createRotation90

CREATEROTATION90  Matrix of a rotation for 90 degrees multiples.

   MAT = createRotation90
   Returns the 3-by-3 matrix corresponding to a rotation by 90 degrees.
   As trigonometric functions are explicitley converted to +1 or -1, the
   resulting matrix obtained with this function is more precise than 
   the one obtained with createRotation.

   MAT = createRotation90(NUM)
   Specifies the number of rotations to performs. NUM should be an integer
   (possibly negative).

   Example
     poly = [10 0;20 0;10 10];
     rot = createRotation90;
     poly2 = transformPoint(poly, rot);
     figure; hold on; axis equal;
     drawPolygon(poly);
     drawPolygon(poly2, 'm');
     legend('original', 'rotated');

     % specify number of rotations, and center
     rot = createRotation90(2, [10 10]);
     poly3 = transformPoint(poly, rot);
     drawPolygon(poly3, 'g');

   See also
   transforms2d, createRotation

 ------
 Author: David Legland
 e-mail: david.legland@grignon.inra.fr
 Created: 2012-06-20,    using Matlab 7.9.0.529 (R2009b)
 Copyright 2012 INRA - Cepia Software Platform.

0001 function mat = createRotation90(varargin)
0002 %CREATEROTATION90  Matrix of a rotation for 90 degrees multiples.
0003 %
0004 %   MAT = createRotation90
0005 %   Returns the 3-by-3 matrix corresponding to a rotation by 90 degrees.
0006 %   As trigonometric functions are explicitley converted to +1 or -1, the
0007 %   resulting matrix obtained with this function is more precise than
0008 %   the one obtained with createRotation.
0009 %
0010 %   MAT = createRotation90(NUM)
0011 %   Specifies the number of rotations to performs. NUM should be an integer
0012 %   (possibly negative).
0013 %
0014 %   Example
0015 %     poly = [10 0;20 0;10 10];
0016 %     rot = createRotation90;
0017 %     poly2 = transformPoint(poly, rot);
0018 %     figure; hold on; axis equal;
0019 %     drawPolygon(poly);
0020 %     drawPolygon(poly2, 'm');
0021 %     legend('original', 'rotated');
0022 %
0023 %     % specify number of rotations, and center
0024 %     rot = createRotation90(2, [10 10]);
0025 %     poly3 = transformPoint(poly, rot);
0026 %     drawPolygon(poly3, 'g');
0027 %
0028 %   See also
0029 %   transforms2d, createRotation
0030 %
0031 % ------
0032 % Author: David Legland
0033 % e-mail: david.legland@grignon.inra.fr
0034 % Created: 2012-06-20,    using Matlab 7.9.0.529 (R2009b)
0035 % Copyright 2012 INRA - Cepia Software Platform.
0036 
0037 % default values
0038 num = 1;
0039 center = [0 0];
0040 
0041 % process input arguments
0042 while ~isempty(varargin)
0043     var = varargin{1};
0044     if isnumeric(var) && isscalar(var)
0045         % extract number of rotations
0046         num = mod(mod(var, 4) + 4, 4);
0047         
0048     elseif isnumeric(var) && length(var) == 2
0049         % extract rotation center
0050         center = var;
0051         
0052     else
0053         % unknown argument
0054         error('MatGeom:createRotation90', ...
0055             'Unable to parse input arguments');
0056     end
0057     varargin(1) = [];
0058 end
0059 
0060 % determine rotation parameters
0061 switch num
0062     case 0
0063         ct = 1;
0064         st = 0;
0065     case 1
0066         ct = 0;
0067         st = 1;
0068     case 2
0069         ct = -1;
0070         st = 0;
0071     case 3
0072         ct = 0;
0073         st = -1;
0074 end
0075 
0076 % compute transform matrix
0077 mat = [ ...
0078     ct -st 0; ...
0079     st ct 0; ...
0080     0 0 1];
0081 
0082 % change center if needed
0083 if sum(center ~= [0 0]) > 0
0084     tra = createTranslation(center);
0085     mat = tra * mat / tra; 
0086 end