#ifndef VEC3_H
#define VEC3_H

#include <cmath>
#include <iostream>

#include "rtweekend.h"

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];
		}

		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));
		}

		bool near_zero() const {
			auto s = 1e-8;
			return fabs(e[0]) < s && fabs(e[1]) < s && fabs(e[2]) < s;
		}

	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]);
}

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

inline vec3 unit_vector(vec3 v) {
	return v / v.length();
}

vec3 random_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 thesame hemisphere as the normal
		return in_unit_sphere;
	else
		return -in_unit_sphere;
}

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

vec3 refract(const vec3& uv, const vec3& n, double etai_over_etat) {
	auto cos_theta = fmin(dot(-uv, n), 1.0);
	vec3 r_out_perp = etai_over_etat * (uv + cos_theta*n);
	vec3 r_out_parrallel = -sqrt(fabs(1.0 - r_out_perp.length_squared())) * n;
	return r_out_perp + r_out_parrallel;
}

#endif