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;

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

bool sphere::hit(const ray& r, double t_min, double t_max, hit_record& rec) const {
    // Equation of the sphere in vector form is: (𝐏−𝐂)⋅(𝐏−𝐂)=𝑟^2; P(t) = A + tb
    // Eqn to check if ray hits sphere: 𝑡^2𝐛⋅𝐛+2𝑡𝐛⋅(𝐀−𝐂)+(𝐀−𝐂)⋅(𝐀−𝐂)−𝑟^2=0 
    // Can use quadratic eqn, check for location of intersections
    vec3 oc = r.origin() - center;
    auto a = r.direction().length_squared(); // v • v = |v|^2
    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;
    }

    // Store useful info in hit_record
    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; 

    return true;
}

#endif