createLineReflection

CREATELINEREFLECTION Create the the 3x3 matrix of a line reflection.

   TRANS = createLineReflection(LINE);
   where line is given as [x0 y0 dx dy], return the affine tansform
   corresponding to the desired line reflection


   See also:
   lines2d, transforms2d, transformPoint,
   createTranslation, createHomothecy, createScaling

   ---------
   author : David Legland
   INRA - TPV URPOI - BIA IMASTE
   created the 19/01/2005.

0001 function trans = createLineReflection(line)
0002 %CREATELINEREFLECTION Create the the 3x3 matrix of a line reflection.
0003 %
0004 %   TRANS = createLineReflection(LINE);
0005 %   where line is given as [x0 y0 dx dy], return the affine tansform
0006 %   corresponding to the desired line reflection
0007 %
0008 %
0009 %   See also:
0010 %   lines2d, transforms2d, transformPoint,
0011 %   createTranslation, createHomothecy, createScaling
0012 %
0013 %   ---------
0014 %   author : David Legland
0015 %   INRA - TPV URPOI - BIA IMASTE
0016 %   created the 19/01/2005.
0017 %
0018 
0019 %   HISTORY
0020 %   22/04/2009: rename as createLineReflection
0021 
0022 % extract line parameters
0023 x0 = line(:,1);
0024 y0 = line(:,2);
0025 dx = line(:,3);
0026 dy = line(:,4);
0027 
0028 % normalisation coefficient of line direction vector
0029 delta = dx*dx + dy*dy;
0030 
0031 % compute coefficients of transform
0032 m00 = (dx*dx - dy*dy)/delta; 
0033 m01 = 2*dx*dy/delta; 
0034 m02 = 2*dy*(dy*x0 - dx*y0)/delta; 
0035 m10 = 2*dx*dy/delta; 
0036 m11 = (dy*dy - dx*dx)/delta; 
0037 m12 = 2*dx*(dx*y0 - dy*x0)/delta; 
0038 
0039 % create transformation
0040 trans = [m00 m01 m02; m10 m11 m12; 0 0 1];