vec3.h

#ifndef VEC3_H
#define VEC3_H

#include <cmath>
#include <iostream>


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]; }

	// for opposite direction
	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*=(double t) {
		e[0] *= t;
		e[1] *= t;
		e[2] *= t;
		return *this;
	}

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

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

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


};

// point3 is just an alias for vec3 , but useful for geometric clarity
using point3 = 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/(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(const vec3& v)
{
	return v / v.length();
}





#endif