// NOTE: Keep in sync with depth.wgsl [[block]] struct View { view_proj: mat4x4; projection: mat4x4; world_position: vec3; }; [[block]] struct Mesh { model: mat4x4; inverse_transpose_model: mat4x4; // 'flags' is a bit field indicating various options. u32 is 32 bits so we have up to 32 options. flags: u32; }; let MESH_FLAGS_SHADOW_RECEIVER_BIT: u32 = 1u; [[group(0), binding(0)]] var view: View; [[group(2), binding(0)]] var mesh: Mesh; struct Vertex { [[location(0)]] position: vec3; [[location(1)]] normal: vec3; [[location(2)]] uv: vec2; }; struct VertexOutput { [[builtin(position)]] clip_position: vec4; [[location(0)]] world_position: vec4; [[location(1)]] world_normal: vec3; [[location(2)]] uv: vec2; }; [[stage(vertex)]] fn vertex(vertex: Vertex) -> VertexOutput { let world_position = mesh.model * vec4(vertex.position, 1.0); var out: VertexOutput; out.uv = vertex.uv; out.world_position = world_position; out.clip_position = view.view_proj * world_position; out.world_normal = mat3x3( mesh.inverse_transpose_model.x.xyz, mesh.inverse_transpose_model.y.xyz, mesh.inverse_transpose_model.z.xyz ) * vertex.normal; return out; } // From the Filament design doc // https://google.github.io/filament/Filament.html#table_symbols // Symbol Definition // v View unit vector // l Incident light unit vector // n Surface normal unit vector // h Half unit vector between l and v // f BRDF // f_d Diffuse component of a BRDF // f_r Specular component of a BRDF // α Roughness, remapped from using input perceptualRoughness // σ Diffuse reflectance // Ω Spherical domain // f0 Reflectance at normal incidence // f90 Reflectance at grazing angle // χ+(a) Heaviside function (1 if a>0 and 0 otherwise) // nior Index of refraction (IOR) of an interface // ⟨n⋅l⟩ Dot product clamped to [0..1] // ⟨a⟩ Saturated value (clamped to [0..1]) // The Bidirectional Reflectance Distribution Function (BRDF) describes the surface response of a standard material // and consists of two components, the diffuse component (f_d) and the specular component (f_r): // f(v,l) = f_d(v,l) + f_r(v,l) // // The form of the microfacet model is the same for diffuse and specular // f_r(v,l) = f_d(v,l) = 1 / { |n⋅v||n⋅l| } ∫_Ω D(m,α) G(v,l,m) f_m(v,l,m) (v⋅m) (l⋅m) dm // // In which: // D, also called the Normal Distribution Function (NDF) models the distribution of the microfacets // G models the visibility (or occlusion or shadow-masking) of the microfacets // f_m is the microfacet BRDF and differs between specular and diffuse components // // The above integration needs to be approximated. [[block]] struct StandardMaterial { base_color: vec4; emissive: vec4; perceptual_roughness: f32; metallic: f32; reflectance: f32; // 'flags' is a bit field indicating various options. u32 is 32 bits so we have up to 32 options. flags: u32; }; let STANDARD_MATERIAL_FLAGS_BASE_COLOR_TEXTURE_BIT: u32 = 1u; let STANDARD_MATERIAL_FLAGS_EMISSIVE_TEXTURE_BIT: u32 = 2u; let STANDARD_MATERIAL_FLAGS_METALLIC_ROUGHNESS_TEXTURE_BIT: u32 = 4u; let STANDARD_MATERIAL_FLAGS_OCCLUSION_TEXTURE_BIT: u32 = 8u; let STANDARD_MATERIAL_FLAGS_DOUBLE_SIDED_BIT: u32 = 16u; let STANDARD_MATERIAL_FLAGS_UNLIT_BIT: u32 = 32u; struct PointLight { projection: mat4x4; color: vec4; position: vec3; inverse_square_range: f32; radius: f32; near: f32; far: f32; shadow_depth_bias: f32; shadow_normal_bias: f32; }; struct DirectionalLight { view_projection: mat4x4; color: vec4; direction_to_light: vec3; shadow_depth_bias: f32; shadow_normal_bias: f32; }; [[block]] struct Lights { // NOTE: this array size must be kept in sync with the constants defined bevy_pbr2/src/render/light.rs // TODO: this can be removed if we move to storage buffers for light arrays point_lights: array; directional_lights: array; ambient_color: vec4; n_point_lights: u32; n_directional_lights: u32; }; [[group(0), binding(1)]] var lights: Lights; [[group(0), binding(2)]] var point_shadow_textures: texture_depth_cube_array; [[group(0), binding(3)]] var point_shadow_textures_sampler: sampler_comparison; [[group(0), binding(4)]] var directional_shadow_textures: texture_depth_2d_array; [[group(0), binding(5)]] var directional_shadow_textures_sampler: sampler_comparison; [[group(1), binding(0)]] var material: StandardMaterial; [[group(1), binding(1)]] var base_color_texture: texture_2d; [[group(1), binding(2)]] var base_color_sampler: sampler; [[group(1), binding(3)]] var emissive_texture: texture_2d; [[group(1), binding(4)]] var emissive_sampler: sampler; [[group(1), binding(5)]] var metallic_roughness_texture: texture_2d; [[group(1), binding(6)]] var metallic_roughness_sampler: sampler; [[group(1), binding(7)]] var occlusion_texture: texture_2d; [[group(1), binding(8)]] var occlusion_sampler: sampler; let PI: f32 = 3.141592653589793; fn saturate(value: f32) -> f32 { return clamp(value, 0.0, 1.0); } // distanceAttenuation is simply the square falloff of light intensity // combined with a smooth attenuation at the edge of the light radius // // light radius is a non-physical construct for efficiency purposes, // because otherwise every light affects every fragment in the scene fn getDistanceAttenuation(distanceSquare: f32, inverseRangeSquared: f32) -> f32 { let factor = distanceSquare * inverseRangeSquared; let smoothFactor = saturate(1.0 - factor * factor); let attenuation = smoothFactor * smoothFactor; return attenuation * 1.0 / max(distanceSquare, 0.0001); } // Normal distribution function (specular D) // Based on https://google.github.io/filament/Filament.html#citation-walter07 // D_GGX(h,α) = α^2 / { π ((n⋅h)^2 (α2−1) + 1)^2 } // Simple implementation, has precision problems when using fp16 instead of fp32 // see https://google.github.io/filament/Filament.html#listing_speculardfp16 fn D_GGX(roughness: f32, NoH: f32, h: vec3) -> f32 { let oneMinusNoHSquared = 1.0 - NoH * NoH; let a = NoH * roughness; let k = roughness / (oneMinusNoHSquared + a * a); let d = k * k * (1.0 / PI); return d; } // Visibility function (Specular G) // V(v,l,a) = G(v,l,α) / { 4 (n⋅v) (n⋅l) } // such that f_r becomes // f_r(v,l) = D(h,α) V(v,l,α) F(v,h,f0) // where // V(v,l,α) = 0.5 / { n⋅l sqrt((n⋅v)^2 (1−α2) + α2) + n⋅v sqrt((n⋅l)^2 (1−α2) + α2) } // Note the two sqrt's, that may be slow on mobile, see https://google.github.io/filament/Filament.html#listing_approximatedspecularv fn V_SmithGGXCorrelated(roughness: f32, NoV: f32, NoL: f32) -> f32 { let a2 = roughness * roughness; let lambdaV = NoL * sqrt((NoV - a2 * NoV) * NoV + a2); let lambdaL = NoV * sqrt((NoL - a2 * NoL) * NoL + a2); let v = 0.5 / (lambdaV + lambdaL); return v; } // Fresnel function // see https://google.github.io/filament/Filament.html#citation-schlick94 // F_Schlick(v,h,f_0,f_90) = f_0 + (f_90 − f_0) (1 − v⋅h)^5 fn F_Schlick_vec(f0: vec3, f90: f32, VoH: f32) -> vec3 { // not using mix to keep the vec3 and float versions identical return f0 + (f90 - f0) * pow(1.0 - VoH, 5.0); } fn F_Schlick(f0: f32, f90: f32, VoH: f32) -> f32 { // not using mix to keep the vec3 and float versions identical return f0 + (f90 - f0) * pow(1.0 - VoH, 5.0); } fn fresnel(f0: vec3, LoH: f32) -> vec3 { // f_90 suitable for ambient occlusion // see https://google.github.io/filament/Filament.html#lighting/occlusion let f90 = saturate(dot(f0, vec3(50.0 * 0.33))); return F_Schlick_vec(f0, f90, LoH); } // Specular BRDF // https://google.github.io/filament/Filament.html#materialsystem/specularbrdf // Cook-Torrance approximation of the microfacet model integration using Fresnel law F to model f_m // f_r(v,l) = { D(h,α) G(v,l,α) F(v,h,f0) } / { 4 (n⋅v) (n⋅l) } fn specular(f0: vec3, roughness: f32, h: vec3, NoV: f32, NoL: f32, NoH: f32, LoH: f32, specularIntensity: f32) -> vec3 { let D = D_GGX(roughness, NoH, h); let V = V_SmithGGXCorrelated(roughness, NoV, NoL); let F = fresnel(f0, LoH); return (specularIntensity * D * V) * F; } // Diffuse BRDF // https://google.github.io/filament/Filament.html#materialsystem/diffusebrdf // fd(v,l) = σ/π * 1 / { |n⋅v||n⋅l| } ∫Ω D(m,α) G(v,l,m) (v⋅m) (l⋅m) dm // // simplest approximation // float Fd_Lambert() { // return 1.0 / PI; // } // // vec3 Fd = diffuseColor * Fd_Lambert(); // // Disney approximation // See https://google.github.io/filament/Filament.html#citation-burley12 // minimal quality difference fn Fd_Burley(roughness: f32, NoV: f32, NoL: f32, LoH: f32) -> f32 { let f90 = 0.5 + 2.0 * roughness * LoH * LoH; let lightScatter = F_Schlick(1.0, f90, NoL); let viewScatter = F_Schlick(1.0, f90, NoV); return lightScatter * viewScatter * (1.0 / PI); } // From https://www.unrealengine.com/en-US/blog/physically-based-shading-on-mobile fn EnvBRDFApprox(f0: vec3, perceptual_roughness: f32, NoV: f32) -> vec3 { let c0 = vec4(-1.0, -0.0275, -0.572, 0.022); let c1 = vec4(1.0, 0.0425, 1.04, -0.04); let r = perceptual_roughness * c0 + c1; let a004 = min(r.x * r.x, exp2(-9.28 * NoV)) * r.x + r.y; let AB = vec2(-1.04, 1.04) * a004 + r.zw; return f0 * AB.x + AB.y; } fn perceptualRoughnessToRoughness(perceptualRoughness: f32) -> f32 { // clamp perceptual roughness to prevent precision problems // According to Filament design 0.089 is recommended for mobile // Filament uses 0.045 for non-mobile let clampedPerceptualRoughness = clamp(perceptualRoughness, 0.089, 1.0); return clampedPerceptualRoughness * clampedPerceptualRoughness; } // from https://64.github.io/tonemapping/ // reinhard on RGB oversaturates colors fn reinhard(color: vec3) -> vec3 { return color / (1.0 + color); } fn reinhard_extended(color: vec3, max_white: f32) -> vec3 { let numerator = color * (1.0 + (color / vec3(max_white * max_white))); return numerator / (1.0 + color); } // luminance coefficients from Rec. 709. // https://en.wikipedia.org/wiki/Rec._709 fn luminance(v: vec3) -> f32 { return dot(v, vec3(0.2126, 0.7152, 0.0722)); } fn change_luminance(c_in: vec3, l_out: f32) -> vec3 { let l_in = luminance(c_in); return c_in * (l_out / l_in); } fn reinhard_luminance(color: vec3) -> vec3 { let l_old = luminance(color); let l_new = l_old / (1.0 + l_old); return change_luminance(color, l_new); } fn reinhard_extended_luminance(color: vec3, max_white_l: f32) -> vec3 { let l_old = luminance(color); let numerator = l_old * (1.0 + (l_old / (max_white_l * max_white_l))); let l_new = numerator / (1.0 + l_old); return change_luminance(color, l_new); } fn point_light( world_position: vec3, light: PointLight, roughness: f32, NdotV: f32, N: vec3, V: vec3, R: vec3, F0: vec3, diffuseColor: vec3 ) -> vec3 { let light_to_frag = light.position.xyz - world_position.xyz; let distance_square = dot(light_to_frag, light_to_frag); let rangeAttenuation = getDistanceAttenuation(distance_square, light.inverse_square_range); // Specular. // Representative Point Area Lights. // see http://blog.selfshadow.com/publications/s2013-shading-course/karis/s2013_pbs_epic_notes_v2.pdf p14-16 let a = roughness; let centerToRay = dot(light_to_frag, R) * R - light_to_frag; let closestPoint = light_to_frag + centerToRay * saturate(light.radius * inverseSqrt(dot(centerToRay, centerToRay))); let LspecLengthInverse = inverseSqrt(dot(closestPoint, closestPoint)); let normalizationFactor = a / saturate(a + (light.radius * 0.5 * LspecLengthInverse)); let specularIntensity = normalizationFactor * normalizationFactor; var L: vec3 = closestPoint * LspecLengthInverse; // normalize() equivalent? var H: vec3 = normalize(L + V); var NoL: f32 = saturate(dot(N, L)); var NoH: f32 = saturate(dot(N, H)); var LoH: f32 = saturate(dot(L, H)); let specular_light = specular(F0, roughness, H, NdotV, NoL, NoH, LoH, specularIntensity); // Diffuse. // Comes after specular since its NoL is used in the lighting equation. L = normalize(light_to_frag); H = normalize(L + V); NoL = saturate(dot(N, L)); NoH = saturate(dot(N, H)); LoH = saturate(dot(L, H)); let diffuse = diffuseColor * Fd_Burley(roughness, NdotV, NoL, LoH); // See https://google.github.io/filament/Filament.html#mjx-eqn-pointLightLuminanceEquation // Lout = f(v,l) Φ / { 4 π d^2 }⟨n⋅l⟩ // where // f(v,l) = (f_d(v,l) + f_r(v,l)) * light_color // Φ is luminous power in lumens // our rangeAttentuation = 1 / d^2 multiplied with an attenuation factor for smoothing at the edge of the non-physical maximum light radius // For a point light, luminous intensity, I, in lumens per steradian is given by: // I = Φ / 4 π // The derivation of this can be seen here: https://google.github.io/filament/Filament.html#mjx-eqn-pointLightLuminousPower // NOTE: light.color.rgb is premultiplied with light.intensity / 4 π (which would be the luminous intensity) on the CPU // TODO compensate for energy loss https://google.github.io/filament/Filament.html#materialsystem/improvingthebrdfs/energylossinspecularreflectance return ((diffuse + specular_light) * light.color.rgb) * (rangeAttenuation * NoL); } fn directional_light(light: DirectionalLight, roughness: f32, NdotV: f32, normal: vec3, view: vec3, R: vec3, F0: vec3, diffuseColor: vec3) -> vec3 { let incident_light = light.direction_to_light.xyz; let half_vector = normalize(incident_light + view); let NoL = saturate(dot(normal, incident_light)); let NoH = saturate(dot(normal, half_vector)); let LoH = saturate(dot(incident_light, half_vector)); let diffuse = diffuseColor * Fd_Burley(roughness, NdotV, NoL, LoH); let specularIntensity = 1.0; let specular_light = specular(F0, roughness, half_vector, NdotV, NoL, NoH, LoH, specularIntensity); return (specular_light + diffuse) * light.color.rgb * NoL; } fn fetch_point_shadow(light_id: i32, frag_position: vec4, surface_normal: vec3) -> f32 { let light = lights.point_lights[light_id]; // because the shadow maps align with the axes and the frustum planes are at 45 degrees // we can get the worldspace depth by taking the largest absolute axis let surface_to_light = light.position.xyz - frag_position.xyz; let surface_to_light_abs = abs(surface_to_light); let distance_to_light = max(surface_to_light_abs.x, max(surface_to_light_abs.y, surface_to_light_abs.z)); // The normal bias here is already scaled by the texel size at 1 world unit from the light. // The texel size increases proportionally with distance from the light so multiplying by // distance to light scales the normal bias to the texel size at the fragment distance. let normal_offset = light.shadow_normal_bias * distance_to_light * surface_normal.xyz; let depth_offset = light.shadow_depth_bias * normalize(surface_to_light.xyz); let offset_position = frag_position.xyz + normal_offset + depth_offset; // similar largest-absolute-axis trick as above, but now with the offset fragment position let frag_ls = light.position.xyz - offset_position.xyz; let abs_position_ls = abs(frag_ls); let major_axis_magnitude = max(abs_position_ls.x, max(abs_position_ls.y, abs_position_ls.z)); // NOTE: These simplifications come from multiplying: // projection * vec4(0, 0, -major_axis_magnitude, 1.0) // and keeping only the terms that have any impact on the depth. // Projection-agnostic approach: let z = -major_axis_magnitude * light.projection[2][2] + light.projection[3][2]; let w = -major_axis_magnitude * light.projection[2][3] + light.projection[3][3]; // For perspective_rh: // let proj_r = light.far / (light.near - light.far); // let z = -major_axis_magnitude * proj_r + light.near * proj_r; // let w = major_axis_magnitude; // For perspective_infinite_reverse_rh: // let z = light.near; // let w = major_axis_magnitude; let depth = z / w; // do the lookup, using HW PCF and comparison // NOTE: Due to the non-uniform control flow above, we must use the Level variant of // textureSampleCompare to avoid undefined behaviour due to some of the fragments in // a quad (2x2 fragments) being processed not being sampled, and this messing with // mip-mapping functionality. The shadow maps have no mipmaps so Level just samples // from LOD 0. return textureSampleCompareLevel(point_shadow_textures, point_shadow_textures_sampler, frag_ls, i32(light_id), depth); } fn fetch_directional_shadow(light_id: i32, frag_position: vec4, surface_normal: vec3) -> f32 { let light = lights.directional_lights[light_id]; // The normal bias is scaled to the texel size. let normal_offset = light.shadow_normal_bias * surface_normal.xyz; let depth_offset = light.shadow_depth_bias * light.direction_to_light.xyz; let offset_position = vec4(frag_position.xyz + normal_offset + depth_offset, frag_position.w); let offset_position_clip = light.view_projection * offset_position; if (offset_position_clip.w <= 0.0) { return 1.0; } let offset_position_ndc = offset_position_clip.xyz / offset_position_clip.w; // No shadow outside the orthographic projection volume if (any(offset_position_ndc.xy < vec2(-1.0)) || offset_position_ndc.z < 0.0 || any(offset_position_ndc > vec3(1.0))) { return 1.0; } // compute texture coordinates for shadow lookup, compensating for the Y-flip difference // between the NDC and texture coordinates let flip_correction = vec2(0.5, -0.5); let light_local = offset_position_ndc.xy * flip_correction + vec2(0.5, 0.5); let depth = offset_position_ndc.z; // do the lookup, using HW PCF and comparison // NOTE: Due to non-uniform control flow above, we must use the level variant of the texture // sampler to avoid use of implicit derivatives causing possible undefined behavior. return textureSampleCompareLevel(directional_shadow_textures, directional_shadow_textures_sampler, light_local, i32(light_id), depth); } struct FragmentInput { [[builtin(front_facing)]] is_front: bool; [[location(0)]] world_position: vec4; [[location(1)]] world_normal: vec3; [[location(2)]] uv: vec2; }; [[stage(fragment)]] fn fragment(in: FragmentInput) -> [[location(0)]] vec4 { var output_color: vec4 = material.base_color; if ((material.flags & STANDARD_MATERIAL_FLAGS_BASE_COLOR_TEXTURE_BIT) != 0u) { output_color = output_color * textureSample(base_color_texture, base_color_sampler, in.uv); } // // NOTE: Unlit bit not set means == 0 is true, so the true case is if lit if ((material.flags & STANDARD_MATERIAL_FLAGS_UNLIT_BIT) == 0u) { // TODO use .a for exposure compensation in HDR var emissive: vec4 = material.emissive; if ((material.flags & STANDARD_MATERIAL_FLAGS_EMISSIVE_TEXTURE_BIT) != 0u) { emissive = vec4(emissive.rgb * textureSample(emissive_texture, emissive_sampler, in.uv).rgb, 1.0); } // calculate non-linear roughness from linear perceptualRoughness var metallic: f32 = material.metallic; var perceptual_roughness: f32 = material.perceptual_roughness; if ((material.flags & STANDARD_MATERIAL_FLAGS_METALLIC_ROUGHNESS_TEXTURE_BIT) != 0u) { let metallic_roughness = textureSample(metallic_roughness_texture, metallic_roughness_sampler, in.uv); // Sampling from GLTF standard channels for now metallic = metallic * metallic_roughness.b; perceptual_roughness = perceptual_roughness * metallic_roughness.g; } let roughness = perceptualRoughnessToRoughness(perceptual_roughness); var occlusion: f32 = 1.0; if ((material.flags & STANDARD_MATERIAL_FLAGS_OCCLUSION_TEXTURE_BIT) != 0u) { occlusion = textureSample(occlusion_texture, occlusion_sampler, in.uv).r; } var N: vec3 = normalize(in.world_normal); // FIXME: Normal maps need an additional vertex attribute and vertex stage output/fragment stage input // Just use a separate shader for lit with normal maps? // # ifdef STANDARDMATERIAL_NORMAL_MAP // vec3 T = normalize(v_WorldTangent.xyz); // vec3 B = cross(N, T) * v_WorldTangent.w; // # endif if ((material.flags & STANDARD_MATERIAL_FLAGS_DOUBLE_SIDED_BIT) != 0u) { if (!in.is_front) { N = -N; } // # ifdef STANDARDMATERIAL_NORMAL_MAP // T = gl_FrontFacing ? T : -T; // B = gl_FrontFacing ? B : -B; // # endif } // # ifdef STANDARDMATERIAL_NORMAL_MAP // mat3 TBN = mat3(T, B, N); // N = TBN * normalize(texture(sampler2D(normal_map, normal_map_sampler), v_Uv).rgb * 2.0 - 1.0); // # endif var V: vec3; if (view.projection.w.w != 1.0) { // If the projection is not orthographic // Only valid for a perpective projection V = normalize(view.world_position.xyz - in.world_position.xyz); } else { // Ortho view vec V = normalize(vec3(view.view_proj.x.z, view.view_proj.y.z, view.view_proj.z.z)); } // Neubelt and Pettineo 2013, "Crafting a Next-gen Material Pipeline for The Order: 1886" let NdotV = max(dot(N, V), 0.0001); // Remapping [0,1] reflectance to F0 // See https://google.github.io/filament/Filament.html#materialsystem/parameterization/remapping let reflectance = material.reflectance; let F0 = 0.16 * reflectance * reflectance * (1.0 - metallic) + output_color.rgb * metallic; // Diffuse strength inversely related to metallicity let diffuse_color = output_color.rgb * (1.0 - metallic); let R = reflect(-V, N); // accumulate color var light_accum: vec3 = vec3(0.0); let n_point_lights = i32(lights.n_point_lights); let n_directional_lights = i32(lights.n_directional_lights); for (var i: i32 = 0; i < n_point_lights; i = i + 1) { let light = lights.point_lights[i]; var shadow: f32; if ((mesh.flags & MESH_FLAGS_SHADOW_RECEIVER_BIT) != 0u) { shadow = fetch_point_shadow(i, in.world_position, in.world_normal); } else { shadow = 1.0; } let light_contrib = point_light(in.world_position.xyz, light, roughness, NdotV, N, V, R, F0, diffuse_color); light_accum = light_accum + light_contrib * shadow; } for (var i: i32 = 0; i < n_directional_lights; i = i + 1) { let light = lights.directional_lights[i]; var shadow: f32; if ((mesh.flags & MESH_FLAGS_SHADOW_RECEIVER_BIT) != 0u) { shadow = fetch_directional_shadow(i, in.world_position, in.world_normal); } else { shadow = 1.0; } let light_contrib = directional_light(light, roughness, NdotV, N, V, R, F0, diffuse_color); light_accum = light_accum + light_contrib * shadow; } let diffuse_ambient = EnvBRDFApprox(diffuse_color, 1.0, NdotV); let specular_ambient = EnvBRDFApprox(F0, perceptual_roughness, NdotV); output_color = vec4( light_accum + (diffuse_ambient + specular_ambient) * lights.ambient_color.rgb * occlusion + emissive.rgb * output_color.a, output_color.a); // tone_mapping output_color = vec4(reinhard_luminance(output_color.rgb), output_color.a); // Gamma correction. // Not needed with sRGB buffer // output_color.rgb = pow(output_color.rgb, vec3(1.0 / 2.2)); } return output_color; }