text: #ifndef GEOMETRY
  #define GEOMETRY
  
  #include <math.h>
  #include <stdlib.h>
  #include <iostream>
  #include <cmath>
  
  class vec2
  {
      public:
      
          // Empty constructor
          vec2() {}
  
          // Define dimensional attributes
          vec2(float e0, float e1) { e[0] = e0; e[1] = e1; }
  
          // Getters for vector magnitudes
          // Note: the "inline" keyword tells the compiler to replace the function
          // call for this function/method with the body of the function itself in
          // order to reduce overhead when calling it.
          inline float x() const { return e[0]; }
          inline float y() const { return e[1]; }
  
          // Vector operations
          inline const vec2& operator+() const { return *this; }
          inline vec2 operator-() const { return vec2(-e[0], -e[1]); }
          inline float operator[](int i) const { return e[i]; }
          inline float& operator[](int i) { return e[i]; }
  
          inline vec2 operator+ (const vec2 &v) { return vec2(e[0] + v.e[0], e[1] + v.e[1]); }
          inline vec2 operator/ (const float t) { return vec2(e[0] / t, e[1] / t); }
          inline vec2 operator* (const float t) { return vec2(e[0] * t, e[1] * t); }
          inline vec2& operator/= (const float t) { e[0] /= t; e[1] /= t; return *this; };
          inline vec2& operator*= (const float t) { e[0] *= t; e[1] *= t; return *this; };
  
          inline float length() const
          {
              return sqrt(e[0]*e[0] + e[1]*e[1]);
          }
  
          inline float squared_length() const
          {
              return e[0]*e[0] + e[1]*e[1];
          }
  
          inline void make_unit_vector();
  
          float e[2];
  };
  
  inline std::istream& operator>>(std::istream &is, vec2 &t)
  {
      is >> t.e[0] >> t.e[1];
      return is;
  }
  
  inline std::ostream& operator<<(std::ostream &os, vec2 &t)
  {
      os << t.e[0] << t.e[1];
      return os;
  }
  
  class vec3
  {
      public:
      
          // Empty constructor
          vec3() {}
  
          // Define dimensional attributes
          vec3(float e0, float e1, float e2) { e[0] = e0; e[1] = e1; e[2] = e2; }
  
          // Getters for vector magnitudes
          // Note: the "inline" keyword tells the compiler to replace the function
          // call for this function/method with the body of the function itself in
          // order to reduce overhead when calling it.
          inline float x() const { return e[0]; }
          inline float y() const { return e[1]; }
          inline float z() const { return e[2]; }
          inline float r() const { return e[0]; }
          inline float g() const { return e[1]; }
          inline float b() const { return e[2]; }
  
          // Vector operations
          inline const vec3& operator+() const { return *this; }
          inline vec3 operator-() const { return vec3(-e[0], -e[1], -e[2]); }
          inline float operator[](int i) const { return e[i]; }
          inline float& 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 float t);
          inline vec3& operator/=(const float t);
  
          inline float length() const
          {
              return sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]);
          }
  
          inline float squared_length() const
          {
              return e[0]*e[0] + e[1]*e[1] + e[2]*e[2];
          }
  
          inline void make_unit_vector();
  
          inline vec3& normalize()
          {
              float n = squared_length();
  
              if (n > 0)
              {
                  float factor = 1 / sqrt(n);
                  e[0] *= factor, e[1] *= factor, e[2] *= factor;
              }
  
              return *this;
          }
  
          float 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, vec3 &t)
  {
      os << t.e[0] << t.e[1] << t.e[2];
      return os;
  }
  
  inline void vec3::make_unit_vector()
  {
      float 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*(float t, const vec3 &v)
  {
      return vec3(t * v.e[0], t * v.e[1], t * v.e[2]);
  }
  
  inline vec3 operator/(const vec3 &v, float t)
  {
      return vec3(v.e[0] / t, v.e[1] / t, v.e[2] / t);
  }
  
  inline vec3 operator*(const vec3 &v, float t)
  {
      return vec3(t * v.e[0], t * v.e[1], t * v.e[2]);
  }
  
  inline float 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] - v1.e[2] * v2.e[1]),
                 (-(v1.e[0] * v2.e[2] - v1.e[2] * v2.e[0])),
                   (v1.e[0] * v2.e[1] - v1.e[1] * v2.e[0]));
  }
  
  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 float t)
  {
      e[0] *= t;
      e[1] *= t;
      e[2] *= t;
      return *this;
  }
  
  inline vec3& vec3::operator/=(const float t)
  {
      float k = 1.0 / t;
      e[0] *= k;
      e[1] *= k;
      e[2] *= k;
      return *this;
  }
  
  inline vec3 unit_vector(vec3 v)
  {
      return v / v.length();
  }
  
  #endif
  