vec3.h

#ifndef VEC3_H
#define VEC3_H

#include <cmath>
#include <iostream>

using std::sqrt;

class vec3 {
 public:
  double e[3];

 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];
  }

  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));
  }
};

using point3 = vec3;
using color = 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/(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(); }

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

vec3 random_unit_vector() {
  auto a = random_double(0, 2 * pi);
  auto z = random_double(-1, 1);
  auto r = sqrt(1 - z * z);
  return vec3(r * cos(a), r * sin(a), z);
}

vec3 random_in_hemisphere(const vec3& normal) {
  vec3 in_unit_sphere = random_in_unit_sphere();
  if (dot(in_unit_sphere, normal) > 0.0)
    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 = dot(-uv, n);
  vec3 r_out_parallel = etai_over_etat * (uv + cos_theta * n);
  vec3 r_out_perp = -sqrt(1.0 - r_out_parallel.length_squared()) * n;
  return r_out_parallel + r_out_perp;
}

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;
  }
}

#endif