vec3.h

#include <math.h>
#include <stdlib.h>
#include <iostream>

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

    inline double x() const {return e[0];}
    inline double y() const {return e[1];}
    inline double z() const {return e[2];}
    inline double r() const {return e[0];}
    inline double g() const {return e[1];}
    inline double b() const {return e[2];}

    inline const vec3& operator+() const {return *this;}
    inline vec3 operator-() const {return vec3(-e[0], -e[1], -e[2]);}
    inline double operator[](int i) const {return e[i];}
    inline double& operator[](int i) {return e[i];}

    inline vec3& operator+=(const vec3& v2);
    inline vec3& operator-=(const vec3& v2);
    inline vec3& operator*=(const vec3& v2);
    inline vec3& operator/=(const vec3& v2);
    inline vec3& operator*=(const double t);
    inline vec3& operator/=(const double t);

    inline double length() const {
      return sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]);
    }
    inline double squaredLength() const {
      return e[0]*e[0] + e[1]*e[1] + e[2]*e[2];
    }
    inline void makeUnitVector();

    double e[3];
};

inline std::istream& operator>>(std::istream &is, vec3 &t) {
  is >> t.e[0] >> t.e[1] >> t.e[2];
  return is;
}

inline std::ostream& operator<<(std::ostream &os, const vec3 &t) {
  os << t.e[0] <<  " " << t.e[1] << " " << t.e[2];
  return os;
}

inline void vec3::makeUnitVector() {
  double k = 1.0 / sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]);
  e[0] *= k;
  e[1] *= k;
  e[2] *= k;
}

inline vec3 operator+(const vec3 &v1, const vec3 &v2) {
  return vec3(v1.e[0] + v2.e[0], v1.e[1] + v2.e[1], v1.e[2] + v2.e[2]);
}

inline vec3 operator-(const vec3 &v1, const vec3 &v2) {
  return vec3(v1.e[0] - v2.e[0], v1.e[1] - v2.e[1], v1.e[2] - v2.e[2]);
}

inline vec3 operator*(const vec3 &v1, const vec3 &v2) {
  return vec3(v1.e[0] * v2.e[0], v1.e[1] * v2.e[1], v1.e[2] * v2.e[2]);
}

inline vec3 operator/(const vec3 &v1, const vec3 &v2) {
  return vec3(v1.e[0] / v2.e[0], v1.e[1] / v2.e[1], v1.e[2] / v2.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 vec3(t * v.e[0], t * v.e[1], t * v.e[2]);
}

inline vec3 operator/(const vec3 &v, double t) {
  return vec3(v.e[0]/t, v.e[1]/t, v.e[2]/t);
}

inline double dot(const vec3 &v1, const vec3 &v2) {
  return v1.e[0] * v2.e[0] + v1.e[1] * v2.e[1] + v1.e[2] * v2.e[2];
}

inline vec3 cross(const vec3 &v1, const vec3 &v2) {
  return vec3(v1.e[1] * v2.e[2] - v2.e[1] * v1.e[2],
    -(v1.e[0] * v2.e[2] - v2.e[0] * v1.e[2]),
      v1.e[0] * v2.e[1] - v2.e[0] * v1.e[1]);
}

inline vec3& vec3::operator+=(const vec3 &v) {
  e[0] += v.e[0];
  e[1] += v.e[1];
  e[2] += v.e[2];
  return *this;
}

inline vec3& vec3::operator-=(const vec3 &v) {
  e[0] -= v.e[0];
  e[1] -= v.e[1];
  e[2] -= v.e[2];
  return *this;
}

inline vec3& vec3::operator*=(const vec3 &v) {
  e[0] *= v.e[0];
  e[1] *= v.e[1];
  e[2] *= v.e[2];
  return *this;
}

inline vec3& vec3::operator/=(const vec3 &v) {
  e[0] /= v.e[0];
  e[1] /= v.e[1];
  e[2] /= v.e[2];
  return *this;
}

inline vec3& vec3::operator*=(const double t) {
  e[0] *= t;
  e[1] *= t;
  e[2] *= t;
  return *this;
}

inline vec3& vec3::operator/=(const double t) {
  double k = 1.0/t;
  e[0] *= k;
  e[1] *= k;
  e[2] *= k;
  return *this;
}

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