hom_mat2d_reflect_local — Add a reflection to a homogeneous 2D transformation matrix.
hom_mat2d_reflect_local( : : HomMat2D, Px, Py : HomMat2DReflect)
hom_mat2d_reflect_local adds a reflection about the axis given by
the two points (0,0) and (Px,Py) to the homogeneous 2D
transformation matrix HomMat2D and returns the resulting matrix
in HomMat2DReflect. The reflection is described by a
2×2 reflection matrix M.
In contrast to hom_mat2d_reflect, 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 axis (0,0)-(Px,Py) is fixed in the transformation,
i.e., the points on the axis remain unchanged when transformed using
HomMat2DReflect.
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.
Px (input_control) point.x → (real / integer)
Point that defines the axis (x coordinate).
Default value: 16
Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024
Py (input_control) point.y → (real / integer)
Point that defines the axis (y coordinate).
Default value: 32
Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024
HomMat2DReflect (output_control) hom_mat2d → (real)
Output transformation matrix.
hom_mat2d_reflect_local returns TRUE if the point
(Px,Py) is not (0,0). 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_local
hom_mat2d_translate_local,
hom_mat2d_scale_local,
hom_mat2d_rotate_local,
hom_mat2d_slant_local,
hom_mat2d_reflect_local
Foundation