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#ifndef OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP
#define OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP

//! @cond IGNORED

namespace cv {
/**
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, _3d, cv


//! @endcond

#endif // OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP