hom_mat2d_scale_local🔗
Short description🔗
hom_mat2d_scale_local — Add a scaling to a homogeneous 2D transformation matrix.
Signature🔗
hom_mat2d_scale_local( hom_mat2d HomMat2D, number Sx, number Sy, out hom_mat2d HomMat2DScale )
Description🔗
hom_mat2d_scale_local adds a scaling by the scale factors Sx
and Sy to the homogeneous 2D transformation matrix HomMat2D
and returns the resulting matrix in HomMat2DScale. The scaling is
described by a 2×2 scaling matrix
S. In contrast to hom_mat2d_scale, it is
performed relative to the local coordinate system, i.e., the coordinate
system described by HomMat2D; this corresponds to the following
chain of transformation matrices:
The fixed point of the transformation is the origin of the local
coordinate system, i.e., this point remains unchanged when
transformed using HomMat2DScale.
Attention🔗
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 \(\mvHomMatrixTwoDElements{ra & rb & tc \\ rd & re & tf}\) 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.
Execution information🔗
Execution information
-
Multithreading type: reentrant (runs in parallel with non-exclusive operators).
-
Multithreading scope: global (may be called from any thread).
-
Processed without parallelization.
Parameters🔗
HomMat2D (input_control) hom_mat2d → (real)
Input transformation matrix.
Sx (input_control) number → (real / integer)
Scale factor along the x-axis.
Default: 2
Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 16
Restriction: Sx != 0
Sy (input_control) number → (real / integer)
Scale factor along the y-axis.
Default: 2
Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 16
Restriction: Sy != 0
HomMat2DScale (output_control) hom_mat2d → (real)
Output transformation matrix.
Result🔗
hom_mat2d_scale_local returns 2 (H_MSG_TRUE) if both scale factors are not
0. If necessary, an exception is raised.
Combinations with other operators🔗
Combinations
Possible predecessors
hom_mat2d_identity, hom_mat2d_translate_local, hom_mat2d_scale_local, hom_mat2d_rotate_local, hom_mat2d_slant_local, hom_mat2d_reflect_local
Possible successors
hom_mat2d_translate_local, hom_mat2d_scale_local, hom_mat2d_rotate_local, hom_mat2d_slant_local, hom_mat2d_reflect_local
See also
Module🔗
Foundation