Once the correction angle has been found, a rotation procedure is implemented. Four possible rotation angles are considered. A 0 angle means no rotation. Three other rotation angles (90 clockwise or counterclockwise and 180 ) may be with or without flip.
For the rotation procedure, let us first consider a coordinate system with the x1 and y1 axes to be rotated without changing the origin. This yields new coordinates, yet the same origin as in the original system (Fig. 11). For a ^ rotation angle the old and new coordinates are related by
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