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  #ifndef OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP
  #define OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP
  
  //! @cond IGNORED
  
  namespace cv { namespace detail {
  /**
  Computes the matrix for the projection onto a tilted image sensor
  \param tauX angular parameter rotation around x-axis
  \param tauY angular parameter rotation around y-axis
  \param matTilt if not NULL returns the matrix
  \f[
  \vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}((\tau_x, \tau_y)}
  {0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
  {0}{0}{1} R(\tau_x, \tau_y)
  \f]
  where
  \f[
  R(\tau_x, \tau_y) =
  \vecthreethree{\cos(\tau_y)}{0}{-\sin(\tau_y)}{0}{1}{0}{\sin(\tau_y)}{0}{\cos(\tau_y)}
  \vecthreethree{1}{0}{0}{0}{\cos(\tau_x)}{\sin(\tau_x)}{0}{-\sin(\tau_x)}{\cos(\tau_x)} =
  \vecthreethree{\cos(\tau_y)}{\sin(\tau_y)\sin(\tau_x)}{-\sin(\tau_y)\cos(\tau_x)}
  {0}{\cos(\tau_x)}{\sin(\tau_x)}
  {\sin(\tau_y)}{-\cos(\tau_y)\sin(\tau_x)}{\cos(\tau_y)\cos(\tau_x)}.
  \f]
  \param dMatTiltdTauX if not NULL it returns the derivative of matTilt with
  respect to \f$\tau_x\f$.
  \param dMatTiltdTauY if not NULL it returns the derivative of matTilt with
  respect to \f$\tau_y\f$.
  \param invMatTilt if not NULL it returns the inverse of matTilt
  **/
  template <typename FLOAT>
  void computeTiltProjectionMatrix(FLOAT tauX,
      FLOAT tauY,
      Matx<FLOAT, 3, 3>* matTilt = 0,
      Matx<FLOAT, 3, 3>* dMatTiltdTauX = 0,
      Matx<FLOAT, 3, 3>* dMatTiltdTauY = 0,
      Matx<FLOAT, 3, 3>* invMatTilt = 0)
  {
      FLOAT cTauX = cos(tauX);
      FLOAT sTauX = sin(tauX);
      FLOAT cTauY = cos(tauY);
      FLOAT sTauY = sin(tauY);
      Matx<FLOAT, 3, 3> matRotX = Matx<FLOAT, 3, 3>(1,0,0,0,cTauX,sTauX,0,-sTauX,cTauX);
      Matx<FLOAT, 3, 3> matRotY = Matx<FLOAT, 3, 3>(cTauY,0,-sTauY,0,1,0,sTauY,0,cTauY);
      Matx<FLOAT, 3, 3> matRotXY = matRotY * matRotX;
      Matx<FLOAT, 3, 3> matProjZ = Matx<FLOAT, 3, 3>(matRotXY(2,2),0,-matRotXY(0,2),0,matRotXY(2,2),-matRotXY(1,2),0,0,1);
      if (matTilt)
      {
          // Matrix for trapezoidal distortion of tilted image sensor
          *matTilt = matProjZ * matRotXY;
      }
      if (dMatTiltdTauX)
      {
          // Derivative with respect to tauX
          Matx<FLOAT, 3, 3> dMatRotXYdTauX = matRotY * Matx<FLOAT, 3, 3>(0,0,0,0,-sTauX,cTauX,0,-cTauX,-sTauX);
          Matx<FLOAT, 3, 3> dMatProjZdTauX = Matx<FLOAT, 3, 3>(dMatRotXYdTauX(2,2),0,-dMatRotXYdTauX(0,2),
            0,dMatRotXYdTauX(2,2),-dMatRotXYdTauX(1,2),0,0,0);
          *dMatTiltdTauX = (matProjZ * dMatRotXYdTauX) + (dMatProjZdTauX * matRotXY);
      }
      if (dMatTiltdTauY)
      {
          // Derivative with respect to tauY
          Matx<FLOAT, 3, 3> dMatRotXYdTauY = Matx<FLOAT, 3, 3>(-sTauY,0,-cTauY,0,0,0,cTauY,0,-sTauY) * matRotX;
          Matx<FLOAT, 3, 3> dMatProjZdTauY = Matx<FLOAT, 3, 3>(dMatRotXYdTauY(2,2),0,-dMatRotXYdTauY(0,2),
            0,dMatRotXYdTauY(2,2),-dMatRotXYdTauY(1,2),0,0,0);
          *dMatTiltdTauY = (matProjZ * dMatRotXYdTauY) + (dMatProjZdTauY * matRotXY);
      }
      if (invMatTilt)
      {
          FLOAT inv = 1./matRotXY(2,2);
          Matx<FLOAT, 3, 3> invMatProjZ = Matx<FLOAT, 3, 3>(inv,0,inv*matRotXY(0,2),0,inv,inv*matRotXY(1,2),0,0,1);
          *invMatTilt = matRotXY.t()*invMatProjZ;
      }
  }
  }} // namespace detail, cv
  
  
  //! @endcond
  
  #endif // OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP
  