createRotation

CREATEROTATION Create the 3*3 matrix of a rotation.

   TRANS = createRotation(THETA);
   Returns the rotation corresponding to angle THETA (in radians)
   The returned matrix has the form :
   [cos(theta) -sin(theta)  0]
   [sin(theta)  cos(theta)  0]
   [0           0           1]

   TRANS = createRotation(POINT, THETA);
   TRANS = createRotation(X0, Y0, THETA);
   Also specifies origin of rotation. The result is similar as performing
   translation(-X0, -Y0), rotation(THETA), and translation(X0, Y0).

   Example
     % apply a rotation on a polygon
     poly = [0 0; 30 0;30 10;10 10;10 20;0 20];
     trans = createRotation([10 20], pi/6);
     polyT = transformPoint(poly, trans);
     % display the original and the rotated polygons
     figure; hold on; axis equal; axis([-10 40 -10 40]);
     drawPolygon(poly, 'k');
     drawPolygon(polyT, 'b');

   See also:
   transforms2d, transformPoint, createRotation90, createTranslation

0001 function trans = createRotation(varargin)
0002 %CREATEROTATION Create the 3*3 matrix of a rotation.
0003 %
0004 %   TRANS = createRotation(THETA);
0005 %   Returns the rotation corresponding to angle THETA (in radians)
0006 %   The returned matrix has the form :
0007 %   [cos(theta) -sin(theta)  0]
0008 %   [sin(theta)  cos(theta)  0]
0009 %   [0           0           1]
0010 %
0011 %   TRANS = createRotation(POINT, THETA);
0012 %   TRANS = createRotation(X0, Y0, THETA);
0013 %   Also specifies origin of rotation. The result is similar as performing
0014 %   translation(-X0, -Y0), rotation(THETA), and translation(X0, Y0).
0015 %
0016 %   Example
0017 %     % apply a rotation on a polygon
0018 %     poly = [0 0; 30 0;30 10;10 10;10 20;0 20];
0019 %     trans = createRotation([10 20], pi/6);
0020 %     polyT = transformPoint(poly, trans);
0021 %     % display the original and the rotated polygons
0022 %     figure; hold on; axis equal; axis([-10 40 -10 40]);
0023 %     drawPolygon(poly, 'k');
0024 %     drawPolygon(polyT, 'b');
0025 %
0026 %   See also:
0027 %   transforms2d, transformPoint, createRotation90, createTranslation
0028 %
0029 
0030 %   ---------
0031 %   author : David Legland
0032 %   INRA - TPV URPOI - BIA IMASTE
0033 %   created the 06/04/2004.
0034 %
0035 
0036 %   HISTORY
0037 %   22/04/2009: rename as createRotation
0038 
0039 % default values
0040 cx = 0;
0041 cy = 0;
0042 theta = 0;
0043 
0044 % get input values
0045 if length(varargin)==1
0046     % only angle
0047     theta = varargin{1};
0048 elseif length(varargin)==2
0049     % origin point (as array) and angle
0050     var = varargin{1};
0051     cx = var(1);
0052     cy = var(2);
0053     theta = varargin{2};
0054 elseif length(varargin)==3
0055     % origin (x and y) and angle
0056     cx = varargin{1};
0057     cy = varargin{2};
0058     theta = varargin{3};
0059 end
0060 
0061 % compute coefs
0062 cot = cos(theta);
0063 sit = sin(theta);
0064 tx =  cy*sit - cx*cot + cx;
0065 ty = -cy*cot - cx*sit + cy;
0066 
0067 % create transformation matrix
0068 trans = [cot -sit tx; sit cot ty; 0 0 1];