vec3.h

#pragma once

#include <cmath>
#include <iostream>

class vec3 
{
public:
    double e[3];

    vec3() : e{0.0,0.0,0.0} {}
    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];}

    double r() const { return e[0];}
    double g() const { return e[1];}
    double b() const { return e[2];}

    vec3 operator-() const { return vec3(-e[0], -e[1], -e[2]); } // Unary operator
    
    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 d)
    {
        e[0] *= d;
        e[1] *= d;
        e[2] *= d;
        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() const
    {
        return sqrt(this->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));
    }

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

using point3 = vec3;
using color = vec3;

// 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/(const 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();
    }

    vec3 random_in_unit_sphere()
    {
        while(true)
        {
            point3 p = vec3::random(-1, 1);
            if (p.length_squared() >= 1) 
                continue;
            return p;
        }
    }

    vec3 random_in_unit_vector()
    {
        return unit_vector(random_in_unit_sphere());
    }

    vec3 random_in_hemisphere(const vec3& normal)
    {
        vec3 in_unit_sphere = random_in_unit_sphere();
        if (dot(in_unit_sphere, normal) > 0.0) // In the same hemisphere as the normal
            return in_unit_sphere;
        else
            return -in_unit_sphere;
    }

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