Function evaluate_brdf

tools/bloom-reference/src/main.rs:1719–1764

Evaluate the BRDF at a surface for a given outgoing (toward-eye) and incoming (toward-light) direction pair. Returns (brdf * N·L) which is what the light-transport equation actually needs, plus the PDF the BRDF sampler would have chosen for this incoming direction — used by MIS to weight NEE vs BRDF samples.

(surface: &SurfaceSample, view: Vec3, light: Vec3)

/// the PDF the BRDF sampler would have chosen for this incoming
/// direction — used by MIS to weight NEE vs BRDF samples.
fn evaluate_brdf(surface: &SurfaceSample, view: Vec3, light: Vec3) -> (Vec3, f32) {
    let n = surface.normal;
    let n_dot_v = n.dot(view).max(0.0);
    let n_dot_l = n.dot(light).max(0.0);
    if n_dot_l <= 0.0 || n_dot_v <= 0.0 {
        return (Vec3::ZERO, 0.0);
    }
    let h = (view + light).normalize_or_zero();
    let n_dot_h = n.dot(h).max(0.0);
    let v_dot_h = view.dot(h).max(0.0);

    let f0 = Vec3::splat(0.04).lerp(surface.base_color, surface.metallic);
    let alpha = surface.roughness * surface.roughness;

    // Specular: F * D * Vsmith. Vsmith is the height-correlated form
    // that already includes the 1/(4·N·V·N·L) term.
    let f = fresnel_schlick(v_dot_h, f0);
    let d = d_ggx(n_dot_h, alpha);
    let vsmith = v_smith(n_dot_v, n_dot_l, alpha);
    let specular = f * d * vsmith;

    // Diffuse: Burley (already 1/pi-normalized). Scale by (1 - F) and
    // (1 - metallic) for energy conservation.
    let fd = burley_diffuse(n_dot_l, n_dot_v, v_dot_h, surface.roughness);
    let diffuse_albedo = surface.base_color * (1.0 - surface.metallic) * (Vec3::ONE - f);
    let diffuse = diffuse_albedo * fd;

    let brdf_cos = (specular + diffuse) * n_dot_l;

    // Rough approximation of the BRDF sampler's PDF for MIS. Uses the
    // same spec/diff split heuristic as `sample_brdf`.
    let spec_weight = (f0.x + f0.y + f0.z) / 3.0;
    let diff_weight = (1.0 - spec_weight) * (1.0 - surface.metallic);
    let total = spec_weight + diff_weight + 1e-6;
    let p_spec = spec_weight / total;
    let p_diff = 1.0 - p_spec;

    // Spec PDF (GGX VNDF): D * G1(V) * max(0, V·H) / (4 * N·V * V·H).
    // We just approximate D·cos/(4·V·H) since we only need a
    // reasonable ratio for MIS — exact matching isn't required.
    let pdf_spec = d * n_dot_h / (4.0 * v_dot_h + 1e-6);
    let pdf_diff = n_dot_l / std::f32::consts::PI;
    let pdf = p_spec * pdf_spec + p_diff * pdf_diff;

    (brdf_cos, pdf.max(0.0))
}

/// Balance heuristic for MIS — weights a sample from strategy A by
/// p_a / (p_a + p_b). Standard in PBRT / Eric Veach's thesis.