text: /*
   * Copyright 1993-2013 NVIDIA Corporation.  All rights reserved.
   *
   * Please refer to the NVIDIA end user license agreement (EULA) associated
   * with this source code for terms and conditions that govern your use of
   * this software. Any use, reproduction, disclosure, or distribution of
   * this software and related documentation outside the terms of the EULA
   * is strictly prohibited.
   *
   */
  
  //
  // Template math library for common 3D functionality
  //
  // nvVector.h - 2-vector, 3-vector, and 4-vector templates and utilities
  //
  // This code is in part deriver from glh, a cross platform glut helper library.
  // The copyright for glh follows this notice.
  //
  // Copyright (c) NVIDIA Corporation. All rights reserved.
  ////////////////////////////////////////////////////////////////////////////////
  
  /*
      Copyright (c) 2000 Cass Everitt
      Copyright (c) 2000 NVIDIA Corporation
      All rights reserved.
  
      Redistribution and use in source and binary forms, with or
      without modification, are permitted provided that the following
      conditions are met:
  
       * Redistributions of source code must retain the above
         copyright notice, this list of conditions and the following
         disclaimer.
  
       * Redistributions in binary form must reproduce the above
         copyright notice, this list of conditions and the following
         disclaimer in the documentation and/or other materials
         provided with the distribution.
  
       * The names of contributors to this software may not be used
         to endorse or promote products derived from this software
         without specific prior written permission.
  
         THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
         ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
         LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
         FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
         REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
         INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
         BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
         LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
         CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
         LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
         ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
         POSSIBILITY OF SUCH DAMAGE.
  
  
      Cass Everitt - cass@r3.nu
  */
  #ifndef NV_VECTOR_H
  #define NV_VECTOR_H
  
  namespace nv
  {
  
      template <class T> class vec2;
      template <class T> class vec3;
      template <class T> class vec4;
  
      //////////////////////////////////////////////////////////////////////
      //
      // vec2 - template class for 2-tuple vector
      //
      //////////////////////////////////////////////////////////////////////
      template <class T>
      class vec2
      {
          public:
  
              typedef T value_type;
              int size() const
              {
                  return 2;
              }
  
              ////////////////////////////////////////////////////////
              //
              //  Constructors
              //
              ////////////////////////////////////////////////////////
  
              // Default/scalar constructor
              vec2(const T &t = T())
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = t;
                  }
              }
  
              // Construct from array
              vec2(const T *tp)
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = tp[i];
                  }
              }
  
              // Construct from explicit values
              vec2(const T v0, const T v1)
              {
                  x = v0;
                  y = v1;
              }
  
              explicit vec2(const vec3<T> &u)
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = u._array[i];
                  }
              }
  
              explicit vec2(const vec4<T> &u)
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = u._array[i];
                  }
              }
  
              const T *get_value() const
              {
                  return _array;
              }
  
              vec2<T> &set_value(const T *rhs)
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = rhs[i];
                  }
  
                  return *this;
              }
  
              // indexing operators
              T &operator [](int i)
              {
                  return _array[i];
              }
  
              const T &operator [](int i) const
              {
                  return _array[i];
              }
  
              // type-cast operators
              operator T *()
              {
                  return _array;
              }
  
              operator const T *() const
              {
                  return _array;
              }
  
              ////////////////////////////////////////////////////////
              //
              //  Math operators
              //
              ////////////////////////////////////////////////////////
  
              // scalar multiply assign
              friend vec2<T> &operator *= (vec2<T> &lhs, T d)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] *= d;
                  }
  
                  return lhs;
              }
  
              // component-wise vector multiply assign
              friend vec2<T> &operator *= (vec2<T> &lhs, const vec2<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] *= rhs[i];
                  }
  
                  return lhs;
              }
  
              // scalar divide assign
              friend vec2<T> &operator /= (vec2<T> &lhs, T d)
              {
                  if (d == 0)
                  {
                      return lhs;
                  }
  
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] /= d;
                  }
  
                  return lhs;
              }
  
              // component-wise vector divide assign
              friend vec2<T> &operator /= (vec2<T> &lhs, const vec2<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] /= rhs._array[i];
                  }
  
                  return lhs;
              }
  
              // component-wise vector add assign
              friend vec2<T> &operator += (vec2<T> &lhs, const vec2<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] += rhs._array[i];
                  }
  
                  return lhs;
              }
  
              // component-wise vector subtract assign
              friend vec2<T> &operator -= (vec2<T> &lhs, const vec2<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] -= rhs._array[i];
                  }
  
                  return lhs;
              }
  
              // unary negate
              friend vec2<T> operator - (const vec2<T> &rhs)
              {
                  vec2<T> rv;
  
                  for (int i = 0; i < rhs.size(); i++)
                  {
                      rv._array[i] = -rhs._array[i];
                  }
  
                  return rv;
              }
  
              // vector add
              friend vec2<T> operator + (const vec2<T> &lhs, const vec2<T> &rhs)
              {
                  vec2<T> rt(lhs);
                  return rt += rhs;
              }
  
              // vector subtract
              friend vec2<T> operator - (const vec2<T> &lhs, const vec2<T> &rhs)
              {
                  vec2<T> rt(lhs);
                  return rt -= rhs;
              }
  
              // scalar multiply
              friend vec2<T> operator * (const vec2<T> &lhs, T rhs)
              {
                  vec2<T> rt(lhs);
                  return rt *= rhs;
              }
  
              // scalar multiply
              friend vec2<T> operator * (T lhs, const vec2<T> &rhs)
              {
                  vec2<T> rt(lhs);
                  return rt *= rhs;
              }
  
              // vector component-wise multiply
              friend vec2<T> operator * (const vec2<T> &lhs, const vec2<T> &rhs)
              {
                  vec2<T> rt(lhs);
                  return rt *= rhs;
              }
  
              // scalar multiply
              friend vec2<T> operator / (const vec2<T> &lhs, T rhs)
              {
                  vec2<T> rt(lhs);
                  return rt /= rhs;
              }
  
              // vector component-wise multiply
              friend vec2<T> operator / (const vec2<T> &lhs, const vec2<T> &rhs)
              {
                  vec2<T> rt(lhs);
                  return rt /= rhs;
              }
  
              ////////////////////////////////////////////////////////
              //
              //  Comparison operators
              //
              ////////////////////////////////////////////////////////
  
              // equality
              friend bool operator == (const vec2<T> &lhs, const vec2<T> &rhs)
              {
                  bool r = true;
  
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      r &= lhs._array[i] == rhs._array[i];
                  }
  
                  return r;
              }
  
              // inequality
              friend bool operator != (const vec2<T> &lhs, const vec2<T> &rhs)
              {
                  bool r = true;
  
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      r &= lhs._array[i] != rhs._array[i];
                  }
  
                  return r;
              }
  
              //data intentionally left public to allow vec2.x
              union
              {
                  struct
                  {
                      T x,y;          // standard names for components
                  };
                  struct
                  {
                      T s,t;          // standard names for components
                  };
                  T _array[2];     // array access
              };
      };
  
      //////////////////////////////////////////////////////////////////////
      //
      // vec3 - template class for 3-tuple vector
      //
      //////////////////////////////////////////////////////////////////////
      template <class T>
      class vec3
      {
          public:
  
              typedef T value_type;
              int size() const
              {
                  return 3;
              }
  
              ////////////////////////////////////////////////////////
              //
              //  Constructors
              //
              ////////////////////////////////////////////////////////
  
              // Default/scalar constructor
              vec3(const T &t = T())
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = t;
                  }
              }
  
              // Construct from array
              vec3(const T *tp)
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = tp[i];
                  }
              }
  
              // Construct from explicit values
              vec3(const T v0, const T v1, const T v2)
              {
                  x = v0;
                  y = v1;
                  z = v2;
              }
  
              explicit vec3(const vec4<T> &u)
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = u._array[i];
                  }
              }
  
              explicit vec3(const vec2<T> &u, T v0)
              {
                  x = u.x;
                  y = u.y;
                  z = v0;
              }
  
              const T *get_value() const
              {
                  return _array;
              }
  
              vec3<T> &set_value(const T *rhs)
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = rhs[i];
                  }
  
                  return *this;
              }
  
              // indexing operators
              T &operator [](int i)
              {
                  return _array[i];
              }
  
              const T &operator [](int i) const
              {
                  return _array[i];
              }
  
              // type-cast operators
              operator T *()
              {
                  return _array;
              }
  
              operator const T *() const
              {
                  return _array;
              }
  
              ////////////////////////////////////////////////////////
              //
              //  Math operators
              //
              ////////////////////////////////////////////////////////
  
              // scalar multiply assign
              friend vec3<T> &operator *= (vec3<T> &lhs, T d)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] *= d;
                  }
  
                  return lhs;
              }
  
              // component-wise vector multiply assign
              friend vec3<T> &operator *= (vec3<T> &lhs, const vec3<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] *= rhs[i];
                  }
  
                  return lhs;
              }
  
              // scalar divide assign
              friend vec3<T> &operator /= (vec3<T> &lhs, T d)
              {
                  if (d == 0)
                  {
                      return lhs;
                  }
  
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] /= d;
                  }
  
                  return lhs;
              }
  
              // component-wise vector divide assign
              friend vec3<T> &operator /= (vec3<T> &lhs, const vec3<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] /= rhs._array[i];
                  }
  
                  return lhs;
              }
  
              // component-wise vector add assign
              friend vec3<T> &operator += (vec3<T> &lhs, const vec3<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] += rhs._array[i];
                  }
  
                  return lhs;
              }
  
              // component-wise vector subtract assign
              friend vec3<T> &operator -= (vec3<T> &lhs, const vec3<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] -= rhs._array[i];
                  }
  
                  return lhs;
              }
  
              // unary negate
              friend vec3<T> operator - (const vec3<T> &rhs)
              {
                  vec3<T> rv;
  
                  for (int i = 0; i < rhs.size(); i++)
                  {
                      rv._array[i] = -rhs._array[i];
                  }
  
                  return rv;
              }
  
              // vector add
              friend vec3<T> operator + (const vec3<T> &lhs, const vec3<T> &rhs)
              {
                  vec3<T> rt(lhs);
                  return rt += rhs;
              }
  
              // vector subtract
              friend vec3<T> operator - (const vec3<T> &lhs, const vec3<T> &rhs)
              {
                  vec3<T> rt(lhs);
                  return rt -= rhs;
              }
  
              // scalar multiply
              friend vec3<T> operator * (const vec3<T> &lhs, T rhs)
              {
                  vec3<T> rt(lhs);
                  return rt *= rhs;
              }
  
              // scalar multiply
              friend vec3<T> operator * (T lhs, const vec3<T> &rhs)
              {
                  vec3<T> rt(lhs);
                  return rt *= rhs;
              }
  
              // vector component-wise multiply
              friend vec3<T> operator * (const vec3<T> &lhs, const vec3<T> &rhs)
              {
                  vec3<T> rt(lhs);
                  return rt *= rhs;
              }
  
              // scalar multiply
              friend vec3<T> operator / (const vec3<T> &lhs, T rhs)
              {
                  vec3<T> rt(lhs);
                  return rt /= rhs;
              }
  
              // vector component-wise multiply
              friend vec3<T> operator / (const vec3<T> &lhs, const vec3<T> &rhs)
              {
                  vec3<T> rt(lhs);
                  return rt /= rhs;
              }
  
              ////////////////////////////////////////////////////////
              //
              //  Comparison operators
              //
              ////////////////////////////////////////////////////////
  
              // equality
              friend bool operator == (const vec3<T> &lhs, const vec3<T> &rhs)
              {
                  bool r = true;
  
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      r &= lhs._array[i] == rhs._array[i];
                  }
  
                  return r;
              }
  
              // inequality
              friend bool operator != (const vec3<T> &lhs, const vec3<T> &rhs)
              {
                  bool r = true;
  
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      r &= lhs._array[i] != rhs._array[i];
                  }
  
                  return r;
              }
  
              ////////////////////////////////////////////////////////////////////////////////
              //
              // dimension specific operations
              //
              ////////////////////////////////////////////////////////////////////////////////
  
              // cross product
              friend vec3<T> cross(const vec3<T> &lhs, const vec3<T> &rhs)
              {
                  vec3<T> r;
  
                  r.x = lhs.y * rhs.z - lhs.z * rhs.y;
                  r.y = lhs.z * rhs.x - lhs.x * rhs.z;
                  r.z = lhs.x * rhs.y - lhs.y * rhs.x;
  
                  return r;
              }
  
              //data intentionally left public to allow vec2.x
              union
              {
                  struct
                  {
                      T x, y, z;          // standard names for components
                  };
                  struct
                  {
                      T s, t, r;          // standard names for components
                  };
                  T _array[3];     // array access
              };
      };
  
      //////////////////////////////////////////////////////////////////////
      //
      // vec4 - template class for 4-tuple vector
      //
      //////////////////////////////////////////////////////////////////////
      template <class T>
      class vec4
      {
          public:
  
              typedef T value_type;
              int size() const
              {
                  return 4;
              }
  
              ////////////////////////////////////////////////////////
              //
              //  Constructors
              //
              ////////////////////////////////////////////////////////
  
              // Default/scalar constructor
              vec4(const T &t = T())
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = t;
                  }
              }
  
              // Construct from array
              vec4(const T *tp)
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = tp[i];
                  }
              }
  
              // Construct from explicit values
              vec4(const T v0, const T v1, const T v2, const T v3)
              {
                  x = v0;
                  y = v1;
                  z = v2;
                  w = v3;
              }
  
              explicit vec4(const vec3<T> &u, T v0)
              {
                  x = u.x;
                  y = u.y;
                  z = u.z;
                  w = v0;
              }
  
              explicit vec4(const vec2<T> &u, T v0, T v1)
              {
                  x = u.x;
                  y = u.y;
                  z = v0;
                  w = v1;
              }
  
              const T *get_value() const
              {
                  return _array;
              }
  
              vec4<T> &set_value(const T *rhs)
              {
                  for (int i = 0; i < size(); i++)
                  {
                      _array[i] = rhs[i];
                  }
  
                  return *this;
              }
  
              // indexing operators
              T &operator [](int i)
              {
                  return _array[i];
              }
  
              const T &operator [](int i) const
              {
                  return _array[i];
              }
  
              // type-cast operators
              operator T *()
              {
                  return _array;
              }
  
              operator const T *() const
              {
                  return _array;
              }
  
              ////////////////////////////////////////////////////////
              //
              //  Math operators
              //
              ////////////////////////////////////////////////////////
  
              // scalar multiply assign
              friend vec4<T> &operator *= (vec4<T> &lhs, T d)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] *= d;
                  }
  
                  return lhs;
              }
  
              // component-wise vector multiply assign
              friend vec4<T> &operator *= (vec4<T> &lhs, const vec4<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] *= rhs[i];
                  }
  
                  return lhs;
              }
  
              // scalar divide assign
              friend vec4<T> &operator /= (vec4<T> &lhs, T d)
              {
                  if (d == 0)
                  {
                      return lhs;
                  }
  
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] /= d;
                  }
  
                  return lhs;
              }
  
              // component-wise vector divide assign
              friend vec4<T> &operator /= (vec4<T> &lhs, const vec4<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] /= rhs._array[i];
                  }
  
                  return lhs;
              }
  
              // component-wise vector add assign
              friend vec4<T> &operator += (vec4<T> &lhs, const vec4<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] += rhs._array[i];
                  }
  
                  return lhs;
              }
  
              // component-wise vector subtract assign
              friend vec4<T> &operator -= (vec4<T> &lhs, const vec4<T> &rhs)
              {
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      lhs._array[i] -= rhs._array[i];
                  }
  
                  return lhs;
              }
  
              // unary negate
              friend vec4<T> operator - (const vec4<T> &rhs)
              {
                  vec4<T> rv;
  
                  for (int i = 0; i < rhs.size(); i++)
                  {
                      rv._array[i] = -rhs._array[i];
                  }
  
                  return rv;
              }
  
              // vector add
              friend vec4<T> operator + (const vec4<T> &lhs, const vec4<T> &rhs)
              {
                  vec4<T> rt(lhs);
                  return rt += rhs;
              }
  
              // vector subtract
              friend vec4<T> operator - (const vec4<T> &lhs, const vec4<T> &rhs)
              {
                  vec4<T> rt(lhs);
                  return rt -= rhs;
              }
  
              // scalar multiply
              friend vec4<T> operator * (const vec4<T> &lhs, T rhs)
              {
                  vec4<T> rt(lhs);
                  return rt *= rhs;
              }
  
              // scalar multiply
              friend vec4<T> operator * (T lhs, const vec4<T> &rhs)
              {
                  vec4<T> rt(lhs);
                  return rt *= rhs;
              }
  
              // vector component-wise multiply
              friend vec4<T> operator * (const vec4<T> &lhs, const vec4<T> &rhs)
              {
                  vec4<T> rt(lhs);
                  return rt *= rhs;
              }
  
              // scalar multiply
              friend vec4<T> operator / (const vec4<T> &lhs, T rhs)
              {
                  vec4<T> rt(lhs);
                  return rt /= rhs;
              }
  
              // vector component-wise multiply
              friend vec4<T> operator / (const vec4<T> &lhs, const vec4<T> &rhs)
              {
                  vec4<T> rt(lhs);
                  return rt /= rhs;
              }
  
              ////////////////////////////////////////////////////////
              //
              //  Comparison operators
              //
              ////////////////////////////////////////////////////////
  
              // equality
              friend bool operator == (const vec4<T> &lhs, const vec4<T> &rhs)
              {
                  bool r = true;
  
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      r &= lhs._array[i] == rhs._array[i];
                  }
  
                  return r;
              }
  
              // inequality
              friend bool operator != (const vec4<T> &lhs, const vec4<T> &rhs)
              {
                  bool r = true;
  
                  for (int i = 0; i < lhs.size(); i++)
                  {
                      r &= lhs._array[i] != rhs._array[i];
                  }
  
                  return r;
              }
  
              //data intentionally left public to allow vec2.x
              union
              {
                  struct
                  {
                      T x, y, z, w;          // standard names for components
                  };
                  struct
                  {
                      T s, t, r, q;          // standard names for components
                  };
                  T _array[4];     // array access
              };
      };
  
      ////////////////////////////////////////////////////////////////////////////////
      //
      // Generic vector operations
      //
      ////////////////////////////////////////////////////////////////////////////////
  
      // compute the dot product of two vectors
      template<class T>
      inline typename T::value_type dot(const T &lhs, const T &rhs)
      {
          typename T::value_type r = 0;
  
          for (int i = 0; i < lhs.size(); i++)
          {
              r += lhs._array[i] * rhs._array[i];
          }
  
          return r;
      }
  
      // return the length of the provided vector
      template< class T>
      inline typename T::value_type length(const T &vec)
      {
          typename T::value_type r = 0;
  
          for (int i = 0; i < vec.size(); i++)
          {
              r += vec._array[i]*vec._array[i];
          }
  
          return typename T::value_type(sqrt(r));
      }
  
      // return the squared norm
      template< class T>
      inline typename T::value_type square_norm(const T &vec)
      {
          typename T::value_type r = 0;
  
          for (int i = 0; i < vec.size(); i++)
          {
              r += vec._array[i]*vec._array[i];
          }
  
          return r;
      }
  
      // return the normalized version of the vector
      template< class T>
      inline T normalize(const T &vec)
      {
          typename T::value_type sum(0);
          T r;
  
          for (int i = 0; i < vec.size(); i++)
          {
              sum += vec._array[i] * vec._array[i];
          }
  
          sum = typename T::value_type(sqrt(sum));
  
          if (sum > 0)
              for (int i = 0; i < vec.size(); i++)
              {
                  r._array[i] = vec._array[i] / sum;
              }
  
          return r;
      }
  
      // In VC8 : min and max are already defined by a #define...
  #ifdef min
  #undef min
  #endif
  #ifdef max
  #undef max
  #endif
      //componentwise min
      template< class T>
      inline T min(const T &lhs, const T &rhs)
      {
          T rt;
  
          for (int i = 0; i < lhs.size(); i++)
          {
              rt._array[i] = std::min(lhs._array[i], rhs._array[i]);
          }
  
          return rt;
      }
  
      // componentwise max
      template< class T>
      inline T max(const T &lhs, const T &rhs)
      {
          T rt;
  
          for (int i = 0; i < lhs.size(); i++)
          {
              rt._array[i] = std::max(lhs._array[i], rhs._array[i]);
          }
  
          return rt;
      }
  
  
  };
  
  #endif
  