hom_mat2d_slant_localT_hom_mat2d_slant_localhom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocal (Operator)

Name

hom_mat2d_slant_localT_hom_mat2d_slant_localhom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocal — Add a slant to a homogeneous 2D transformation matrix.

Signature

hom_mat2d_slant_local( : : HomMat2D, Theta, Axis : HomMat2DSlant)

hom_mat2d_slant_localhom_mat2d_slant_localhom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocal adds a slant by the angle ThetaThetaThetaThetatheta to the homogeneous 2D transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D and returns the resulting matrix in HomMat2DSlantHomMat2DSlantHomMat2DSlantHomMat2DSlanthomMat2DSlant. A slant is an affine transformation in which one coordinate axis remains fixed, while the other coordinate axis is rotated counterclockwise by an angle ThetaThetaThetaThetatheta. The parameter AxisAxisAxisAxisaxis determines which coordinate axis is slanted. For AxisAxisAxisAxisaxis = 'x'"x""x""x""x", the x-axis is slanted and the y-axis remains fixed, while for AxisAxisAxisAxisaxis = 'y'"y""y""y""y" the y-axis is slanted and the x-axis remains fixed. In contrast to hom_mat2d_slanthom_mat2d_slanthom_mat2d_slantHomMat2dSlantHomMat2dSlant, the slanting is performed relative to the local coordinate system, i.e., the coordinate system described by HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D; this corresponds to the following chains of transformation matrices:

                                          / cos(Theta) 0 0 \
  Axis = 'x':  HomMat2DSlant = HomMat2D * | sin(Theta) 1 0 |
                                          \    0       0 1 /

                                          / 1 -sin(Theta) 0 \
  Axis = 'y':  HomMat2DSlant = HomMat2D * | 0  cos(Theta) 0 |
                                          \ 0     0       1 /

The fixed point of the transformation is the origin of the local coordinate system, i.e., this point remains unchanged when transformed using HomMat2DSlantHomMat2DSlantHomMat2DSlantHomMat2DSlanthomMat2DSlant.

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 (RowRowRowRowrow,ColumnColumnColumnColumncolumn). 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

    / ra rb tc \
    | rd re tf |
    \ 0  0  1  /

is stored as the tuple [ra, rb, tc, rd, re, tf]. However, it is also possible to process full 3x3 matrices, which represent a projective 2D transformation.

Parallelization

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters

HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D (input_control) hom_mat2d-array → (real)

Input transformation matrix.

ThetaThetaThetaThetatheta (input_control) angle.rad → (real / integer)

Slant 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 ≤ Theta Theta Theta Theta theta ≤ 6.28318530718

AxisAxisAxisAxisaxis (input_control) string → (string)

Coordinate axis that is slanted.

Default value: 'x' "x" "x" "x" "x"

List of values: 'x'"x""x""x""x", 'y'"y""y""y""y"

HomMat2DSlantHomMat2DSlantHomMat2DSlantHomMat2DSlanthomMat2DSlant (output_control) hom_mat2d-array → (real)

Output transformation matrix.

Result

If the parameters are valid, the operator hom_mat2d_slant_localhom_mat2d_slant_localhom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocal returns 2 (H_MSG_TRUE). If necessary, an exception is raised.