hom_mat2d_slant_local — Add a slant to a homogeneous 2D transformation matrix.
hom_mat2d_slant_local adds a slant by the angle Theta to the homogeneous 2D transformation matrix HomMat2D and returns the resulting matrix in HomMat2DSlant. A slant is an affine transformation in which one coordinate axis remains fixed, while the other coordinate axis is rotated counterclockwise by an angle Theta. The parameter Axis determines which coordinate axis is slanted. For Axis = 'x', the x-axis is slanted and the y-axis remains fixed, while for Axis = 'y' the y-axis is slanted and the x-axis remains fixed. In contrast to hom_mat2d_slant, the slanting is performed relative to the local coordinate system, i.e., the coordinate system described by HomMat2D; this corresponds to the following chains of transformation matrices:
/ cos(Theta) 0 0 \ Axis = 'x': HomMat2DSlant = HomMat2D * | sin(Theta) 1 0 | \ 0 0 1 / / 1 -sin(Theta) 0 \ Axis = 'y': HomMat2DSlant = HomMat2D * | 0 cos(Theta) 0 | \ 0 0 1 /
The fixed point of the transformation is the origin of the local coordinate system, i.e., this point remains unchanged when transformed using HomMat2DSlant.
It should be noted that homogeneous transformation matrices refer to a general right-handed mathematical coordinate system. If a homogeneous transformation matrix is used to transform images, regions, XLD contours, or any other data that has been extracted from images, the row coordinates of the transformation must be passed in the x coordinates, while the column coordinates must be passed in the y coordinates. Consequently, the order of passing row and column coordinates follows the usual order (Row,Column). This convention is essential to obtain a right-handed coordinate system for the transformation of iconic data, and consequently to ensure in particular that rotations are performed in the correct mathematical direction.
Note that homogeneous matrices are stored row-by-row as a tuple; the last row is usually not stored because it is identical for all homogeneous matrices that describe an affine transformation. For example, the homogeneous matrix
/ ra rb tc \ | rd re tf | \ 0 0 1 /
is stored as the tuple [ra, rb, tc, rd, re, tf]. However, it is also possible to process full 3×3 matrices, which represent a projective 2D transformation.
Input transformation matrix.
Default value: 0.78
Suggested values: 0.1, 0.2, 0.3, 0.4, 0.78, 1.57, 3.14
Typical range of values: 0 ≤ Theta ≤ 6.28318530718
Coordinate axis that is slanted.
Default value: 'x'
List of values: 'x', 'y'
Output transformation matrix.
If the parameters are valid, the operator hom_mat2d_slant_local returns 2 (H_MSG_TRUE). If necessary, an exception is raised.
hom_mat2d_identity, hom_mat2d_translate_local, hom_mat2d_scale_local, hom_mat2d_rotate_local, hom_mat2d_slant_local, hom_mat2d_reflect
hom_mat2d_translate_local, hom_mat2d_scale_local, hom_mat2d_rotate_local, hom_mat2d_slant_local, hom_mat2d_reflect_local