vec3.h

#ifndef VEC3_H
#define VEC3_H

#include <cmath>
#include <iostream>
#include "util.h"

using std::sqrt;

class vec3 {
    public:
        double e[3];

        vec3() : e{0,0,0} {}
        vec3(double e1, double e2, double e3) : e{e1,e2,e3} {}

        double x() const {return e[0];}
        double y() const {return e[1];}
        double z() const {return e[2];}

        vec3 operator-() const { return vec3(-e[0], -e[1], -e[2]); }
        double operator[](int i) const {return e[i];}
        double& operator[](int i) {return e[i];}

        vec3& operator+=(const vec3 &v) {
            e[0] += v.e[0];
            e[1] += v.e[1];
            e[2] += v.e[2];
            return *this;
        }

        vec3& operator*=(float t) {
            e[0] *= t;
            e[1] *= t;
            e[2] *= t;
            return *this;
        }

        vec3& operator/=(float t) {
            return *this *= 1/t;
        }

        double length_square() const {
            return e[0]*e[0] + e[1]*e[1] + e[2]*e[2];
        }

        double length() const {
            return sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]);
        }

        static vec3 random(){
            return vec3(random_double(), random_double(), random_double());
        }

        static vec3 random(double min, double max) {
            return vec3(random_double(min,max), random_double(min,max), random_double(min,max));
        }

        bool near_zero() const {
            // Return true if the vector is close to zero in all dimensions.
            auto s = 1e-8;
            return (fabs(e[0]) < s) && (fabs(e[1]) < s) && (fabs(e[2]) < s);
        }

};

using point3 = vec3;
using color = vec3;

// Vector Utility Functions

inline std::ostream& operator<<(std::ostream &out, const vec3 &v) {
    return out << v.e[0] << ' ' << v.e[1] << ' ' << v.e[2];
}

inline vec3 operator+(const vec3 &u, const vec3 &v) {
    return vec3(u.e[0] + v.e[0], u.e[1] + v.e[1], u.e[2] + v.e[2]);
}

inline vec3 operator-(const vec3 &u, const vec3 &v) {
    return vec3(u.e[0] - v.e[0], u.e[1] - v.e[1], u.e[2] - v.e[2]);
}

inline vec3 operator*(const vec3 &u, const vec3 &v) {
    return vec3(u.e[0] * v.e[0], u.e[1] * v.e[1], u.e[2] * v.e[2]);
}

inline vec3 operator*(double t, const vec3 &v) {
    return vec3(t*v.e[0], t*v.e[1], t*v.e[2]);
}

inline vec3 operator*(const vec3 &v, double t) {
    return t * v;
}

inline vec3 operator/(vec3 v, double t) {
    return (1/t) * v;
}

inline double dot(const vec3 &u, const vec3 &v) {
    return u.e[0] * v.e[0]
         + u.e[1] * v.e[1]
         + u.e[2] * v.e[2];
}

inline vec3 cross(const vec3 &u, const vec3 &v) {
    return vec3(u.e[1] * v.e[2] - u.e[2] * v.e[1],
                u.e[2] * v.e[0] - u.e[0] * v.e[2],
                u.e[0] * v.e[1] - u.e[1] * v.e[0]);
}

inline vec3 unit_vector(vec3 v) {
    return v / v.length();
}

inline vec3 random_in_unit_sphere() {
    while (true) {
        auto p = vec3::random(-1,1);
        if (p.length() < 1) {
            return p;
        }
    }
}

// does normalizing a random vector that is randomly generated from inside a sphere guarantee then it starts from the point of intersection???
inline vec3 random_unit_vector() {
    return unit_vector(random_in_unit_sphere());
}

inline vec3 random_on_hemisphere(const vec3& normal) {
    auto ray_bounce = random_unit_vector();
    if (dot(normal, ray_bounce) <= 0) {
        // if the conditional is satisfied, it means that the ray_bounce produced goes into the object not bounce off of it
        // to guarantee that we return a ray that bounces off the object, we invert the ray bounce
        return -ray_bounce;
    }
    return ray_bounce;
}

vec3 reflect(const vec3& v, const vec3& n) {
    return v - 2*dot(v,n)*n;
}

vec3 refract(const vec3& incoming_ray, const vec3& normal, const double eta_over_eta_prime) {
    auto cos_theta = fmin(dot(-incoming_ray, normal), 1.0);
    auto r_perp = eta_over_eta_prime*(incoming_ray+(cos_theta*normal));
    auto r_parallel = -sqrt(fabs(1.0-r_perp.length_square()))*normal;
  return r_perp + r_parallel;
}

inline vec3 random_in_unit_disk() {
    while (true) {
        auto p = vec3(random_double(-1,1), random_double(-1,1), 0);
        if (p.length_square() < 1)
            return p;
    }
}

#endif