bevy/crates/bevy_pbr/src/render/pbr_lighting.wgsl

#define_import_path bevy_pbr::lighting

#import bevy_pbr::{
    mesh_view_types::POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE,
    mesh_view_bindings as view_bindings,
}
#import bevy_render::maths::PI

const LAYER_BASE: u32 = 0;
const LAYER_CLEARCOAT: u32 = 1;

// 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.

// Input to a lighting function for a single layer (either the base layer or the
// clearcoat layer).
struct LayerLightingInput {
    // The normal vector.
    N: vec3<f32>,
    // The reflected vector.
    R: vec3<f32>,
    // The normal vector ⋅ the view vector.
    NdotV: f32,

    // The perceptual roughness of the layer.
    perceptual_roughness: f32,
    // The roughness of the layer.
    roughness: f32,
}

// Input to a lighting function (`point_light`, `spot_light`,
// `directional_light`).
struct LightingInput {
#ifdef STANDARD_MATERIAL_CLEARCOAT
    layers: array<LayerLightingInput, 2>,
#else   // STANDARD_MATERIAL_CLEARCOAT
    layers: array<LayerLightingInput, 1>,
#endif  // STANDARD_MATERIAL_CLEARCOAT

    // The world-space position.
    P: vec3<f32>,
    // The vector to the light.
    V: vec3<f32>,

    // The diffuse color of the material.
    diffuse_color: vec3<f32>,

    // Specular reflectance at the normal incidence angle.
    //
    // This should be read F₀, but due to Naga limitations we can't name it that.
    F0_: vec3<f32>,
    // Constants for the BRDF approximation.
    //
    // See `EnvBRDFApprox` in
    // <https://www.unrealengine.com/en-US/blog/physically-based-shading-on-mobile>.
    // What we call `F_ab` they call `AB`.
    F_ab: vec2<f32>,

#ifdef STANDARD_MATERIAL_CLEARCOAT
    // The strength of the clearcoat layer.
    clearcoat_strength: f32,
#endif  // STANDARD_MATERIAL_CLEARCOAT
}

// Values derived from the `LightingInput` for both diffuse and specular lights.
struct DerivedLightingInput {
    // The half-vector between L, the incident light vector, and V, the view
    // vector.
    H: vec3<f32>,
    // The normal vector ⋅ the incident light vector.
    NdotL: f32,
    // The normal vector ⋅ the half-vector.
    NdotH: f32,
    // The incident light vector ⋅ the half-vector.
    LdotH: f32,
}

// 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, NdotH: f32, h: vec3<f32>) -> f32 {
    let oneMinusNdotHSquared = 1.0 - NdotH * NdotH;
    let a = NdotH * roughness;
    let k = roughness / (oneMinusNdotHSquared + 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, NdotV: f32, NdotL: f32) -> f32 {
    let a2 = roughness * roughness;
    let lambdaV = NdotL * sqrt((NdotV - a2 * NdotV) * NdotV + a2);
    let lambdaL = NdotV * sqrt((NdotL - a2 * NdotL) * NdotL + a2);
    let v = 0.5 / (lambdaV + lambdaL);
    return v;
}

// A simpler, but nonphysical, alternative to Smith-GGX. We use this for
// clearcoat, per the Filament spec.
//
// https://google.github.io/filament/Filament.html#materialsystem/clearcoatmodel#toc4.9.1
fn V_Kelemen(LdotH: f32) -> f32 {
    return 0.25 / (LdotH * LdotH);
}

// 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<f32>, f90: f32, VdotH: f32) -> vec3<f32> {
    // not using mix to keep the vec3 and float versions identical
    return f0 + (f90 - f0) * pow(1.0 - VdotH, 5.0);
}

fn F_Schlick(f0: f32, f90: f32, VdotH: f32) -> f32 {
    // not using mix to keep the vec3 and float versions identical
    return f0 + (f90 - f0) * pow(1.0 - VdotH, 5.0);
}

fn fresnel(f0: vec3<f32>, LdotH: f32) -> vec3<f32> {
    // f_90 suitable for ambient occlusion
    // see https://google.github.io/filament/Filament.html#lighting/occlusion
    let f90 = saturate(dot(f0, vec3<f32>(50.0 * 0.33)));
    return F_Schlick_vec(f0, f90, LdotH);
}

// Specular BRDF
// https://google.github.io/filament/Filament.html#materialsystem/specularbrdf

// N, V, and L must all be normalized.
fn derive_lighting_input(N: vec3<f32>, V: vec3<f32>, L: vec3<f32>) -> DerivedLightingInput {
    var input: DerivedLightingInput;
    var H: vec3<f32> = normalize(L + V);
    input.H = H;
    input.NdotL = saturate(dot(N, L));
    input.NdotH = saturate(dot(N, H));
    input.LdotH = saturate(dot(L, H));
    return input;
}

// Returns L in the `xyz` components and the specular intensity in the `w` component.
fn compute_specular_layer_values_for_point_light(
    input: ptr<function, LightingInput>,
    layer: u32,
    V: vec3<f32>,
    light_to_frag: vec3<f32>,
    light_position_radius: f32,
) -> vec4<f32> {
    // Unpack.
    let R = (*input).layers[layer].R;
    let a = (*input).layers[layer].roughness;

    // Representative Point Area Lights.
    // see http://blog.selfshadow.com/publications/s2013-shading-course/karis/s2013_pbs_epic_notes_v2.pdf p14-16
    let centerToRay = dot(light_to_frag, R) * R - light_to_frag;
    let closestPoint = light_to_frag + centerToRay * saturate(
        light_position_radius * inverseSqrt(dot(centerToRay, centerToRay)));
    let LspecLengthInverse = inverseSqrt(dot(closestPoint, closestPoint));
    let normalizationFactor = a / saturate(a + (light_position_radius * 0.5 * LspecLengthInverse));
    let intensity = normalizationFactor * normalizationFactor;

    let L: vec3<f32> = closestPoint * LspecLengthInverse; // normalize() equivalent?
    return vec4(L, intensity);
}

// 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(
    input: ptr<function, LightingInput>,
    derived_input: ptr<function, DerivedLightingInput>,
    specular_intensity: f32,
) -> vec3<f32> {
    // Unpack.
    let roughness = (*input).layers[LAYER_BASE].roughness;
    let NdotV = (*input).layers[LAYER_BASE].NdotV;
    let F0 = (*input).F0_;
    let F_ab = (*input).F_ab;
    let H = (*derived_input).H;
    let NdotL = (*derived_input).NdotL;
    let NdotH = (*derived_input).NdotH;
    let LdotH = (*derived_input).LdotH;

    // Calculate distribution.
    let D = D_GGX(roughness, NdotH, H);
    // Calculate visibility.
    let V = V_SmithGGXCorrelated(roughness, NdotV, NdotL);
    // Calculate the Fresnel term.
    let F = fresnel(F0, LdotH);

    // Calculate the specular light.
    // Multiscattering approximation:
    // <https://google.github.io/filament/Filament.html#listing_energycompensationimpl>
    var Fr = (specular_intensity * D * V) * F;
    Fr *= 1.0 + F0 * (1.0 / F_ab.x - 1.0);
    return Fr;
}

// Calculates the specular light for the clearcoat layer. Returns Fc, the
// Fresnel term, in the first channel, and Frc, the specular clearcoat light, in
// the second channel.
//
// <https://google.github.io/filament/Filament.html#listing_clearcoatbrdf>
fn specular_clearcoat(
    input: ptr<function, LightingInput>,
    derived_input: ptr<function, DerivedLightingInput>,
    clearcoat_strength: f32,
    specular_intensity: f32,
) -> vec2<f32> {
    // Unpack.
    let roughness = (*input).layers[LAYER_CLEARCOAT].roughness;
    let H = (*derived_input).H;
    let NdotH = (*derived_input).NdotH;
    let LdotH = (*derived_input).LdotH;

    // Calculate distribution.
    let Dc = D_GGX(roughness, NdotH, H);
    // Calculate visibility.
    let Vc = V_Kelemen(LdotH);
    // Calculate the Fresnel term.
    let Fc = F_Schlick(0.04, 1.0, LdotH) * clearcoat_strength;
    // Calculate the specular light.
    let Frc = (specular_intensity * Dc * Vc) * Fc;
    return vec2(Fc, Frc);
}

// 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(
    input: ptr<function, LightingInput>,
    derived_input: ptr<function, DerivedLightingInput>,
) -> f32 {
    // Unpack.
    let roughness = (*input).layers[LAYER_BASE].roughness;
    let NdotV = (*input).layers[LAYER_BASE].NdotV;
    let NdotL = (*derived_input).NdotL;
    let LdotH = (*derived_input).LdotH;

    let f90 = 0.5 + 2.0 * roughness * LdotH * LdotH;
    let lightScatter = F_Schlick(1.0, f90, NdotL);
    let viewScatter = F_Schlick(1.0, f90, NdotV);
    return lightScatter * viewScatter * (1.0 / PI);
}

// Scale/bias approximation
// https://www.unrealengine.com/en-US/blog/physically-based-shading-on-mobile
// TODO: Use a LUT (more accurate)
fn F_AB(perceptual_roughness: f32, NdotV: f32) -> vec2<f32> {
    let c0 = vec4<f32>(-1.0, -0.0275, -0.572, 0.022);
    let c1 = vec4<f32>(1.0, 0.0425, 1.04, -0.04);
    let r = perceptual_roughness * c0 + c1;
    let a004 = min(r.x * r.x, exp2(-9.28 * NdotV)) * r.x + r.y;
    return vec2<f32>(-1.04, 1.04) * a004 + r.zw;
}

fn EnvBRDFApprox(F0: vec3<f32>, F_ab: vec2<f32>) -> vec3<f32> {
    return F0 * F_ab.x + F_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;
}

fn point_light(light_id: u32, input: ptr<function, LightingInput>) -> vec3<f32> {
    // Unpack.
    let diffuse_color = (*input).diffuse_color;
    let P = (*input).P;
    let N = (*input).layers[LAYER_BASE].N;
    let V = (*input).V;

    let light = &view_bindings::point_lights.data[light_id];
    let light_to_frag = (*light).position_radius.xyz - P;
    let distance_square = dot(light_to_frag, light_to_frag);
    let rangeAttenuation = getDistanceAttenuation(distance_square, (*light).color_inverse_square_range.w);

    // Base layer

    let specular_L_intensity = compute_specular_layer_values_for_point_light(
        input,
        LAYER_BASE,
        V,
        light_to_frag,
        (*light).position_radius.w,
    );
    var specular_derived_input = derive_lighting_input(N, V, specular_L_intensity.xyz);

    let specular_intensity = specular_L_intensity.w;
    let specular_light = specular(input, &specular_derived_input, specular_intensity);

    // Clearcoat

#ifdef STANDARD_MATERIAL_CLEARCOAT
    // Unpack.
    let clearcoat_N = (*input).layers[LAYER_CLEARCOAT].N;
    let clearcoat_strength = (*input).clearcoat_strength;

    // Perform specular input calculations again for the clearcoat layer. We
    // can't reuse the above because the clearcoat normal might be different
    // from the main layer normal.
    let clearcoat_specular_L_intensity = compute_specular_layer_values_for_point_light(
        input,
        LAYER_CLEARCOAT,
        V,
        light_to_frag,
        (*light).position_radius.w,
    );
    var clearcoat_specular_derived_input =
        derive_lighting_input(clearcoat_N, V, clearcoat_specular_L_intensity.xyz);

    // Calculate the specular light.
    let clearcoat_specular_intensity = clearcoat_specular_L_intensity.w;
    let Fc_Frc = specular_clearcoat(
        input,
        &clearcoat_specular_derived_input,
        clearcoat_strength,
        clearcoat_specular_intensity
    );
    let inv_Fc = 1.0 - Fc_Frc.r;    // Inverse Fresnel term.
    let Frc = Fc_Frc.g;             // Clearcoat light.
#endif  // STANDARD_MATERIAL_CLEARCOAT

    // Diffuse.
    // Comes after specular since its N⋅L is used in the lighting equation.
    let L = normalize(light_to_frag);
    var derived_input = derive_lighting_input(N, V, L);
    let diffuse = diffuse_color * Fd_Burley(input, &derived_input);

    // 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 rangeAttenuation = 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

    var color: vec3<f32>;
#ifdef STANDARD_MATERIAL_CLEARCOAT
    // Account for the Fresnel term from the clearcoat darkening the main layer.
    //
    // <https://google.github.io/filament/Filament.html#materialsystem/clearcoatmodel/integrationinthesurfaceresponse>
    color = (diffuse + specular_light * inv_Fc) * inv_Fc + Frc;
#else   // STANDARD_MATERIAL_CLEARCOAT
    color = diffuse + specular_light;
#endif  // STANDARD_MATERIAL_CLEARCOAT

    return color * (*light).color_inverse_square_range.rgb *
        (rangeAttenuation * derived_input.NdotL);
}

fn spot_light(light_id: u32, input: ptr<function, LightingInput>) -> vec3<f32> {
    // reuse the point light calculations
    let point_light = point_light(light_id, input);

    let light = &view_bindings::point_lights.data[light_id];

    // reconstruct spot dir from x/z and y-direction flag
    var spot_dir = vec3<f32>((*light).light_custom_data.x, 0.0, (*light).light_custom_data.y);
    spot_dir.y = sqrt(max(0.0, 1.0 - spot_dir.x * spot_dir.x - spot_dir.z * spot_dir.z));
    if ((*light).flags & POINT_LIGHT_FLAGS_SPOT_LIGHT_Y_NEGATIVE) != 0u {
        spot_dir.y = -spot_dir.y;
    }
    let light_to_frag = (*light).position_radius.xyz - (*input).P.xyz;

    // calculate attenuation based on filament formula https://google.github.io/filament/Filament.html#listing_glslpunctuallight
    // spot_scale and spot_offset have been precomputed
    // note we normalize here to get "l" from the filament listing. spot_dir is already normalized
    let cd = dot(-spot_dir, normalize(light_to_frag));
    let attenuation = saturate(cd * (*light).light_custom_data.z + (*light).light_custom_data.w);
    let spot_attenuation = attenuation * attenuation;

    return point_light * spot_attenuation;
}

fn directional_light(light_id: u32, input: ptr<function, LightingInput>) -> vec3<f32> {
    // Unpack.
    let diffuse_color = (*input).diffuse_color;
    let NdotV = (*input).layers[LAYER_BASE].NdotV;
    let N = (*input).layers[LAYER_BASE].N;
    let V = (*input).V;
    let roughness = (*input).layers[LAYER_BASE].roughness;

    let light = &view_bindings::lights.directional_lights[light_id];

    let incident_light = (*light).direction_to_light.xyz;
    var derived_input = derive_lighting_input(N, V, incident_light);

    let diffuse = diffuse_color * Fd_Burley(input, &derived_input);

    let specular_light = specular(input, &derived_input, 1.0);

#ifdef STANDARD_MATERIAL_CLEARCOAT
    let clearcoat_N = (*input).layers[LAYER_CLEARCOAT].N;
    let clearcoat_strength = (*input).clearcoat_strength;

    // Perform specular input calculations again for the clearcoat layer. We
    // can't reuse the above because the clearcoat normal might be different
    // from the main layer normal.
    var derived_clearcoat_input = derive_lighting_input(clearcoat_N, V, incident_light);

    let Fc_Frc =
        specular_clearcoat(input, &derived_clearcoat_input, clearcoat_strength, 1.0);
    let inv_Fc = 1.0 - Fc_Frc.r;
    let Frc = Fc_Frc.g;
#endif  // STANDARD_MATERIAL_CLEARCOAT

    var color: vec3<f32>;
#ifdef STANDARD_MATERIAL_CLEARCOAT
    // Account for the Fresnel term from the clearcoat darkening the main layer.
    //
    // <https://google.github.io/filament/Filament.html#materialsystem/clearcoatmodel/integrationinthesurfaceresponse>
    color = (diffuse + specular_light * inv_Fc) * inv_Fc * derived_input.NdotL +
        Frc * derived_clearcoat_input.NdotL;
#else   // STANDARD_MATERIAL_CLEARCOAT
    color = (diffuse + specular_light) * derived_input.NdotL;
#endif  // STANDARD_MATERIAL_CLEARCOAT

    return color * (*light).color.rgb;
}