pbrt/src/shapes/sphere.rs

358 lines
14 KiB
Rust

use super::{
Bounds3f, DirectionCone, Float, Interaction, Normal3f, PI, Point2f, Point3f, Point3fi,
QuadricIntersection, Ray, ShapeIntersection, ShapeSample, ShapeSampleContext, ShapeTrait,
SphereShape, SurfaceInteraction, Transform, Vector3f, Vector3fi,
};
use crate::core::interaction::InteractionTrait;
use crate::core::pbrt::{clamp_t, gamma};
use crate::geometry::{Frame, Sqrt, VectorLike, spherical_direction};
use crate::utils::interval::Interval;
use crate::utils::math::{difference_of_products, radians, safe_acos, safe_sqrt, square};
use crate::utils::sampling::sample_uniform_sphere;
use std::mem;
use std::sync::Arc;
impl SphereShape {
pub fn new(
render_from_object: Arc<Transform<Float>>,
object_from_render: Arc<Transform<Float>>,
reverse_orientation: bool,
radius: Float,
z_min: Float,
z_max: Float,
phi_max: Float,
) -> Self {
let theta_z_min = clamp_t(z_min.min(z_max) / radius, -1., 1.).acos();
let theta_z_max = clamp_t(z_max.min(z_max) / radius, -1., 1.).acos();
let phi_max = radians(clamp_t(phi_max, 0., 360.0));
Self {
render_from_object: render_from_object.clone(),
object_from_render: object_from_render.clone(),
radius,
z_min: clamp_t(z_min.min(z_max), -radius, radius),
z_max: clamp_t(z_min.max(z_max), -radius, radius),
theta_z_max,
theta_z_min,
phi_max,
reverse_orientation,
transform_swap_handedness: render_from_object.swaps_handedness(),
}
}
fn basic_intersect(&self, ray: &Ray, t_max: Float) -> Option<QuadricIntersection> {
let oi: Point3fi = self
.object_from_render
.apply_to_interval(&Point3fi::new_from_point(ray.o));
let di: Vector3fi = self
.object_from_render
.apply_to_interval(&Point3fi::new_from_point(Point3f::from(ray.d)))
.into();
let a: Interval = square(di.x()) + square(di.y()) + square(di.z());
let b: Interval = 2. * (di.x() * oi.x() + di.y() * oi.y() + di.z() * oi.z());
let c: Interval =
square(oi.x()) + square(oi.y()) + square(oi.z()) - square(Interval::new(self.radius));
let v: Vector3fi = (oi - b / Vector3fi::from((2. * a) * di)).into();
let length: Interval = v.norm();
let discrim =
4. * a * (Interval::new(self.radius) + length) * (Interval::new(self.radius) - length);
if discrim.low < 0. {
return None;
}
let root_discrim = discrim.sqrt();
let q = if Float::from(b) < 0. {
-0.5 * (b - root_discrim)
} else {
-0.5 * (b + root_discrim)
};
let mut t0 = q / a;
let mut t1 = c / q;
if t0.low > t1.low {
mem::swap(&mut t0, &mut t1);
}
if t0.high > t_max || t1.low < 0. {
return None;
}
let mut t_shape_hit = t0;
if t_shape_hit.low <= 0. {
t_shape_hit = t1;
if t_shape_hit.high > t_max {
return None;
}
}
let mut p_hit = Point3f::from(oi) + Float::from(t_shape_hit) * Vector3f::from(di);
if p_hit.x() == 0. && p_hit.y() == 0. {
p_hit[0] = 1e-5 * self.radius;
}
let mut phi = p_hit.y().atan2(p_hit.x());
if phi < 0. {
phi += 2. * PI;
}
if self.z_min > -self.radius && p_hit.z() < self.z_min
|| self.z_max < self.radius && p_hit.z() > self.z_max
|| phi > self.phi_max
{
if t_shape_hit == t1 {
return None;
}
if t1.high > t_max {
return None;
}
t_shape_hit = t1;
let mut p_hit_vec =
Vector3f::from(Point3f::from(oi) + Float::from(t_shape_hit) * Vector3f::from(di));
p_hit_vec *= self.radius / p_hit.distance(Point3f::zero());
p_hit = Point3f::from(p_hit_vec);
if p_hit.x() == 0. && p_hit.y() == 0. {
p_hit[0] = 1e-5 * self.radius;
}
phi = p_hit.y().atan2(p_hit.x());
if phi < 0. {
phi += 2. * PI;
}
if self.z_min > -self.radius && p_hit.z() < self.z_min
|| self.z_max < self.radius && p_hit.z() > self.z_max
|| phi > self.phi_max
{
return None;
}
}
Some(QuadricIntersection::new(t_shape_hit.into(), p_hit, phi))
}
fn interaction_from_intersection(
&self,
isect: QuadricIntersection,
wo: Vector3f,
time: Float,
) -> SurfaceInteraction {
let p_hit = isect.p_obj;
let phi = isect.phi;
let u = phi / self.phi_max;
let cos_theta = p_hit.z() / self.radius;
let theta = safe_acos(cos_theta);
let v = (theta - self.theta_z_min) / (self.theta_z_max - self.theta_z_min);
let z_radius = (square(p_hit.x()) + square(p_hit.y())).sqrt();
let cos_phi = p_hit.x() / z_radius;
let sin_phi = p_hit.y() / z_radius;
let dpdu = Vector3f::new(-self.phi_max * p_hit.y(), self.phi_max * p_hit.x(), 0.);
let sin_theta = safe_sqrt(1. - square(cos_theta));
let dpdv = (self.theta_z_max - self.theta_z_min)
* Vector3f::new(
p_hit.z() * cos_phi,
p_hit.z() * sin_phi,
-self.radius * sin_theta,
);
let d2pduu = -self.phi_max * self.phi_max * Vector3f::new(p_hit.x(), p_hit.y(), 0.);
let d2pduv = (self.theta_z_max - self.theta_z_min)
* p_hit.z()
* self.phi_max
* Vector3f::new(-sin_phi, cos_phi, 0.);
let d2pdvv = -square(self.theta_z_max - self.theta_z_min) * Vector3f::from(p_hit);
let e = dpdu.dot(dpdu);
let f = dpdu.dot(dpdv);
let g = dpdv.dot(dpdv);
let n = dpdu.cross(dpdv).normalize();
let e_min = n.dot(d2pduu);
let f_min = n.dot(d2pduv);
let g_min = n.dot(d2pdvv);
let efg2 = difference_of_products(e, g, f, f);
let inv_efg2 = if efg2 == 0. { 0. } else { 1. / efg2 };
let dndu = Normal3f::from(
(f_min * f - e_min * g) * inv_efg2 * dpdu + (e_min * f - f_min * e) * inv_efg2 * dpdv,
);
let dndv = Normal3f::from(
(g_min * f - f_min * g) * inv_efg2 * dpdu + (f_min * f - g_min * e) * inv_efg2 * dpdv,
);
let p_error = gamma(5) * Vector3f::from(p_hit).abs();
let flip_normal = self.reverse_orientation ^ self.transform_swap_handedness;
let wo_object = self.object_from_render.apply_to_vector(wo);
SurfaceInteraction::new(
Point3fi::new_with_error(p_hit, p_error),
Point2f::new(u, v),
wo_object,
dpdu,
dpdv,
dndu,
dndv,
time,
flip_normal,
)
}
}
impl ShapeTrait for SphereShape {
fn bounds(&self) -> Bounds3f {
self.render_from_object
.apply_to_bounds(Bounds3f::from_points(
Point3f::new(-self.radius, -self.radius, self.z_min),
Point3f::new(self.radius, self.radius, self.z_max),
))
}
fn normal_bounds(&self) -> DirectionCone {
DirectionCone::entire_sphere()
}
fn area(&self) -> Float {
self.phi_max * self.radius * (self.z_max - self.z_min)
}
fn pdf(&self, _interaction: &Interaction) -> Float {
1. / self.area()
}
fn intersect(&self, ray: &Ray, t_max: Option<Float>) -> Option<ShapeIntersection> {
let t = t_max.unwrap_or(Float::INFINITY);
if let Some(isect) = self.basic_intersect(ray, t) {
let intr = self.interaction_from_intersection(isect.clone(), -ray.d, ray.time);
Some(ShapeIntersection::new(intr, isect.t_hit))
} else {
None
}
}
fn intersect_p(&self, ray: &Ray, t_max: Option<Float>) -> bool {
if let Some(t) = t_max {
self.basic_intersect(ray, t).is_some()
} else {
self.basic_intersect(ray, Float::INFINITY).is_some()
}
}
fn pdf_from_context(&self, ctx: &ShapeSampleContext, wi: Vector3f) -> Float {
let p_center = self
.object_from_render
.apply_to_point(Point3f::new(0., 0., 0.));
let p_origin = ctx.offset_ray_origin(p_center.into());
// Return solid angle PDF for point inside sphere
if p_origin.distance_squared(p_center) <= square(self.radius) {
let ray = ctx.spawn_ray(wi);
let isect = self.intersect(&ray, None).expect("Return 0");
let absdot = isect.intr.n().dot(-Normal3f::from(wi));
// Compute PDF in solid angle measure from shape intersection point
let pdf = (1. / self.area()) / (absdot / ctx.p().distance_squared(isect.intr.p()));
if pdf.is_infinite() {
return 0.;
}
return pdf;
}
let sin2_theta_max = self.radius * self.radius / ctx.p().distance_squared(p_center);
let cos_theta_max = safe_sqrt(1. - sin2_theta_max);
let mut one_minus_cos_theta_max = 1. - cos_theta_max;
// Compute more accurate cos theta max for small solid angle
if sin2_theta_max < 0.00068523 {
one_minus_cos_theta_max = sin2_theta_max / 2.;
}
1. / (2. * PI * one_minus_cos_theta_max)
}
fn sample(&self, u: Point2f) -> Option<ShapeSample> {
let p_obj = Point3f::new(0., 0., 0.) + self.radius * sample_uniform_sphere(u);
let mut p_obj_vec = Vector3f::from(p_obj);
p_obj_vec *= self.radius / p_obj.distance(Point3f::zero());
let p_obj_error = gamma(5) * p_obj_vec.abs();
let n_obj = Normal3f::from(p_obj_vec);
let mut n = self.render_from_object.apply_to_normal(n_obj).normalize();
if self.reverse_orientation {
n *= -1.;
}
let theta = safe_acos(p_obj_vec.z() / self.radius);
let mut phi = p_obj_vec.y().atan2(p_obj_vec.x());
if phi < 0. {
phi += 2. * PI;
}
let uv = Point2f::new(
phi / self.phi_max,
(theta - self.theta_z_min) / (self.theta_z_max - self.theta_z_min),
);
let pi = self
.render_from_object
.apply_to_interval(&Point3fi::new_with_error(
Point3f::from(p_obj_vec),
p_obj_error,
));
let si = SurfaceInteraction::new_simple(pi, n, uv);
Some(ShapeSample {
intr: Arc::new(si),
pdf: 1. / self.area(),
})
}
fn sample_from_context(&self, ctx: &ShapeSampleContext, u: Point2f) -> Option<ShapeSample> {
let p_center = self.render_from_object.apply_to_point(Point3f::zero());
let p_origin = ctx.offset_ray_origin_from_point(p_center);
if p_origin.distance_squared(p_center) <= square(self.radius) {
let mut ss = self.sample(u)?;
let intr = Arc::make_mut(&mut ss.intr);
intr.get_common_mut().time = ctx.time;
let mut wi = ss.intr.p() - ctx.p();
if wi.norm_squared() == 0. {
return None;
}
wi = wi.normalize();
ss.pdf =
Vector3f::from(ss.intr.n()).dot(-wi).abs() / ctx.p().distance_squared(ss.intr.p());
if ss.pdf.is_infinite() {
return None;
}
return Some(ss);
}
let sin_theta_max = self.radius / ctx.p().distance(p_center);
let sin2_theta_max = square(sin_theta_max);
let cos_theta_max = safe_sqrt(1. - sin2_theta_max);
let mut one_minus_cos_theta_max = 1. - cos_theta_max;
let mut cos_theta = (cos_theta_max - 1.) * u[0] + 1.;
let mut sin2_theta = 1. - square(cos_theta);
// Compute more accurate cos theta max for small solid angle
if sin2_theta_max < 0.00068523 {
sin2_theta = sin2_theta_max * u[0];
cos_theta = (1. - sin2_theta).sqrt();
one_minus_cos_theta_max = sin2_theta_max / 2.;
}
// Compute angle alpha from center of sphere to sampled point on surface
let cos_alpha = sin2_theta / sin_theta_max
+ cos_theta * safe_sqrt(1. - sin2_theta / square(sin_theta_max));
let sin_alpha = safe_sqrt(1. - square(cos_alpha));
let phi = u[1] * 2. * PI;
let w = spherical_direction(sin_alpha, cos_alpha, phi);
let sampling_frame = Frame::from_z((p_center - ctx.p()).normalize());
let mut n: Normal3f = sampling_frame.from_local(-w).into();
let p = p_center + self.radius * Vector3f::from(n);
if self.reverse_orientation {
n *= -1.;
}
let p_error = gamma(5) * Vector3f::from(p).abs();
// Compute (u, v) coordinates for sampled point on sphere
let p_obj = self.object_from_render.apply_to_point(Point3f::from(p));
let theta = safe_acos(p_obj.z() / self.radius);
let mut sphere_phi = p_obj.y().atan2(p_obj.x());
if sphere_phi < 0. {
sphere_phi += 2. * PI;
}
let uv = Point2f::new(
sphere_phi / self.phi_max,
(theta - self.theta_z_min) / (self.theta_z_max - self.theta_z_min),
);
let pi = Point3fi::new_with_error(p_obj, p_error);
let si = SurfaceInteraction::new_simple(pi, n, uv);
Some(ShapeSample {
intr: Arc::new(si),
pdf: 1. / (2. * PI * one_minus_cos_theta_max),
})
}
}