#ifndef VEC3_H
#define VEC3_H

#include <cmath>
#include <iostream>

using std::sqrt;

class vec3 {
	public:
		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() {
			return sqrt(length_squared());
		}

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

	public:
		double e[3];
};

// 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/(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();
}

#endif