vec3.h

#ifndef VEC3_H
#define VEC3_H


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]; }

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

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

		static vec3 random(){
			return vec3(random_double(), random_double(), random_double());
		}

		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 (std::fabs(e[0]) < s) && (std::fabs(e[1]) < s) && (std::fabs(e[2]) < s);
		}
};

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*(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();
}

inline vec3 random_in_unit_disk(){
    while (true) {
        auto p = vec3(random_double(-1,1), random_double(-1,1), 0);
        if (p.length_squared() < 1)
            return p;
    }
}

inline vec3 random_unit_vector(){
	while(true){
		auto p = vec3::random(-1, 1);
		auto lensq = p.length_squared();
		if(1e-160 < lensq && lensq <= 1){
			return p / sqrt(lensq);
		}
	}
}

inline vec3 random_on_hemisphere(const vec3& normal){
	vec3 on_unit_sphere = random_unit_vector();
	if(dot(on_unit_sphere, normal) > 0.0)
		return on_unit_sphere;
	else
		return -on_unit_sphere;
}

inline vec3 reflect(const vec3& v, const vec3& n){
	//  assume that n is a unit vector
	return v - 2 * dot(v, n)*n;
}

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

#endif