sphere.h

#ifndef SPHERE_H
#define SPHERE_H

#include "hittable.h"
#include "vec3.h"

class sphere : public hittable {
    public:
	sphere() {}
	sphere(point3 cen, double r, shared_ptr<material> m) : center(cen), radius(r), mat_ptr(m) {};

	virtual bool hit(
	    const ray& r, double t_min, double t_max, hit_record& rec) const override;

	virtual bool bounding_box(double time0, double time1, aabb& output_box) const override;

    public:
	point3 center;
	double radius;
	shared_ptr<material> mat_ptr;

    private:
	static void get_sphere_uv(const point3& p, double& u, double& v) {
	    // p: a given point on the sphere of radius one, centered at the origin.
	    // u: returned value [0,1] of angle around the Y axis from X=-1.
	    // v: returned value [0,1] of angle from Y=-1 to Y=+1.
	    //	   <1 0 0> yields <0.50 0.50>	    <-1 0 0> yields <0.00 0.50>
	    //	   <0 1 0> yields <0.50 1.00>	    <0 -1 0> yields <0.50 0.00>
	    //	   <0 0 1> yields <0.25 0.50>	    <0 0 -1> yields <0.75 0.50>

	    auto theta = acos(-p.y());
	    auto phi = atan2(-p.z(), p.x()) + pi;

	    u = phi / (2*pi);
	    v = theta / pi;
	}
};

bool sphere::hit(const ray& r, double t_min, double t_max, hit_record& rec) const {
    vec3 oc = r.origin() - center;
    auto a = r.direction().length_squared();
    auto half_b = dot(oc, r.direction());
    auto c = oc.length_squared() - radius*radius;

    auto discriminant = half_b*half_b - a*c;
    if (discriminant < 0) return false;
    auto sqrtd = sqrt(discriminant);

    // Find the nearest root that lies in the acceptable range.
    auto root = (-half_b - sqrtd) / a;
    if (root < t_min || t_max < root) {
	root = (-half_b + sqrtd) / a;
	if (root < t_min || t_max < root)
	    return false;
    }

    rec.t = root;
    rec.p = r.at(rec.t);
    vec3 outward_normal = (rec.p - center) / radius;
    rec.set_face_normal(r, outward_normal);
    rec.mat_ptr = mat_ptr;
    get_sphere_uv(outward_normal, rec.u, rec.v);

    return true;
}

bool sphere::bounding_box(double time0, double time1, aabb& output_box) const {
    output_box = aabb(
	center - vec3(radius, radius, radius),
	center + vec3(radius, radius, radius));
    return true;
}

#endif