vec3.h

#pragma once

#include <iostream>

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

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

	void write_color(std::ostream& out) {
		//write the translated [0,255] value of each colour component
		out << static_cast<int>(255.999 * e[0]) << ' '
			<< static_cast<int>(255.999 * e[1]) << ' '
			<< static_cast<int>(255.999 * e[2]) << '\n';
	}

	//returns random double in [0, 1)
	inline static vec3 random() {
		return vec3(random_double(), random_double(), random_double());
	}

	//returns random double in range
	inline static vec3 random(double min, double max) {
		return vec3(random_double(min, max), random_double(min, max), random_double(min, max));
	}

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

	

public:
	double e[3];


};


//type aliases

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/(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();
}

//keeps making new random vectors until a vector within a unit sphere is achieved
vec3 random_in_unit_sphere() {
	while (true) {
		auto p = vec3::random(-1, 1);
		if (p.length_squared() >= 1) continue;
		return p;
	}
}

//returns random unit vector within a unit sphere that has length 1
vec3 random_unit_vector() {
	return unit_vector(random_in_unit_sphere());
}

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

//returns snell's law defined reflected vector given normal and incident ray
vec3 reflect(const vec3& vector, const vec3& normal) {
	return vector - 2 * dot(vector, normal) * normal;
}

//returns refracted ray through medium depending on snell's law
vec3 refract_ray(const vec3& uv, const vec3& n, double etai_over_etat) {
	auto cos_theta = fmin(dot(-uv, n), 1.0);
	vec3 r_out_perpendicular = etai_over_etat * (uv + cos_theta * n);
	vec3 r_out_parallel = -sqrt(fabs(1.0 - r_out_perpendicular.length_squared())) * n;
	return r_out_perpendicular + r_out_parallel;
}