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

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 % E-mail: david.legland@inrae.fr
0016 % Created: 2005-01-19
0017 % Copyright 2005-2024 INRA - TPV URPOI - BIA IMASTE
0018 
0019 % extract line parameters
0020 x0 = line(:,1);
0021 y0 = line(:,2);
0022 dx = line(:,3);
0023 dy = line(:,4);
0024 
0025 % normalisation coefficient of line direction vector
0026 delta = dx*dx + dy*dy;
0027 
0028 % compute coefficients of transform
0029 m00 = (dx*dx - dy*dy)/delta; 
0030 m01 = 2*dx*dy/delta; 
0031 m02 = 2*dy*(dy*x0 - dx*y0)/delta; 
0032 m10 = 2*dx*dy/delta; 
0033 m11 = (dy*dy - dx*dx)/delta; 
0034 m12 = 2*dx*(dx*y0 - dy*x0)/delta; 
0035 
0036 % create transformation
0037 trans = [m00 m01 m02; m10 m11 m12; 0 0 1];