hom_mat2d_rotate — Add a rotation to a homogeneous 2D transformation matrix.
hom_mat2d_rotate( : : HomMat2D, Phi, Px, Py : HomMat2DRotate)
hom_mat2d_rotate adds a rotation by the angle Phi to the
homogeneous 2D transformation matrix HomMat2D and returns the
resulting matrix in HomMat2DRotate. The rotation is described by a
2×2 rotation matrix R. It is
performed relative to the global (i.e., fixed) coordinate system; this
corresponds to the following chain of transformation matrices:
The point (Px,Py) is the fixed point of the transformation,
i.e., this point remains unchanged when transformed using
HomMat2DRotate. 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 rotation is added, and
finally a translation that moves the fixed point back to its original
position. This corresponds to the following chain of transformations:
To perform the transformation in the local coordinate system, i.e.,
the one described by HomMat2D, use
hom_mat2d_rotate_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.
Phi (input_control) angle.rad → (real / integer)
Rotation angle.
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
≤
Phi
≤
6.28318530718
Px (input_control) point.x → (real / integer)
Fixed point of the transformation (x coordinate).
Default value: 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 value: 0
Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024
HomMat2DRotate (output_control) hom_mat2d → (real)
Output transformation matrix.
If the parameters are valid, the operator hom_mat2d_rotate returns
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