vec3.h

#ifndef VEC_3H
#define VEC_3H

#include <cmath>
#include <iostream>

class vec3 {
    public:
        float e[3];

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

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

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

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

        float length() const { return std::sqrt(length_squared()); }
};

using point3 = vec3;

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

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

inline vec3 operator/(const vec3& v, float t)
{
    return 1/t * v;
}

inline float 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(const vec3& v)
{
    return v / v.length();
}

#endif