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  //                For Open Source Computer Vision Library
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  #include "precomp.hpp"
  #include "distortion_model.hpp"
  
  #include "calib3d_c_api.h"
  
  #include "undistort.simd.hpp"
  #include "undistort.simd_declarations.hpp" // defines CV_CPU_DISPATCH_MODES_ALL=AVX2,...,BASELINE based on CMakeLists.txt content
  
  namespace cv
  {
  
  Mat getDefaultNewCameraMatrix( InputArray _cameraMatrix, Size imgsize,
                                 bool centerPrincipalPoint )
  {
      Mat cameraMatrix = _cameraMatrix.getMat();
      if( !centerPrincipalPoint && cameraMatrix.type() == CV_64F )
          return cameraMatrix;
  
      Mat newCameraMatrix;
      cameraMatrix.convertTo(newCameraMatrix, CV_64F);
      if( centerPrincipalPoint )
      {
          newCameraMatrix.ptr<double>()[2] = (imgsize.width-1)*0.5;
          newCameraMatrix.ptr<double>()[5] = (imgsize.height-1)*0.5;
      }
      return newCameraMatrix;
  }
  
  namespace {
  Ptr<ParallelLoopBody> getInitUndistortRectifyMapComputer(Size _size, Mat &_map1, Mat &_map2, int _m1type,
                                                           const double* _ir, Matx33d &_matTilt,
                                                           double _u0, double _v0, double _fx, double _fy,
                                                           double _k1, double _k2, double _p1, double _p2,
                                                           double _k3, double _k4, double _k5, double _k6,
                                                           double _s1, double _s2, double _s3, double _s4)
  {
      CV_INSTRUMENT_REGION();
  
      CV_CPU_DISPATCH(getInitUndistortRectifyMapComputer, (_size, _map1, _map2, _m1type, _ir, _matTilt, _u0, _v0, _fx, _fy, _k1, _k2, _p1, _p2, _k3, _k4, _k5, _k6, _s1, _s2, _s3, _s4),
          CV_CPU_DISPATCH_MODES_ALL);
  }
  }
  
  void initUndistortRectifyMap( InputArray _cameraMatrix, InputArray _distCoeffs,
                                InputArray _matR, InputArray _newCameraMatrix,
                                Size size, int m1type, OutputArray _map1, OutputArray _map2 )
  {
      Mat cameraMatrix = _cameraMatrix.getMat(), distCoeffs = _distCoeffs.getMat();
      Mat matR = _matR.getMat(), newCameraMatrix = _newCameraMatrix.getMat();
  
      if( m1type <= 0 )
          m1type = CV_16SC2;
      CV_Assert( m1type == CV_16SC2 || m1type == CV_32FC1 || m1type == CV_32FC2 );
      _map1.create( size, m1type );
      Mat map1 = _map1.getMat(), map2;
      if( m1type != CV_32FC2 )
      {
          _map2.create( size, m1type == CV_16SC2 ? CV_16UC1 : CV_32FC1 );
          map2 = _map2.getMat();
      }
      else
          _map2.release();
  
      Mat_<double> R = Mat_<double>::eye(3, 3);
      Mat_<double> A = Mat_<double>(cameraMatrix), Ar;
  
      if( !newCameraMatrix.empty() )
          Ar = Mat_<double>(newCameraMatrix);
      else
          Ar = getDefaultNewCameraMatrix( A, size, true );
  
      if( !matR.empty() )
          R = Mat_<double>(matR);
  
      if( !distCoeffs.empty() )
          distCoeffs = Mat_<double>(distCoeffs);
      else
      {
          distCoeffs.create(14, 1, CV_64F);
          distCoeffs = 0.;
      }
  
      CV_Assert( A.size() == Size(3,3) && A.size() == R.size() );
      CV_Assert( Ar.size() == Size(3,3) || Ar.size() == Size(4, 3));
      Mat_<double> iR = (Ar.colRange(0,3)*R).inv(DECOMP_LU);
      const double* ir = &iR(0,0);
  
      double u0 = A(0, 2),  v0 = A(1, 2);
      double fx = A(0, 0),  fy = A(1, 1);
  
      CV_Assert( distCoeffs.size() == Size(1, 4) || distCoeffs.size() == Size(4, 1) ||
                 distCoeffs.size() == Size(1, 5) || distCoeffs.size() == Size(5, 1) ||
                 distCoeffs.size() == Size(1, 8) || distCoeffs.size() == Size(8, 1) ||
                 distCoeffs.size() == Size(1, 12) || distCoeffs.size() == Size(12, 1) ||
                 distCoeffs.size() == Size(1, 14) || distCoeffs.size() == Size(14, 1));
  
      if( distCoeffs.rows != 1 && !distCoeffs.isContinuous() )
          distCoeffs = distCoeffs.t();
  
      const double* const distPtr = distCoeffs.ptr<double>();
      double k1 = distPtr[0];
      double k2 = distPtr[1];
      double p1 = distPtr[2];
      double p2 = distPtr[3];
      double k3 = distCoeffs.cols + distCoeffs.rows - 1 >= 5 ? distPtr[4] : 0.;
      double k4 = distCoeffs.cols + distCoeffs.rows - 1 >= 8 ? distPtr[5] : 0.;
      double k5 = distCoeffs.cols + distCoeffs.rows - 1 >= 8 ? distPtr[6] : 0.;
      double k6 = distCoeffs.cols + distCoeffs.rows - 1 >= 8 ? distPtr[7] : 0.;
      double s1 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[8] : 0.;
      double s2 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[9] : 0.;
      double s3 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[10] : 0.;
      double s4 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[11] : 0.;
      double tauX = distCoeffs.cols + distCoeffs.rows - 1 >= 14 ? distPtr[12] : 0.;
      double tauY = distCoeffs.cols + distCoeffs.rows - 1 >= 14 ? distPtr[13] : 0.;
  
      // Matrix for trapezoidal distortion of tilted image sensor
      Matx33d matTilt = Matx33d::eye();
      detail::computeTiltProjectionMatrix(tauX, tauY, &matTilt);
  
      parallel_for_(Range(0, size.height), *getInitUndistortRectifyMapComputer(
          size, map1, map2, m1type, ir, matTilt, u0, v0,
          fx, fy, k1, k2, p1, p2, k3, k4, k5, k6, s1, s2, s3, s4));
  }
  
  
  void undistort( InputArray _src, OutputArray _dst, InputArray _cameraMatrix,
                  InputArray _distCoeffs, InputArray _newCameraMatrix )
  {
      CV_INSTRUMENT_REGION();
  
      Mat src = _src.getMat(), cameraMatrix = _cameraMatrix.getMat();
      Mat distCoeffs = _distCoeffs.getMat(), newCameraMatrix = _newCameraMatrix.getMat();
  
      _dst.create( src.size(), src.type() );
      Mat dst = _dst.getMat();
  
      CV_Assert( dst.data != src.data );
  
      int stripe_size0 = std::min(std::max(1, (1 << 12) / std::max(src.cols, 1)), src.rows);
      Mat map1(stripe_size0, src.cols, CV_16SC2), map2(stripe_size0, src.cols, CV_16UC1);
  
      Mat_<double> A, Ar, I = Mat_<double>::eye(3,3);
  
      cameraMatrix.convertTo(A, CV_64F);
      if( !distCoeffs.empty() )
          distCoeffs = Mat_<double>(distCoeffs);
      else
      {
          distCoeffs.create(5, 1, CV_64F);
          distCoeffs = 0.;
      }
  
      if( !newCameraMatrix.empty() )
          newCameraMatrix.convertTo(Ar, CV_64F);
      else
          A.copyTo(Ar);
  
      double v0 = Ar(1, 2);
      for( int y = 0; y < src.rows; y += stripe_size0 )
      {
          int stripe_size = std::min( stripe_size0, src.rows - y );
          Ar(1, 2) = v0 - y;
          Mat map1_part = map1.rowRange(0, stripe_size),
              map2_part = map2.rowRange(0, stripe_size),
              dst_part = dst.rowRange(y, y + stripe_size);
  
          initUndistortRectifyMap( A, distCoeffs, I, Ar, Size(src.cols, stripe_size),
                                   map1_part.type(), map1_part, map2_part );
          remap( src, dst_part, map1_part, map2_part, INTER_LINEAR, BORDER_CONSTANT );
      }
  }
  
  }
  
  CV_IMPL void
  cvUndistort2( const CvArr* srcarr, CvArr* dstarr, const CvMat* Aarr, const CvMat* dist_coeffs, const CvMat* newAarr )
  {
      cv::Mat src = cv::cvarrToMat(srcarr), dst = cv::cvarrToMat(dstarr), dst0 = dst;
      cv::Mat A = cv::cvarrToMat(Aarr), distCoeffs = cv::cvarrToMat(dist_coeffs), newA;
      if( newAarr )
          newA = cv::cvarrToMat(newAarr);
  
      CV_Assert( src.size() == dst.size() && src.type() == dst.type() );
      cv::undistort( src, dst, A, distCoeffs, newA );
  }
  
  
  CV_IMPL void cvInitUndistortMap( const CvMat* Aarr, const CvMat* dist_coeffs,
                                   CvArr* mapxarr, CvArr* mapyarr )
  {
      cv::Mat A = cv::cvarrToMat(Aarr), distCoeffs = cv::cvarrToMat(dist_coeffs);
      cv::Mat mapx = cv::cvarrToMat(mapxarr), mapy, mapx0 = mapx, mapy0;
  
      if( mapyarr )
          mapy0 = mapy = cv::cvarrToMat(mapyarr);
  
      cv::initUndistortRectifyMap( A, distCoeffs, cv::Mat(), A,
                                   mapx.size(), mapx.type(), mapx, mapy );
      CV_Assert( mapx0.data == mapx.data && mapy0.data == mapy.data );
  }
  
  void
  cvInitUndistortRectifyMap( const CvMat* Aarr, const CvMat* dist_coeffs,
      const CvMat *Rarr, const CvMat* ArArr, CvArr* mapxarr, CvArr* mapyarr )
  {
      cv::Mat A = cv::cvarrToMat(Aarr), distCoeffs, R, Ar;
      cv::Mat mapx = cv::cvarrToMat(mapxarr), mapy, mapx0 = mapx, mapy0;
  
      if( mapyarr )
          mapy0 = mapy = cv::cvarrToMat(mapyarr);
  
      if( dist_coeffs )
          distCoeffs = cv::cvarrToMat(dist_coeffs);
      if( Rarr )
          R = cv::cvarrToMat(Rarr);
      if( ArArr )
          Ar = cv::cvarrToMat(ArArr);
  
      cv::initUndistortRectifyMap( A, distCoeffs, R, Ar, mapx.size(), mapx.type(), mapx, mapy );
      CV_Assert( mapx0.data == mapx.data && mapy0.data == mapy.data );
  }
  
  static void cvUndistortPointsInternal( const CvMat* _src, CvMat* _dst, const CvMat* _cameraMatrix,
                     const CvMat* _distCoeffs,
                     const CvMat* matR, const CvMat* matP, cv::TermCriteria criteria)
  {
      CV_Assert(criteria.isValid());
      double A[3][3], RR[3][3], k[14]={0,0,0,0,0,0,0,0,0,0,0,0,0,0};
      CvMat matA=cvMat(3, 3, CV_64F, A), _Dk;
      CvMat _RR=cvMat(3, 3, CV_64F, RR);
      cv::Matx33d invMatTilt = cv::Matx33d::eye();
      cv::Matx33d matTilt = cv::Matx33d::eye();
  
      CV_Assert( CV_IS_MAT(_src) && CV_IS_MAT(_dst) &&
          (_src->rows == 1 || _src->cols == 1) &&
          (_dst->rows == 1 || _dst->cols == 1) &&
          _src->cols + _src->rows - 1 == _dst->rows + _dst->cols - 1 &&
          (CV_MAT_TYPE(_src->type) == CV_32FC2 || CV_MAT_TYPE(_src->type) == CV_64FC2) &&
          (CV_MAT_TYPE(_dst->type) == CV_32FC2 || CV_MAT_TYPE(_dst->type) == CV_64FC2));
  
      CV_Assert( CV_IS_MAT(_cameraMatrix) &&
          _cameraMatrix->rows == 3 && _cameraMatrix->cols == 3 );
  
      cvConvert( _cameraMatrix, &matA );
  
  
      if( _distCoeffs )
      {
          CV_Assert( CV_IS_MAT(_distCoeffs) &&
              (_distCoeffs->rows == 1 || _distCoeffs->cols == 1) &&
              (_distCoeffs->rows*_distCoeffs->cols == 4 ||
               _distCoeffs->rows*_distCoeffs->cols == 5 ||
               _distCoeffs->rows*_distCoeffs->cols == 8 ||
               _distCoeffs->rows*_distCoeffs->cols == 12 ||
               _distCoeffs->rows*_distCoeffs->cols == 14));
  
          _Dk = cvMat( _distCoeffs->rows, _distCoeffs->cols,
              CV_MAKETYPE(CV_64F,CV_MAT_CN(_distCoeffs->type)), k);
  
          cvConvert( _distCoeffs, &_Dk );
          if (k[12] != 0 || k[13] != 0)
          {
              cv::detail::computeTiltProjectionMatrix<double>(k[12], k[13], NULL, NULL, NULL, &invMatTilt);
              cv::detail::computeTiltProjectionMatrix<double>(k[12], k[13], &matTilt, NULL, NULL);
          }
      }
  
      if( matR )
      {
          CV_Assert( CV_IS_MAT(matR) && matR->rows == 3 && matR->cols == 3 );
          cvConvert( matR, &_RR );
      }
      else
          cvSetIdentity(&_RR);
  
      if( matP )
      {
          double PP[3][3];
          CvMat _P3x3, _PP=cvMat(3, 3, CV_64F, PP);
          CV_Assert( CV_IS_MAT(matP) && matP->rows == 3 && (matP->cols == 3 || matP->cols == 4));
          cvConvert( cvGetCols(matP, &_P3x3, 0, 3), &_PP );
          cvMatMul( &_PP, &_RR, &_RR );
      }
  
      const CvPoint2D32f* srcf = (const CvPoint2D32f*)_src->data.ptr;
      const CvPoint2D64f* srcd = (const CvPoint2D64f*)_src->data.ptr;
      CvPoint2D32f* dstf = (CvPoint2D32f*)_dst->data.ptr;
      CvPoint2D64f* dstd = (CvPoint2D64f*)_dst->data.ptr;
      int stype = CV_MAT_TYPE(_src->type);
      int dtype = CV_MAT_TYPE(_dst->type);
      int sstep = _src->rows == 1 ? 1 : _src->step/CV_ELEM_SIZE(stype);
      int dstep = _dst->rows == 1 ? 1 : _dst->step/CV_ELEM_SIZE(dtype);
  
      double fx = A[0][0];
      double fy = A[1][1];
      double ifx = 1./fx;
      double ify = 1./fy;
      double cx = A[0][2];
      double cy = A[1][2];
  
      int n = _src->rows + _src->cols - 1;
      for( int i = 0; i < n; i++ )
      {
          double x, y, x0 = 0, y0 = 0, u, v;
          if( stype == CV_32FC2 )
          {
              x = srcf[i*sstep].x;
              y = srcf[i*sstep].y;
          }
          else
          {
              x = srcd[i*sstep].x;
              y = srcd[i*sstep].y;
          }
          u = x; v = y;
          x = (x - cx)*ifx;
          y = (y - cy)*ify;
  
          if( _distCoeffs ) {
              // compensate tilt distortion
              cv::Vec3d vecUntilt = invMatTilt * cv::Vec3d(x, y, 1);
              double invProj = vecUntilt(2) ? 1./vecUntilt(2) : 1;
              x0 = x = invProj * vecUntilt(0);
              y0 = y = invProj * vecUntilt(1);
  
              double error = std::numeric_limits<double>::max();
              // compensate distortion iteratively
  
              for( int j = 0; ; j++ )
              {
                  if ((criteria.type & cv::TermCriteria::COUNT) && j >= criteria.maxCount)
                      break;
                  if ((criteria.type & cv::TermCriteria::EPS) && error < criteria.epsilon)
                      break;
                  double r2 = x*x + y*y;
                  double icdist = (1 + ((k[7]*r2 + k[6])*r2 + k[5])*r2)/(1 + ((k[4]*r2 + k[1])*r2 + k[0])*r2);
                  if (icdist < 0)  // test: undistortPoints.regression_14583
                  {
                      x = (u - cx)*ifx;
                      y = (v - cy)*ify;
                      break;
                  }
                  double deltaX = 2*k[2]*x*y + k[3]*(r2 + 2*x*x)+ k[8]*r2+k[9]*r2*r2;
                  double deltaY = k[2]*(r2 + 2*y*y) + 2*k[3]*x*y+ k[10]*r2+k[11]*r2*r2;
                  x = (x0 - deltaX)*icdist;
                  y = (y0 - deltaY)*icdist;
  
                  if(criteria.type & cv::TermCriteria::EPS)
                  {
                      double r4, r6, a1, a2, a3, cdist, icdist2;
                      double xd, yd, xd0, yd0;
                      cv::Vec3d vecTilt;
  
                      r2 = x*x + y*y;
                      r4 = r2*r2;
                      r6 = r4*r2;
                      a1 = 2*x*y;
                      a2 = r2 + 2*x*x;
                      a3 = r2 + 2*y*y;
                      cdist = 1 + k[0]*r2 + k[1]*r4 + k[4]*r6;
                      icdist2 = 1./(1 + k[5]*r2 + k[6]*r4 + k[7]*r6);
                      xd0 = x*cdist*icdist2 + k[2]*a1 + k[3]*a2 + k[8]*r2+k[9]*r4;
                      yd0 = y*cdist*icdist2 + k[2]*a3 + k[3]*a1 + k[10]*r2+k[11]*r4;
  
                      vecTilt = matTilt*cv::Vec3d(xd0, yd0, 1);
                      invProj = vecTilt(2) ? 1./vecTilt(2) : 1;
                      xd = invProj * vecTilt(0);
                      yd = invProj * vecTilt(1);
  
                      double x_proj = xd*fx + cx;
                      double y_proj = yd*fy + cy;
  
                      error = sqrt( pow(x_proj - u, 2) + pow(y_proj - v, 2) );
                  }
              }
          }
  
          double xx = RR[0][0]*x + RR[0][1]*y + RR[0][2];
          double yy = RR[1][0]*x + RR[1][1]*y + RR[1][2];
          double ww = 1./(RR[2][0]*x + RR[2][1]*y + RR[2][2]);
          x = xx*ww;
          y = yy*ww;
  
          if( dtype == CV_32FC2 )
          {
              dstf[i*dstep].x = (float)x;
              dstf[i*dstep].y = (float)y;
          }
          else
          {
              dstd[i*dstep].x = x;
              dstd[i*dstep].y = y;
          }
      }
  }
  
  void cvUndistortPoints(const CvMat* _src, CvMat* _dst, const CvMat* _cameraMatrix,
                         const CvMat* _distCoeffs,
                         const CvMat* matR, const CvMat* matP)
  {
      cvUndistortPointsInternal(_src, _dst, _cameraMatrix, _distCoeffs, matR, matP,
                                cv::TermCriteria(cv::TermCriteria::COUNT, 5, 0.01));
  }
  
  namespace cv {
  
  void undistortPoints(InputArray _src, OutputArray _dst,
                       InputArray _cameraMatrix,
                       InputArray _distCoeffs,
                       InputArray _Rmat,
                       InputArray _Pmat)
  {
      undistortPoints(_src, _dst, _cameraMatrix, _distCoeffs, _Rmat, _Pmat, TermCriteria(TermCriteria::MAX_ITER, 5, 0.01));
  }
  
  void undistortPoints(InputArray _src, OutputArray _dst,
                       InputArray _cameraMatrix,
                       InputArray _distCoeffs,
                       InputArray _Rmat,
                       InputArray _Pmat,
                       TermCriteria criteria)
  {
      Mat src = _src.getMat(), cameraMatrix = _cameraMatrix.getMat();
      Mat distCoeffs = _distCoeffs.getMat(), R = _Rmat.getMat(), P = _Pmat.getMat();
  
      int npoints = src.checkVector(2), depth = src.depth();
      if (npoints < 0)
          src = src.t();
      npoints = src.checkVector(2);
      CV_Assert(npoints >= 0 && src.isContinuous() && (depth == CV_32F || depth == CV_64F));
  
      if (src.cols == 2)
          src = src.reshape(2);
  
      _dst.create(npoints, 1, CV_MAKETYPE(depth, 2), -1, true);
      Mat dst = _dst.getMat();
  
      CvMat _csrc = cvMat(src), _cdst = cvMat(dst), _ccameraMatrix = cvMat(cameraMatrix);
      CvMat matR, matP, _cdistCoeffs, *pR=0, *pP=0, *pD=0;
      if( !R.empty() )
          pR = &(matR = cvMat(R));
      if( !P.empty() )
          pP = &(matP = cvMat(P));
      if( !distCoeffs.empty() )
          pD = &(_cdistCoeffs = cvMat(distCoeffs));
      cvUndistortPointsInternal(&_csrc, &_cdst, &_ccameraMatrix, pD, pR, pP, criteria);
  }
  
  static Point2f mapPointSpherical(const Point2f& p, float alpha, Vec4d* J, enum UndistortTypes projType)
  {
      double x = p.x, y = p.y;
      double beta = 1 + 2*alpha;
      double v = x*x + y*y + 1, iv = 1/v;
      double u = std::sqrt(beta*v + alpha*alpha);
  
      double k = (u - alpha)*iv;
      double kv = (v*beta/u - (u - alpha)*2)*iv*iv;
      double kx = kv*x, ky = kv*y;
  
      if( projType == PROJ_SPHERICAL_ORTHO )
      {
          if(J)
              *J = Vec4d(kx*x + k, kx*y, ky*x, ky*y + k);
          return Point2f((float)(x*k), (float)(y*k));
      }
      if( projType == PROJ_SPHERICAL_EQRECT )
      {
          // equirectangular
          double iR = 1/(alpha + 1);
          double x1 = std::max(std::min(x*k*iR, 1.), -1.);
          double y1 = std::max(std::min(y*k*iR, 1.), -1.);
  
          if(J)
          {
              double fx1 = iR/std::sqrt(1 - x1*x1);
              double fy1 = iR/std::sqrt(1 - y1*y1);
              *J = Vec4d(fx1*(kx*x + k), fx1*ky*x, fy1*kx*y, fy1*(ky*y + k));
          }
          return Point2f((float)asin(x1), (float)asin(y1));
      }
      CV_Error(Error::StsBadArg, "Unknown projection type");
  }
  
  
  static Point2f invMapPointSpherical(Point2f _p, float alpha, enum UndistortTypes projType)
  {
      double eps = 1e-12;
      Vec2d p(_p.x, _p.y), q(_p.x, _p.y), err;
      Vec4d J;
      int i, maxiter = 5;
  
      for( i = 0; i < maxiter; i++ )
      {
          Point2f p1 = mapPointSpherical(Point2f((float)q[0], (float)q[1]), alpha, &J, projType);
          err = Vec2d(p1.x, p1.y) - p;
          if( err[0]*err[0] + err[1]*err[1] < eps )
              break;
  
          Vec4d JtJ(J[0]*J[0] + J[2]*J[2], J[0]*J[1] + J[2]*J[3],
                    J[0]*J[1] + J[2]*J[3], J[1]*J[1] + J[3]*J[3]);
          double d = JtJ[0]*JtJ[3] - JtJ[1]*JtJ[2];
          d = d ? 1./d : 0;
          Vec4d iJtJ(JtJ[3]*d, -JtJ[1]*d, -JtJ[2]*d, JtJ[0]*d);
          Vec2d JtErr(J[0]*err[0] + J[2]*err[1], J[1]*err[0] + J[3]*err[1]);
  
          q -= Vec2d(iJtJ[0]*JtErr[0] + iJtJ[1]*JtErr[1], iJtJ[2]*JtErr[0] + iJtJ[3]*JtErr[1]);
          //Matx22d J(kx*x + k, kx*y, ky*x, ky*y + k);
          //q -= Vec2d((J.t()*J).inv()*(J.t()*err));
      }
  
      return i < maxiter ? Point2f((float)q[0], (float)q[1]) : Point2f(-FLT_MAX, -FLT_MAX);
  }
  
  float initWideAngleProjMap(InputArray _cameraMatrix0, InputArray _distCoeffs0,
                             Size imageSize, int destImageWidth, int m1type,
                             OutputArray _map1, OutputArray _map2,
                             enum UndistortTypes projType, double _alpha)
  {
      Mat cameraMatrix0 = _cameraMatrix0.getMat(), distCoeffs0 = _distCoeffs0.getMat();
      double k[14] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0}, M[9]={0,0,0,0,0,0,0,0,0};
      Mat distCoeffs(distCoeffs0.rows, distCoeffs0.cols, CV_MAKETYPE(CV_64F,distCoeffs0.channels()), k);
      Mat cameraMatrix(3,3,CV_64F,M);
      Point2f scenter((float)cameraMatrix.at<double>(0,2), (float)cameraMatrix.at<double>(1,2));
      Point2f dcenter((destImageWidth-1)*0.5f, 0.f);
      float xmin = FLT_MAX, xmax = -FLT_MAX, ymin = FLT_MAX, ymax = -FLT_MAX;
      int N = 9;
      std::vector<Point2f> uvec(1), vvec(1);
      Mat I = Mat::eye(3,3,CV_64F);
      float alpha = (float)_alpha;
  
      int ndcoeffs = distCoeffs0.cols*distCoeffs0.rows*distCoeffs0.channels();
      CV_Assert((distCoeffs0.cols == 1 || distCoeffs0.rows == 1) &&
                (ndcoeffs == 4 || ndcoeffs == 5 || ndcoeffs == 8 || ndcoeffs == 12 || ndcoeffs == 14));
      CV_Assert(cameraMatrix0.size() == Size(3,3));
      distCoeffs0.convertTo(distCoeffs,CV_64F);
      cameraMatrix0.convertTo(cameraMatrix,CV_64F);
  
      alpha = std::min(alpha, 0.999f);
  
      for( int i = 0; i < N; i++ )
          for( int j = 0; j < N; j++ )
          {
              Point2f p((float)j*imageSize.width/(N-1), (float)i*imageSize.height/(N-1));
              uvec[0] = p;
              undistortPoints(uvec, vvec, cameraMatrix, distCoeffs, I, I);
              Point2f q = mapPointSpherical(vvec[0], alpha, 0, projType);
              if( xmin > q.x ) xmin = q.x;
              if( xmax < q.x ) xmax = q.x;
              if( ymin > q.y ) ymin = q.y;
              if( ymax < q.y ) ymax = q.y;
          }
  
      float scale = (float)std::min(dcenter.x/fabs(xmax), dcenter.x/fabs(xmin));
      Size dsize(destImageWidth, cvCeil(std::max(scale*fabs(ymin)*2, scale*fabs(ymax)*2)));
      dcenter.y = (dsize.height - 1)*0.5f;
  
      Mat mapxy(dsize, CV_32FC2);
      double k1 = k[0], k2 = k[1], k3 = k[2], p1 = k[3], p2 = k[4], k4 = k[5], k5 = k[6], k6 = k[7], s1 = k[8], s2 = k[9], s3 = k[10], s4 = k[11];
      double fx = cameraMatrix.at<double>(0,0), fy = cameraMatrix.at<double>(1,1), cx = scenter.x, cy = scenter.y;
      cv::Matx33d matTilt;
      cv::detail::computeTiltProjectionMatrix(k[12], k[13], &matTilt);
  
      for( int y = 0; y < dsize.height; y++ )
      {
          Point2f* mxy = mapxy.ptr<Point2f>(y);
          for( int x = 0; x < dsize.width; x++ )
          {
              Point2f p = (Point2f((float)x, (float)y) - dcenter)*(1.f/scale);
              Point2f q = invMapPointSpherical(p, alpha, projType);
              if( q.x <= -FLT_MAX && q.y <= -FLT_MAX )
              {
                  mxy[x] = Point2f(-1.f, -1.f);
                  continue;
              }
              double x2 = q.x*q.x, y2 = q.y*q.y;
              double r2 = x2 + y2, _2xy = 2*q.x*q.y;
              double kr = 1 + ((k3*r2 + k2)*r2 + k1)*r2/(1 + ((k6*r2 + k5)*r2 + k4)*r2);
              double xd = (q.x*kr + p1*_2xy + p2*(r2 + 2*x2) + s1*r2+ s2*r2*r2);
              double yd = (q.y*kr + p1*(r2 + 2*y2) + p2*_2xy + s3*r2+ s4*r2*r2);
              cv::Vec3d vecTilt = matTilt*cv::Vec3d(xd, yd, 1);
              double invProj = vecTilt(2) ? 1./vecTilt(2) : 1;
              double u = fx*invProj*vecTilt(0) + cx;
              double v = fy*invProj*vecTilt(1) + cy;
  
              mxy[x] = Point2f((float)u, (float)v);
          }
      }
  
      if(m1type == CV_32FC2)
      {
          _map1.create(mapxy.size(), mapxy.type());
          Mat map1 = _map1.getMat();
          mapxy.copyTo(map1);
          _map2.release();
      }
      else
          convertMaps(mapxy, Mat(), _map1, _map2, m1type, false);
  
      return scale;
  }
  
  } // namespace
  /*  End of file  */
  