hom_mat2d_slant — Add a slant to a homogeneous 2D transformation matrix.
hom_mat2d_slant 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. The slanting is performed relative to the global (i.e.,
fixed) coordinate system; this corresponds to the following chains of
transformation matrices:
The point (Px,Py) is the fixed point of the transformation,
i.e., this point remains unchanged when transformed using
HomMat2DSlant. To obtain this behavior, first a translation is added
to the input transformation matrix that moves the fixed point onto the origin
of the global coordinate system. Then, the slant is added, and finally a
translation that moves the fixed point back to its original position. This
corresponds to the following chain of transformations for Axis =
'x':
To perform the transformation in the local coordinate system, i.e.,
the one described by HomMat2D, use
hom_mat2d_slant_local.
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 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.
HomMat2D (input_control) hom_mat2d → (real)
Input transformation matrix.
Theta (input_control) angle.rad → (real / integer)
Slant angle.
Default: 0.78
Suggested values: 0.1, 0.2, 0.3, 0.4, 0.78, 1.57, 3.14
Value range:
0
≤
Theta
≤
6.28318530718
Axis (input_control) string → (string)
Coordinate axis that is slanted.
Default: 'x'
List of values: 'x', 'y'
Px (input_control) point.x → (real / integer)
Fixed point of the transformation (x coordinate).
Default: 0
Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024
Py (input_control) point.y → (real / integer)
Fixed point of the transformation (y coordinate).
Default: 0
Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024
HomMat2DSlant (output_control) hom_mat2d → (real)
Output transformation matrix.
If the parameters are valid, the operator hom_mat2d_slant returns
2 (
H_MSG_TRUE)
. If necessary, an exception is raised.
hom_mat2d_identity,
hom_mat2d_translate,
hom_mat2d_scale,
hom_mat2d_rotate,
hom_mat2d_slant,
hom_mat2d_reflect
hom_mat2d_translate,
hom_mat2d_scale,
hom_mat2d_rotate,
hom_mat2d_slant,
hom_mat2d_reflect
Foundation