vec3.h

#ifndef VEC3_H
#define VEC3_H

#include "rtweekend.h"

#include <cmath>
#include <iostream>

using std::sqrt;

class vec3{
public:
  vec3(){
    e[0] = 0;
    e[1] = 0;
    e[2] = 0;
  };
  vec3(double e0, double e1, double e2) {
    e[0] = e0;
    e[1] = e1;
    e[2] = 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));
  }

  bool near_zero() const {
    // return true if the vector is close to zero in all dimensions
    const auto s = 1e-8;
    return (fabs(e[0]) < s) && (fabs(e[1]) < s) && (fabs(e[2]) < s);
  }
public:
  double e[3];
};

using point3 = vec3;
using 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; // this * means the above code, smart
}

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(){
  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 the hemisphere as the normal
    return in_unit_sphere;
  else
    return -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;
  }
}

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 cost_theta = fmin(dot(-uv, n), 1.0);
  vec3 r_out_perp = etai_over_etat * (uv + cost_theta * n);
  vec3 r_out_parallel = -sqrt(fabs(1.0 - r_out_perp.length_squared())) * n;
  return r_out_perp + r_out_parallel;
}

#endif