/*M///////////////////////////////////////////////////////////////////////////////////////
//
//  IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
//  By downloading, copying, installing or using the software you agree to this license.
//  If you do not agree to this license, do not download, install,
//  copy or use the software.
//
//
//                           License Agreement
//                For Open Source Computer Vision Library
//
// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
//   * Redistribution's of source code must retain the above copyright notice,
//     this list of conditions and the following disclaimer.
//
//   * Redistribution's 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 name of the copyright holders 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 Intel Corporation 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.
//
//M*/

#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