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
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
HomMat2D; this corresponds to the following chains of
The fixed point of the transformation is the origin of the local
coordinate system, i.e., this point remains unchanged when
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
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 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.
→(real / integer)
Default value: 0.78
Suggested values: 0.1, 0.2, 0.3, 0.4, 0.78, 1.57, 3.14
Typical range of values:
Coordinate axis that is slanted.
Default value: 'x'
List of values: 'x', 'y'
Output transformation matrix.
If the parameters are valid, the operator
TRUE. If necessary, an exception is raised.