geo/tcAffineTransform.cpp

   1 /***************************************************************************
   2  *   This file is part of Tecorrec.                                        *
   3  *   Copyright 2008 James Hogan <james@albanarts.com>                      *
   4  *                                                                         *
   5  *   Tecorrec is free software: you can redistribute it and/or modify      *
   6  *   it under the terms of the GNU General Public License as published by  *
   7  *   the Free Software Foundation, either version 2 of the License, or     *
   8  *   (at your option) any later version.                                   *
   9  *                                                                         *
  10  *   Tecorrec is distributed in the hope that it will be useful,           *
  11  *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
  12  *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
  13  *   GNU General Public License for more details.                          *
  14  *                                                                         *
  15  *   You should have received a copy of the GNU General Public License     *
  16  *   along with Tecorrec.  If not, write to the Free Software Foundation,  *
  17  *   Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.   *
  18  ***************************************************************************/
  19
  20 /**
  21  * @file tcAffineTransform.cpp
  22  * @brief Affine transformation between 2d linear coordinate spaces.
  23  */
  24
  25 #include "tcAffineTransform.h"
  26
  27 #include <gdal_priv.h>
  28
  29 /// Find the inverse.
  30 template <>
  31 tcAffineTransform2<double> tcAffineTransform2<double>::inverse() const
  32 {
  33   /// @todo Implement independently of GDAL
  34   /*
  35    * [a,b,c;d,e,f].[1;x;y] = [n;t]
  36    * n = a + b*x + c*y (1)
  37    * t = d + e*x + f*y (2)
  38    * (rearrange to make x subject of (2))
  39    * x = (t - d - f*y)/e (3)
  40    * (substitude (3) into (1))
  41    * n = a + b*(t - d - f*y)/e + c*y (4)
  42    * (rearrange to make y subject of (4))
  43    * n = a + b*(t - d)/e - b*f*y/e + c*y
  44    * n = a + b*(t - d)/e + y*(c - b*f/e)
  45    * y = (n - a + b*(d - t)/e ) / (c - b*f/e)
  46    * y = (n + (b*d/e - a) - t*b/e ) / (c - b*f/e)
  47    * (rearrange to make y subject of ..)
  48    * ..
  49    * [1;x;y] = [g,h,i;j,k,m].[n;t]
  50    * j = (b*d/e - a) / (c - b*f/e)
  51    * k = 1 / (c - b*f/e)
  52    * m = - b/(e*c - b*f)
  53    */
  54   tcAffineTransform2 result;
  55   GDALInvGeoTransform((double*)&m_transform[0][0], result);
  56   return result;
  57 }