 //197 // [2]: https://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law199 // Use Beer's law again to accumulate the ambient light all along the path.200 var accumulated_color = exp(-ray_length_view * (absorption + scattering)) * ambient_color *201 ambient_intensity;203 // This is the amount of the background that shows through. We're actually204 // going to recompute this over and over again for each directional light,205 // coming up with the same values each time.206 var background_alpha = 1.0;208 // If we have a density texture, transform to its local space.209#ifdef DENSITY_TEXTURE210 let Ro_uvw = (uvw_from_world * vec4(Ro_world, 1.0)).xyz;211 let Rd_step_uvw = mat3x3(uvw_from_world[0].xyz, uvw_from_world[1].xyz, uvw_from_world[2].xyz) *212 (Rd_world * step_size_world);213#endif // DENSITY_TEXTURE215 for (var light_index = 0u; light_index < directional_light_count; light_index += 1u) {216 // Volumetric lights are all sorted first, so the first time we come to217 // a non-volumetric light, we know we've seen them all.218 let light = &lights.directional_lights[light_index];219 if (((*light).flags & DIRECTIONAL_LIGHT_FLAGS_VOLUMETRIC_BIT) == 0) {220 break;221 }223 // Offset the depth value by the bias.224 let depth_offset = (*light).shadow_depth_bias * (*light).direction_to_light.xyz;226 // Compute phase, which determines the fraction of light that's227 // scattered toward the camera instead of away from it.228 let neg_LdotV = dot(normalize((*light).direction_to_light.xyz), Rd_world);229 let phase = henyey_greenstein(neg_LdotV);231 // Reset `background_alpha` for a new raymarch.232 background_alpha = 1.0;234 // Start raymarching.235 for (var step = 0u; step < step_count; step += 1u) {236 // As an optimization, break if we've gotten too dark.237 if (background_alpha < 0.001) {238 break;239 }241 // Calculate where we are in the ray.242 let P_world = Ro_world + Rd_world * f32(step) * step_size_world;243 let P_view = Rd_view * f32(step) * step_size_world;245 var density = density_factor;246#ifdef DENSITY_TEXTURE247 // Take the density texture into account, if there is one.248 //249 // The uvs should never go outside the (0, 0, 0) to (1, 1, 1) box,250 // but sometimes due to floating point error they can. Handle this251 // case.252 let P_uvw = Ro_uvw + Rd_step_uvw * f32(step);253 if (all(P_uvw >= vec3(0.0)) && all(P_uvw <= vec3(1.0))) {254 density *= textureSample(density_texture, density_sampler, P_uvw + density_texture_offset).r;255 } else {256 density = 0.0;257 }258#endif // DENSITY_TEXTURE260 // Calculate absorption (amount of light absorbed by the fog) and261 // out-scattering (amount of light the fog scattered away).262 let sample_attenuation = exp(-step_size_world * density * (absorption + scattering));264 // Process absorption and out-scattering.265 background_alpha *= sample_attenuation;267 // Compute in-scattering (amount of light other fog particles268 // scattered into this ray). This is where any directional light is269 // scattered in.271 // Prepare to sample the shadow map.272 let cascade_index = get_cascade_index(light_index, P_view.z);273 let light_local = world_to_directional_light_local(274 light_index,275 cascade_index,276 vec4(P_world + depth_offset, 1.0)277 );279 // If we're outside the shadow map entirely, local light attenuation280 // is zero.281 var local_light_attenuation = f32(light_local.w != 0.0);283 // Otherwise, sample the shadow map to determine whether, and by how284 // much, this sample is in the light.285 if (local_light_attenuation != 0.0) {286 let cascade = &(*light).cascades[cascade_index];287 let array_index = i32((*light).depth_texture_base_index + cascade_index);288 local_light_attenuation =289 sample_shadow_map_hardware(light_local.xy, light_local.z, array_index);290 }292 if (local_light_attenuation != 0.0) {293 let light_attenuation = exp(-density * bounding_radius * (absorption + scattering));294 let light_factors_per_step = fog_color * light_tint * light_attenuation *295 scattering * density * step_size_world * light_intensity * exposure;297 // Modulate the factor we calculated above by the phase, fog color,298 // light color, light tint.299 let light_color_per_step = (*light).color.rgb * phase * light_factors_per_step;301 // Accumulate the light.302 accumulated_color += light_color_per_step * local_light_attenuation *303 background_alpha;304 }305 }306 }308 // Point lights and Spot lights309 let view_z = view_start_pos.z;310 let is_orthographic = view.clip_from_view[3].w == 1.0;311 let cluster_index = clustering::fragment_cluster_index(frag_coord.xy, view_z, is_orthographic);312 let offset_and_counts = clustering::unpack_offset_and_counts(cluster_index);313 let spot_light_start_index = offset_and_counts[0] + offset_and_counts[1];314 for (var i: u32 = offset_and_counts[0]; i < offset_and_counts[0] + offset_and_counts[1] + offset_and_counts[2]; i = i + 1u) {315 let light_id = clustering::get_clusterable_object_id(i);316 let light = &clusterable_objects.data[light_id];317 if (((*light).flags & POINT_LIGHT_FLAGS_VOLUMETRIC_BIT) == 0) {318 continue;319 }321 // Reset `background_alpha` for a new raymarch.322 background_alpha = 1.0;324 // Start raymarching.325 for (var step = 0u; step < step_count; step += 1u) {326 // As an optimization, break if we've gotten too dark.327 if (background_alpha < 0.001) {328 break;329 }331 // Calculate where we are in the ray.332 let P_world = Ro_world + Rd_world * f32(step) * step_size_world;333 let P_view = Rd_view * f32(step) * step_size_world;335 var density = density_factor;337 let light_to_frag = (*light).position_radius.xyz - P_world;338 let V = Rd_world;339 let L = normalize(light_to_frag);340 let distance_square = dot(light_to_frag, light_to_frag);341 let distance_atten = getDistanceAttenuation(distance_square, (*light).color_inverse_square_range.w);342 var local_light_attenuation = distance_atten;343 if (i < spot_light_start_index) {344 var shadow: f32 = 1.0;345 if (((*light).flags & POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT) != 0u) {346 shadow = fetch_point_shadow_without_normal(light_id, vec4(P_world, 1.0));347 }348 local_light_attenuation *= shadow;349 } else {350 // spot light attenuation351 // reconstruct spot dir from x/z and y-direction flag352 var spot_dir = vec3<f32>((*light).light_custom_data.x, 0.0, (*light).light_custom_data.y);353 spot_dir.y = sqrt(max(0.0, 1.0 - spot_dir.x * spot_dir.x - spot_dir.z * spot_dir.z));354 if ((*light).flags & POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE) != 0u {355 spot_dir.y = -spot_dir.y;356 }357 let light_to_frag = (*light).position_radius.xyz - P_world;359 // calculate attenuation based on filament formula https://google.github.io/filament/Filament.html#listing_glslpunctuallight360 // spot_scale and spot_offset have been precomputed361 // note we normalize here to get "l" from the filament listing. spot_dir is already normalized362 let cd = dot(-spot_dir, normalize(light_to_frag));363 let attenuation = saturate(cd * (*light).light_custom_data.z + (*light).light_custom_data.w);364 let spot_attenuation = attenuation * attenuation;366 var shadow: f32 = 1.0;367 if (((*light).flags & POINT_LIGHT_FLAGS_SHADOWS_ENABLED_BIT) != 0u) {368 shadow = fetch_spot_shadow_without_normal(light_id, vec4(P_world, 1.0));369 }370 local_light_attenuation *= spot_attenuation * shadow;371 }373 // Calculate absorption (amount of light absorbed by the fog) and374 // out-scattering (amount of light the fog scattered away).375 let sample_attenuation = exp(-step_size_world * density * (absorption + scattering));377 // Process absorption and out-scattering.378 background_alpha *= sample_attenuation;380 let light_attenuation = exp(-density * bounding_radius * (absorption + scattering));381 let light_factors_per_step = fog_color * light_tint * light_attenuation *382 scattering * density * step_size_world * light_intensity * 0.1;384 // Modulate the factor we calculated above by the phase, fog color,385 // light color, light tint.386 let light_color_per_step = (*light).color_inverse_square_range.rgb * light_factors_per_step;388 // Accumulate the light.389 accumulated_color += light_color_per_step * local_light_attenuation *390 background_alpha;391 }392 }394 // We're done! Return the color with alpha so it can be blended onto the395 // render target.396 return vec4(accumulated_color, 1.0 - background_alpha);397}399fn fetch_point_shadow_without_normal(light_id: u32, frag_position: vec4<f32>) -> f32 {400 let light = &clusterable_objects.data[light_id];402 // because the shadow maps align with the axes and the frustum planes are at 45 degrees403 // we can get the worldspace depth by taking the largest absolute axis404 let surface_to_light = (*light).position_radius.xyz - frag_position.xyz;405 let surface_to_light_abs = abs(surface_to_light);406 let distance_to_light = max(surface_to_light_abs.x, max(surface_to_light_abs.y, surface_to_light_abs.z));408 // The normal bias here is already scaled by the texel size at 1 world unit from the light.409 // The texel size increases proportionally with distance from the light so multiplying by410 // distance to light scales the normal bias to the texel size at the fragment distance.411 let depth_offset = (*light).shadow_depth_bias * normalize(surface_to_light.xyz);412 let offset_position = frag_position.xyz + depth_offset;414 // similar largest-absolute-axis trick as above, but now with the offset fragment position415 let frag_ls = offset_position.xyz - (*light).position_radius.xyz ;416 let abs_position_ls = abs(frag_ls);417 let major_axis_magnitude = max(abs_position_ls.x, max(abs_position_ls.y, abs_position_ls.z));419 // NOTE: These simplifications come from multiplying:420 // projection * vec4(0, 0, -major_axis_magnitude, 1.0)421 // and keeping only the terms that have any impact on the depth.422 // Projection-agnostic approach:423 let zw = -major_axis_magnitude * (*light).light_custom_data.xy + (*light).light_custom_data.zw;424 let depth = zw.x / zw.y;426 // Do the lookup, using HW PCF and comparison. Cubemaps assume a left-handed coordinate space,427 // so we have to flip the z-axis when sampling.428 let flip_z = vec3(1.0, 1.0, -1.0);429 return sample_shadow_cubemap(frag_ls * flip_z, distance_to_light, depth, light_id);430}432fn fetch_spot_shadow_without_normal(light_id: u32, frag_position: vec4<f32>) -> f32 {433 let light = &clusterable_objects.data[light_id];435 let surface_to_light = (*light).position_radius.xyz - frag_position.xyz;437 // construct the light view matrix438 var spot_dir = vec3<f32>((*light).light_custom_data.x, 0.0, (*light).light_custom_data.y);439 // reconstruct spot dir from x/z and y-direction flag440 spot_dir.y = sqrt(max(0.0, 1.0 - spot_dir.x * spot_dir.x - spot_dir.z * spot_dir.z));441 if (((*light).flags & POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE) != 0u) {442 spot_dir.y = -spot_dir.y;443 }445 // view matrix z_axis is the reverse of transform.forward()446 let fwd = -spot_dir;447 let offset_position =448 -surface_to_light449 + ((*light).shadow_depth_bias * normalize(surface_to_light));451 // the construction of the up and right vectors needs to precisely mirror the code452 // in render/light.rs:spot_light_view_matrix453 var sign = -1.0;454 if (fwd.z >= 0.0) {455 sign = 1.0;456 }457 let a = -1.0 / (fwd.z + sign);458 let b = fwd.x * fwd.y * a;459 let up_dir = vec3<f32>(1.0 + sign * fwd.x * fwd.x * a, sign * b, -sign * fwd.x);460 let right_dir = vec3<f32>(-b, -sign - fwd.y * fwd.y * a, fwd.y);461 let light_inv_rot = mat3x3<f32>(right_dir, up_dir, fwd);463 // because the matrix is a pure rotation matrix, the inverse is just the transpose, and to calculate464 // the product of the transpose with a vector we can just post-multiply instead of pre-multiplying.465 // this allows us to keep the matrix construction code identical between CPU and GPU.466 let projected_position = offset_position * light_inv_rot;468 // divide xy by perspective matrix "f" and by -projected.z (projected.z is -projection matrix's w)469 // to get ndc coordinates470 let f_div_minus_z = 1.0 / ((*light).spot_light_tan_angle * -projected_position.z);471 let shadow_xy_ndc = projected_position.xy * f_div_minus_z;472 // convert to uv coordinates473 let shadow_uv = shadow_xy_ndc * vec2<f32>(0.5, -0.5) + vec2<f32>(0.5, 0.5);475 // 0.1 must match POINT_LIGHT_NEAR_Z476 let depth = 0.1 / -projected_position.z;478 return sample_shadow_map(479 shadow_uv,480 depth,481 i32(light_id) + lights.spot_light_shadowmap_offset,482 SPOT_SHADOW_TEXEL_SIZE483 );484}
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