pbrt/shared/src/shapes/bilinear.rs

722 lines
24 KiB
Rust

use super::{
BilinearIntersection, BilinearPatchShape, Bounds3f, DirectionCone, Interaction, Normal3f,
Point2f, Point3f, Point3fi, Ray, ShapeIntersection, ShapeSample, ShapeSampleContext,
ShapeTrait, SurfaceInteraction, Transform, Vector3f,
};
use crate::core::geometry::{Tuple, VectorLike, spherical_quad_area};
use crate::core::interaction::InteractionTrait;
use crate::core::pbrt::{Float, gamma};
use crate::utils::math::{SquareMatrix, clamp, difference_of_products, lerp, quadratic};
use crate::utils::mesh::BilinearPatchMesh;
use crate::utils::sampling::{
bilinear_pdf, invert_spherical_rectangle_sample, sample_bilinear, sample_spherical_rectangle,
};
use std::sync::Arc;
use std::sync::OnceLock;
struct PatchData<'a> {
mesh: &'a BilinearPatchMesh,
p00: Point3f,
p10: Point3f,
p01: Point3f,
p11: Point3f,
n: Option<[Normal3f; 4]>,
uv: Option<[Point2f; 4]>,
}
struct IntersectionData {
t: Float,
u: Float,
v: Float,
}
struct TextureDerivative {
duds: Float,
dvds: Float,
dudt: Float,
dvdt: Float,
}
static BILINEAR_MESHES: OnceLock<Vec<Arc<BilinearPatchMesh>>> = OnceLock::new();
impl BilinearPatchShape {
pub const MIN_SPHERICAL_SAMPLE_AREA: Float = 1e-4;
pub fn new(_mesh: BilinearPatchMesh, mesh_index: usize, blp_index: usize) -> Self {
let mut bp = BilinearPatchShape {
mesh_index,
blp_index,
area: 0.,
rectangle: false,
};
let (p00, p10, p01, p11) = {
let data = bp.get_data();
(data.p00, data.p10, data.p01, data.p11)
};
bp.rectangle = bp.is_rectangle(p00, p10, p01, p11);
if bp.rectangle {
bp.area = p00.distance(p01) + p00.distance(p10);
} else {
const NA: usize = 3;
let mut p = [[Point3f::default(); NA + 1]; NA + 1];
#[allow(clippy::needless_range_loop)]
for i in 0..=NA {
let u = i as Float / NA as Float;
for j in 0..=NA {
let v = j as Float / NA as Float;
p[i][j] = lerp(u, lerp(v, p00, p01), lerp(v, p10, p11));
}
}
let mut area = 0.;
for i in 0..NA {
for j in 0..NA {
let diag1 = p[i + 1][j + 1] - p[i][j];
let diag2 = p[i + 1][j] - p[i][j + 1];
let quad_area = 0.5 * diag1.cross(diag2).norm();
area += quad_area;
}
}
bp.area = area;
}
bp
}
fn mesh(&self) -> &Arc<BilinearPatchMesh> {
let meshes = BILINEAR_MESHES
.get()
.expect("Mesh has not been initialized");
&meshes[self.mesh_index]
}
fn get_data(&self) -> PatchData<'_> {
let mesh = self.mesh();
let start_index = 4 * self.blp_index;
let v = &mesh.vertex_indices[start_index..start_index + 4];
let p00: Point3f = mesh.p[v[0]];
let p10: Point3f = mesh.p[v[1]];
let p01: Point3f = mesh.p[v[2]];
let p11: Point3f = mesh.p[v[3]];
let n = mesh
.n
.as_ref()
.map(|normals| [normals[v[0]], normals[v[1]], normals[v[2]], normals[v[3]]]);
let uv = mesh
.uv
.as_ref()
.map(|uvs| [uvs[v[0]], uvs[v[1]], uvs[v[2]], uvs[v[3]]]);
PatchData {
mesh,
p00,
p10,
p01,
p11,
n,
uv,
}
}
fn is_rectangle(&self, p00: Point3f, p10: Point3f, p01: Point3f, p11: Point3f) -> bool {
if p00 == p01 || p01 == p11 || p11 == p10 || p10 == p00 {
return false;
}
let n = Normal3f::from((p10 - p00).cross(p01 - p00).normalize());
if (p11 - p00).normalize().dot(n.into()).abs() > 1e-5 {
return false;
}
let p_center_vec = Vector3f::from(p00 + p01.into() + p10.into() + p11.into()) / 4.;
let p_center = Point3f::from(p_center_vec);
let d2 = [
p00.distance_squared(p_center),
p01.distance_squared(p_center),
p10.distance_squared(p_center),
p11.distance_squared(p_center),
];
for i in 0..4 {
if (d2[i] - d2[0]).abs() / d2[0] > 1e-4 {
return false;
}
}
true
}
fn intersect_bilinear_patch(
&self,
ray: &Ray,
t_max: Float,
data: &PatchData,
) -> Option<BilinearIntersection> {
let a = (data.p10 - data.p00).cross(data.p01 - data.p11).dot(ray.d);
let c = (data.p00 - ray.o).cross(ray.d).dot(data.p01 - data.p00);
let b = (data.p10 - ray.o).cross(ray.d).dot(data.p11 - data.p10) - (a + c);
let (u1, u2) = quadratic(a, b, c)?;
let eps = gamma(10)
* (ray.o.abs().max_component_value()
+ ray.d.abs().max_component_value()
+ data.p00.abs().max_component_value()
+ data.p10.abs().max_component_value()
+ data.p01.abs().max_component_value()
+ data.p11.abs().max_component_value());
let hit1 = self.check_candidate(u1, ray, data);
let hit2 = if u1 != u2 {
self.check_candidate(u2, ray, data)
} else {
None
};
// Find best hit from candidates
[hit1, hit2]
.into_iter()
.flatten()
.filter(|hit| hit.t < t_max && hit.t > eps)
.min_by(|a, b| a.t.partial_cmp(&b.t).unwrap())
.map(|best_hit| {
BilinearIntersection::new(Point2f::new(best_hit.u, best_hit.v), best_hit.t)
})
}
fn check_candidate(&self, u: Float, ray: &Ray, data: &PatchData) -> Option<IntersectionData> {
if !(0.0..=1.0).contains(&u) {
return None;
}
let uo: Point3f = lerp(u, data.p00, data.p10);
let ud: Point3f = Point3f::from(lerp(u, data.p01, data.p11) - uo);
let deltao = uo - ray.o;
let perp = ray.d.cross(ud.into());
let p2 = perp.norm_squared();
if p2 == 0. {
return None;
}
let v_det = SquareMatrix::<Float, 3>::new([
[deltao.x(), ray.d.x(), perp.x()],
[deltao.y(), ray.d.y(), perp.y()],
[deltao.z(), ray.d.z(), perp.z()],
])
.determinant();
if !(0.0..=p2).contains(&v_det) {
return None;
}
let t_det = SquareMatrix::<Float, 3>::new([
[deltao.x(), ud.x(), perp.x()],
[deltao.y(), ud.y(), perp.y()],
[deltao.z(), ud.z(), perp.z()],
])
.determinant();
Some(IntersectionData {
t: t_det / p2,
u,
v: v_det / p2,
})
}
fn interaction_from_intersection(
&self,
data: &PatchData,
uv: Point2f,
time: Float,
wo: Vector3f,
) -> SurfaceInteraction {
// Base geom and derivatives
let p = lerp(
uv[0],
lerp(uv[1], data.p00, data.p01),
lerp(uv[1], data.p10, data.p11),
);
let mut dpdu = lerp(uv[1], data.p10, data.p11) - lerp(uv[1], data.p00, data.p01);
let mut dpdv = lerp(uv[0], data.p01, data.p11) - lerp(uv[0], data.p00, data.p10);
// If textured, apply coordinates
let (st, derivatives) = self.apply_texture_coordinates(data, uv, &mut dpdu, &mut dpdv);
// Compute second moments
let n = Normal3f::from(dpdu.cross(dpdv).normalize());
let (mut dndu, mut dndv) = self.calculate_surface_curvature(data, &dpdu, &dpdv, n);
if let Some(ref deriv) = derivatives {
let dnds = Normal3f::from(dndu * deriv.duds + dndv * deriv.dvds);
let dndt = Normal3f::from(dndu * deriv.dudt + dndv * deriv.dvdt);
dndu = dnds;
dndv = dndt;
}
let p_abs_sum = data.p00.abs()
+ Vector3f::from(data.p01.abs())
+ Vector3f::from(data.p10.abs())
+ Vector3f::from(data.p11.abs());
let p_error = gamma(6) * Vector3f::from(p_abs_sum);
let flip_normal = data.mesh.reverse_orientation ^ data.mesh.transform_swaps_handedness;
let pi = Point3fi::new_with_error(p, p_error);
let mut isect =
SurfaceInteraction::new(pi, st, wo, dpdu, dpdv, dndu, dndv, time, flip_normal);
if data.n.is_some() {
self.apply_shading_normals(&mut isect, data, uv, derivatives);
}
isect
}
fn apply_texture_coordinates(
&self,
data: &PatchData,
uv: Point2f,
dpdu: &mut Vector3f,
dpdv: &mut Vector3f,
) -> (Point2f, Option<TextureDerivative>) {
let Some(uvs) = data.uv else {
return (uv, None);
};
let uv00 = uvs[0];
let uv01 = uvs[1];
let uv10 = uvs[2];
let uv11 = uvs[3];
// Compute partial derivatives of (u, v) with respect to (s, t)
let st = lerp(uv[0], lerp(uv[1], uv00, uv01), lerp(uv[1], uv10, uv11));
let dstdu = lerp(uv[1], uv10, uv11) - lerp(uv[1], uv00, uv01);
let dstdv = lerp(uv[0], uv01, uv11) - lerp(uv[0], uv00, uv10);
let det = difference_of_products(dstdu[0], dstdv[1], dstdu[1], dstdv[0]);
let inv_det = if det == 0.0 { 0.0 } else { 1.0 / det };
let duds = dstdv[1] * inv_det;
let dvds = -dstdv[0] * inv_det;
let dudt = -dstdu[1] * inv_det;
let dvdt = dstdu[0] * inv_det;
let dpds = *dpdu * duds + *dpdv * dvds;
let mut dpdt = *dpdu * dudt + *dpdv * dvdt;
if dpdu.cross(*dpdv).dot(dpds.cross(dpdt)) < 0. {
dpdt = -dpdt;
}
*dpdu = dpds;
*dpdv = dpdt;
let factors = TextureDerivative {
duds,
dvds,
dudt,
dvdt,
};
(st, Some(factors))
}
fn calculate_base_derivatives(
&self,
data: &PatchData,
uv: Point2f,
) -> (Point3f, Vector3f, Vector3f) {
let p = lerp(
uv[0],
lerp(uv[1], data.p00, data.p01),
lerp(uv[1], data.p10, data.p11),
);
let dpdu = lerp(uv[1], data.p10, data.p11) - lerp(uv[1], data.p00, data.p01);
let dpdv = lerp(uv[0], data.p01, data.p11) - lerp(uv[0], data.p00, data.p10);
(p, dpdu, dpdv)
}
fn calculate_surface_curvature(
&self,
data: &PatchData,
dpdu: &Vector3f,
dpdv: &Vector3f,
n: Normal3f,
) -> (Normal3f, Normal3f) {
let e = dpdu.dot(*dpdu);
let f = dpdu.dot(*dpdv);
let g = dpdv.dot(*dpdv);
let d2pduv = (data.p00 - data.p01) + (data.p11 - data.p10);
let d2pduu = Vector3f::zero();
let d2pdvv = Vector3f::zero();
let e_min = n.dot(d2pduu.into());
let f_min = n.dot(d2pduv.into());
let g_min = n.dot(d2pdvv.into());
let egf2 = difference_of_products(e, g, f, f);
let inv_egf2 = if egf2 == 0. { 0. } else { 1. / egf2 };
let dndu = Normal3f::from(
(f_min * f - e_min * g) * inv_egf2 * *dpdu + (e_min * f - f_min * e) * inv_egf2 * *dpdv,
);
let dndv = Normal3f::from(
(g_min * f - f_min * g) * inv_egf2 * *dpdu + (f_min * f - g_min * e) * inv_egf2 * *dpdv,
);
(dndu, dndv)
}
fn apply_shading_normals(
&self,
isect: &mut SurfaceInteraction,
data: &PatchData,
uv: Point2f,
derivatives: Option<TextureDerivative>,
) {
let Some(normals) = data.n else { return };
let n00 = normals[1];
let n10 = normals[1];
let n01 = normals[2];
let n11 = normals[3];
let ns = lerp(uv[0], lerp(uv[1], n00, n01), lerp(uv[1], n10, n11)).normalize();
let mut dndu = lerp(uv[1], n10, n11) - lerp(uv[1], n00, n01);
let mut dndv = lerp(uv[0], n01, n11) - lerp(uv[0], n00, n10);
if let Some(deriv) = derivatives {
let dnds = dndu * deriv.duds + dndv * deriv.dvds;
let dndt = dndu * deriv.dudt + dndv * deriv.dvdt;
dndu = dnds;
dndv = dndt;
}
let r = Transform::rotate_from_to(isect.n().normalize().into(), ns.into());
isect.set_shading_geom(
ns,
r.apply_to_vector(isect.dpdu),
r.apply_to_vector(isect.dpdv),
dndu,
r.apply_to_normal(dndv),
true,
);
}
fn sample_area_and_pdf(&self, ctx: &ShapeSampleContext, u: Point2f) -> Option<ShapeSample> {
let mut ss = self.sample(u)?;
let mut intr_clone = (*ss.intr).clone();
intr_clone.common.time = ctx.time;
ss.intr = Arc::new(intr_clone);
let mut wi = ss.intr.p() - ctx.p();
let dist_sq = wi.norm_squared();
if dist_sq == 0. {
return None;
}
wi = wi.normalize();
let abs_dot = Vector3f::from(ss.intr.n()).abs_dot(-wi);
if abs_dot == 0. {
return None;
}
ss.pdf *= dist_sq / abs_dot;
if ss.pdf.is_infinite() { None } else { Some(ss) }
}
fn sample_parametric_coords(&self, data: &PatchData, u: Point2f) -> (Point2f, Float) {
if let Some(image_distrib) = &data.mesh.image_distribution {
let (uv, pdf, _) = image_distrib.sample(u);
(uv, pdf)
} else if !self.rectangle {
let w = [
(data.p10 - data.p00).cross(data.p01 - data.p00).norm(),
(data.p10 - data.p00).cross(data.p11 - data.p10).norm(),
(data.p01 - data.p00).cross(data.p11 - data.p01).norm(),
(data.p11 - data.p10).cross(data.p11 - data.p01).norm(),
];
let uv = sample_bilinear(u, &w);
let pdf = bilinear_pdf(uv, &w);
(uv, pdf)
} else {
(u, 1.0)
}
}
fn sample_solid_angle(
&self,
data: &PatchData,
ctx: &ShapeSampleContext,
u: Point2f,
corner_dirs: &[Vector3f; 4],
) -> Option<ShapeSample> {
let mut pdf = 1.;
if ctx.ns != Normal3f::zero() {
let w = [
0.01_f32.max(corner_dirs[0].dot(ctx.ns.into()).abs()),
0.01_f32.max(corner_dirs[1].dot(ctx.ns.into()).abs()),
0.01_f32.max(corner_dirs[2].dot(ctx.ns.into()).abs()),
0.01_f32.max(corner_dirs[3].dot(ctx.ns.into()).abs()),
];
let u = sample_bilinear(u, &w);
pdf *= bilinear_pdf(u, &w);
}
let eu = data.p10 - data.p00;
let ev = data.p01 - data.p00;
let (p, quad_pdf) = sample_spherical_rectangle(ctx.p(), data.p00, eu, ev, u);
pdf *= quad_pdf?;
// Compute (u, v) and surface normal for sampled points on rectangle
let uv = Point2f::new(
(p - data.p00).dot(eu) / data.p10.distance_squared(data.p00),
(p - data.p00).dot(ev) / data.p01.distance_squared(data.p00),
);
let n = self.compute_sampled_normal(data, &eu, &ev, uv);
let st = data.uv.map_or(uv, |uvs| {
lerp(
uv[0],
lerp(uv[1], uvs[0], uvs[1]),
lerp(uv[1], uvs[2], uvs[3]),
)
});
let pi = Point3fi::new_from_point(p);
let mut intr = SurfaceInteraction::new_simple(pi, n, st);
intr.common.time = ctx.time;
Some(ShapeSample {
intr: Arc::new(intr),
pdf,
})
}
fn compute_sampled_normal(
&self,
data: &PatchData,
dpdu: &Vector3f,
dpdv: &Vector3f,
uv: Point2f,
) -> Normal3f {
let mut n = Normal3f::from(dpdu.cross(*dpdv).normalize());
if let Some(normals) = data.n {
// Apply interpolated shading normal to orient the geometric normal
let ns = lerp(
uv[0],
lerp(uv[1], normals[0], normals[2]),
lerp(uv[1], normals[1], normals[3]),
);
n = n.face_forward(ns.into());
} else if data.mesh.reverse_orientation ^ data.mesh.transform_swaps_handedness {
n = -n;
}
n
}
}
impl ShapeTrait for BilinearPatchShape {
#[inline]
fn area(&self) -> Float {
self.area
}
#[inline]
fn normal_bounds(&self) -> DirectionCone {
let data = self.get_data();
if data.p00 == data.p10
|| data.p10 == data.p11
|| data.p11 == data.p01
|| data.p01 == data.p00
{
let dpdu = lerp(0.5, data.p10, data.p11) - lerp(0.5, data.p00, data.p01);
let dpdv = lerp(0.5, data.p01, data.p11) - lerp(0.5, data.p00, data.p10);
let mut n = Normal3f::from(dpdu.cross(dpdv).normalize());
if let Some(normals) = data.n {
let interp_n = (normals[0] + normals[1] + normals[2] + normals[3]) / 4.;
n = n.face_forward(interp_n.into());
} else if data.mesh.reverse_orientation ^ data.mesh.transform_swaps_handedness {
n *= -1.;
}
return DirectionCone::new_from_vector(Vector3f::from(n));
}
// Compute bilinear patch normals n10, n01, and n11
let mut n00 = Normal3f::from((data.p10 - data.p00).cross(data.p01 - data.p00).normalize());
let mut n10 = Normal3f::from((data.p11 - data.p10).cross(data.p00 - data.p10).normalize());
let mut n01 = Normal3f::from((data.p00 - data.p01).cross(data.p11 - data.p01).normalize());
let mut n11 = Normal3f::from((data.p01 - data.p11).cross(data.p10 - data.p11).normalize());
if let Some(normals) = data.n {
n00 = n00.face_forward(normals[0].into());
n10 = n10.face_forward(normals[1].into());
n01 = n01.face_forward(normals[2].into());
n11 = n11.face_forward(normals[3].into());
} else if data.mesh.reverse_orientation ^ data.mesh.transform_swaps_handedness {
n00 = -n00;
n10 = -n10;
n01 = -n01;
n11 = -n11;
}
// Compute average normal and return normal bounds for patch
let n_avg = (n00 + n10 + n01 + n11).normalize();
let cos_theta = n_avg
.dot(n00)
.min(n_avg.dot(n10))
.min(n_avg.dot(n01))
.min(n_avg.dot(n11));
DirectionCone::new(n_avg.into(), clamp(cos_theta, -1., 1.))
}
#[inline]
fn bounds(&self) -> Bounds3f {
let data = self.get_data();
Bounds3f::from_points(data.p00, data.p01).union(Bounds3f::from_points(data.p10, data.p11))
}
#[inline]
fn intersect(&self, ray: &Ray, t_max: Option<Float>) -> Option<ShapeIntersection> {
let t_max_val = t_max?;
let data = self.get_data();
if let Some(bilinear_hit) = self.intersect_bilinear_patch(ray, t_max_val, &data) {
let intr = self.interaction_from_intersection(&data, bilinear_hit.uv, ray.time, -ray.d);
Some(ShapeIntersection {
intr,
t_hit: bilinear_hit.t,
})
} else {
None
}
}
#[inline]
fn intersect_p(&self, ray: &Ray, t_max: Option<Float>) -> bool {
let t_max_val = t_max.unwrap_or(Float::INFINITY);
let data = self.get_data();
self.intersect_bilinear_patch(ray, t_max_val, &data)
.is_some()
}
#[inline]
fn sample(&self, u: Point2f) -> Option<ShapeSample> {
let data = self.get_data();
// Sample bilinear patch parametric coordinate (u, v)
let (uv, pdf) = self.sample_parametric_coords(&data, u);
// Compute bilinear patch geometric quantities at sampled (u, v)
let (p, dpdu, dpdv) = self.calculate_base_derivatives(&data, uv);
if dpdu.norm_squared() == 0. || dpdv.norm_squared() == 0. {
return None;
}
// Compute surface normal for sampled bilinear patch (u, v)
let n = self.compute_sampled_normal(&data, &dpdu, &dpdv, uv);
let st = data.uv.map_or(uv, |patch_uvs| {
lerp(
uv[0],
lerp(uv[1], patch_uvs[0], patch_uvs[1]),
lerp(uv[1], patch_uvs[2], patch_uvs[3]),
)
});
let p_abs_sum = data.p00.abs()
+ Vector3f::from(data.p01.abs())
+ Vector3f::from(data.p10.abs())
+ Vector3f::from(data.p11.abs());
let p_error = gamma(6) * Vector3f::from(p_abs_sum);
let pi = Point3fi::new_with_error(p, p_error);
Some(ShapeSample {
intr: Arc::new(SurfaceInteraction::new_simple(pi, n, st)),
pdf: pdf / dpdu.cross(dpdv).norm(),
})
}
#[inline]
fn sample_from_context(&self, ctx: &ShapeSampleContext, u: Point2f) -> Option<ShapeSample> {
let data = self.get_data();
let v00 = (data.p00 - ctx.p()).normalize();
let v10 = (data.p10 - ctx.p()).normalize();
let v01 = (data.p01 - ctx.p()).normalize();
let v11 = (data.p11 - ctx.p()).normalize();
let use_area_sampling = self.rectangle
|| data.mesh.image_distribution.is_some()
|| spherical_quad_area(v00, v10, v11, v01) <= Self::MIN_SPHERICAL_SAMPLE_AREA;
if use_area_sampling {
self.sample_area_and_pdf(ctx, u)
} else {
self.sample_solid_angle(&data, ctx, u, &[v00, v10, v01, v11])
}
}
#[inline]
fn pdf(&self, intr: &Interaction) -> Float {
let Interaction::Surface(si) = intr else {
return 0.0;
};
let data = self.get_data();
let uv = if let Some(uvs) = &data.mesh.uv {
Point2f::invert_bilinear(si.uv, uvs)
} else {
si.uv
};
let param_pdf = if let Some(image_distrib) = &data.mesh.image_distribution {
image_distrib.pdf(uv)
} else if self.rectangle {
let w = [
(data.p10 - data.p00).cross(data.p01 - data.p00).norm(),
(data.p10 - data.p00).cross(data.p11 - data.p10).norm(),
(data.p01 - data.p00).cross(data.p11 - data.p01).norm(),
(data.p11 - data.p10).cross(data.p11 - data.p01).norm(),
];
bilinear_pdf(uv, &w)
} else {
1.
};
let (_, dpdu, dpdv) = self.calculate_base_derivatives(&data, uv);
let cross = dpdu.cross(dpdv).norm();
if cross == 0. { 0. } else { param_pdf / cross }
}
#[inline]
fn pdf_from_context(&self, ctx: &ShapeSampleContext, wi: Vector3f) -> Float {
let ray = ctx.spawn_ray(wi);
let Some(isect) = self.intersect(&ray, None) else {
return 0.;
};
let data = self.get_data();
let v00 = (data.p00 - ctx.p()).normalize();
let v10 = (data.p10 - ctx.p()).normalize();
let v01 = (data.p01 - ctx.p()).normalize();
let v11 = (data.p11 - ctx.p()).normalize();
let use_area_sampling = !self.rectangle
|| data.mesh.image_distribution.is_some()
|| spherical_quad_area(v00, v10, v01, v11) <= Self::MIN_SPHERICAL_SAMPLE_AREA;
if use_area_sampling {
let intr_wrapper = Interaction::Surface(isect.intr.clone());
let isect_pdf = self.pdf(&intr_wrapper);
let distsq = ctx.p().distance_squared(isect.intr.p());
let absdot = Vector3f::from(isect.intr.n()).abs_dot(-wi);
if absdot == 0. {
return 0.;
}
let pdf = isect_pdf * distsq / absdot;
if pdf.is_infinite() { 0. } else { pdf }
} else {
let mut pdf = 1. / spherical_quad_area(v00, v10, v01, v11);
if ctx.ns != Normal3f::zero() {
let w = [
0.01_f32.max(v00.dot(ctx.ns.into()).abs()),
0.01_f32.max(v10.dot(ctx.ns.into()).abs()),
0.01_f32.max(v01.dot(ctx.ns.into()).abs()),
0.01_f32.max(v11.dot(ctx.ns.into()).abs()),
];
let u = invert_spherical_rectangle_sample(
ctx.p(),
data.p00,
data.p10 - data.p00,
data.p01 - data.p00,
isect.intr.p(),
);
pdf *= bilinear_pdf(u, &w);
}
pdf
}
}
}