vec3.h

#ifndef VEC3_H
#define VEC3_H

#include <cmath>
#include <iostream>

class vec3;
double dot(const vec3 &u, const vec3 &v);

class vec3 {
   public:
    double e[3];

    vec3() : e{0, 0, 0} {}
    vec3(double e0, double e1, double e2) : e{e0, e1, e2} {}

    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*=(const double t) {
        e[0] *= t;
        e[1] *= t;
        e[2] *= t;
        return *this;
    }

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

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

    double length() { return sqrt(length_squared()); }

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

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

    static vec3 random_in_unit_sphere() {
        while (true) {
            auto p = random(-1, 1);
            if (p.length_squared() >= 1) continue;
            return p;
        }
    }

    static vec3 random_unit_vector() {
        auto a = random_double(0, 2 * pi);
        auto z = random_double(-1, 1);
        auto r = sqrt(1 - z * z);
        return vec3(r * cos(a), r * sin(a), z);
    }
};

// Type aliases for vec3
using point3 = vec3;  // 3D point
using color = vec3;   // RGB color

// vec3 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]);
}

// Returns the unit vector of v
inline vec3 unit_vector(vec3 v) { return v / v.length(); }

// Returns reflected ray v with normal n
vec3 reflect(const vec3 &v, const vec3 &n) { return v - 2 * dot(v, n) * n; }

/**
 * uv: incoming ray, n: normal, etai_over_etat: eta/eta'
 */
vec3 refract(const vec3 &uv, const vec3 &n, double etai_over_etat) {
    auto cos_theta = dot(-uv, n);
    vec3 r_out_parallel = etai_over_etat * (uv + cos_theta * n);
    vec3 r_out_perp = -sqrt(1.0 - r_out_parallel.length_squared()) * n;
    return r_out_parallel + r_out_perp;
}

// Return a vector in a unit disk originated at (0, 0, 0)
vec3 random_in_unit_disk() {
    while (true) {
        auto p = vec3(random_double(-1, 1), random_double(-1, 1), 0);
        if (p.length_squared() >= 1) continue;
        return p;
    }
}

#endif