pbrt/shared/src/shapes/cylinder.rs

use super::{
    Bounds3f, CylinderShape, DirectionCone, Float, Interaction, Normal3f, PI, Point2f, Point3f,
    Point3fi, QuadricIntersection, Ray, ShapeIntersection, ShapeSample, ShapeSampleContext,
    ShapeTrait, SurfaceInteraction, Transform, Vector3f, Vector3fi,
};
use crate::core::geometry::{Sqrt, Tuple, VectorLike};
use crate::core::interaction::InteractionTrait;
use crate::core::pbrt::gamma;
use crate::utils::interval::Interval;
use crate::utils::math::{difference_of_products, lerp, square};
use std::mem;
use std::sync::Arc;

impl CylinderShape {
    pub fn new(
        render_from_object: Arc<Transform>,
        object_from_render: Arc<Transform>,
        reverse_orientation: bool,
        radius: Float,
        z_min: Float,
        z_max: Float,
        phi_max: Float,
    ) -> Self {
        Self {
            radius,
            z_min,
            z_max,
            phi_max,
            render_from_object: render_from_object.clone(),
            object_from_render,
            reverse_orientation,
            transform_swap_handedness: render_from_object.swaps_handedness(),
        }
    }

    fn basic_intersect(&self, r: &Ray, t_max: Float) -> Option<QuadricIntersection> {
        // Transform Ray origin and direction to object space
        let oi = self
            .object_from_render
            .apply_to_interval(&Point3fi::new_from_point(r.o));
        let di = self
            .object_from_render
            .apply_to_vector_interval(&Vector3fi::new_from_vector(r.d));
        // Solve quadratic equation to find cylinder t0 and t1 values>>
        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 f = b / (2. * a);
        let vx: Interval = oi.x() - f * di.x();
        let vy: Interval = oi.y() - f * di.y();
        let length: Interval = (square(vx) + square(vy)).sqrt();
        let discrim: Interval =
            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);
        }

        // Check quadric shape t0 and t1 for nearest intersection
        if t0.high > t_max || t1.low < 0. {
            return None;
        }

        let mut t_shape_hit: Interval = t0;
        if t_shape_hit.low <= 0. {
            t_shape_hit = t1;
            if t_shape_hit.high > t_max {
                return None;
            }
        }

        // Compute cylinder hit point and phi
        let mut p_hit = Point3f::from(oi) + Float::from(t_shape_hit) * Vector3f::from(di);
        let hit_rad = (square(p_hit.x()) + square(p_hit.y())).sqrt();
        p_hit[0] *= self.radius / hit_rad;
        p_hit[1] *= self.radius / hit_rad;

        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 =
                Vector3f::from(Point3f::from(oi) + Float::from(t_shape_hit) * Vector3f::from(di));
            let hit_rad = (square(p_hit.x()) + square(p_hit.y())).sqrt();
            p_hit[0] *= self.radius / hit_rad;
            p_hit[1] *= self.radius / hit_rad;
            phi = p_hit.y().atan2(p_hit.x());
            if phi < 0. {
                phi += 2. * PI;
            }

            if p_hit.z() < self.z_min || 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 v = (p_hit.z() - self.z_min) / (self.z_max - self.z_min);
        let dpdu = Vector3f::new(-self.phi_max * p_hit.y(), self.phi_max * p_hit.x(), 0.);
        let dpdv = Vector3f::new(0., 0., self.z_max - self.z_min);
        let d2pduu = -self.phi_max * self.phi_max * Vector3f::new(p_hit.x(), p_hit.y(), 0.);
        let d2pduv = Vector3f::zero();
        let d2pdvv = Vector3f::zero();
        let e = dpdu.dot(dpdu);
        let f = dpdu.dot(dpdv);
        let g = dpdv.dot(dpdv);
        let n: Vector3f = dpdu.cross(dpdv).normalize();
        let e_min = n.dot(d2pduu);
        let f_min = n.dot(d2pduv);
        let g_min = n.dot(d2pdvv);
        // Compute dn/du and dn/dv from fundamental form coefficients
        let efg2 = difference_of_products(e, f, 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(3) * Vector3f::new(p_hit.x(), p_hit.y(), 0.).abs();
        let flip_normal = self.reverse_orientation ^ self.transform_swap_handedness;
        let wo_object = self.object_from_render.apply_to_vector(wo);
        // (*renderFromObject)
        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 CylinderShape {
    fn area(&self) -> Float {
        (self.z_max - self.z_min) * self.radius * self.phi_max
    }

    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 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(&self, _interaction: &Interaction) -> Float {
        1. / self.area()
    }

    fn pdf_from_context(&self, ctx: &ShapeSampleContext, wi: Vector3f) -> Float {
        let ray = ctx.spawn_ray(wi);
        if let Some(isect) = self.intersect(&ray, None) {
            let n = isect.intr.n();
            let absdot = Vector3f::from(n).dot(-wi).abs();
            let pdf = (1. / self.area()) / (absdot / ctx.p().distance_squared(isect.intr.p()));
            if pdf.is_infinite() {
                return 0.;
            }
            pdf
        } else {
            0.
        }
    }

    fn sample(&self, u: Point2f) -> Option<ShapeSample> {
        let z = lerp(u[0], self.z_min, self.z_max);
        let phi = u[1] * self.phi_max;
        let mut p_obj = Point3f::new(self.radius * phi.cos(), self.radius * phi.sin(), z);
        let hit_rad = (square(p_obj.x()) + square(p_obj.y())).sqrt();
        p_obj[0] *= self.radius / hit_rad;
        p_obj[1] *= self.radius / hit_rad;
        let p_obj_error = gamma(3) * Vector3f::new(p_obj.x(), p_obj.y(), 0.).abs();
        let pi = self
            .render_from_object
            .apply_to_interval(&Point3fi::new_with_error(p_obj, p_obj_error));
        let mut n = self
            .render_from_object
            .apply_to_normal(Normal3f::new(p_obj.x(), p_obj.y(), 0.))
            .normalize();
        if self.reverse_orientation {
            n *= -1.;
        }

        let uv = Point2f::new(
            phi / self.phi_max,
            (p_obj.z() - self.z_min) / (self.z_max - self.z_min),
        );
        Some(ShapeSample {
            intr: Arc::new(SurfaceInteraction::new_simple(pi, n, uv)),
            pdf: 1. / self.area(),
        })
    }

    fn sample_from_context(&self, ctx: &ShapeSampleContext, u: Point2f) -> Option<ShapeSample> {
        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;
        }
        Some(ss)
    }
}