hom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocalhom_mat2d_slant_localT_hom_mat2d_slant_local🔗

Short description🔗

hom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocalhom_mat2d_slant_localT_hom_mat2d_slant_local — Add a slant to a homogeneous 2D transformation matrix.

Signature🔗

hom_mat2d_slant_local( hom_mat2d HomMat2D, angle.rad Theta, string Axis, out hom_mat2d HomMat2DSlant )

Description🔗

hom_mat2d_slant_localHomMat2dSlantLocal adds a slant by the angle Thetathetatheta to the homogeneous 2D transformation matrix HomMat2DhomMat2Dhom_mat_2d and returns the resulting matrix in HomMat2DSlanthomMat2DSlanthom_mat_2dslant. A slant is an affine transformation in which one coordinate axis remains fixed, while the other coordinate axis is rotated counterclockwise by an angle Thetathetatheta. The parameter Axisaxisaxis determines which coordinate axis is slanted. For Axisaxisaxis = 'x'"x", the x-axis is slanted and the y-axis remains fixed, while for Axisaxisaxis = 'y'"y" the y-axis is slanted and the x-axis remains fixed. In contrast to hom_mat2d_slantHomMat2dSlant, the slanting is performed relative to the local coordinate system, i.e., the coordinate system described by HomMat2DhomMat2Dhom_mat_2d; this corresponds to the following chains of transformation matrices:

\[\begin{eqnarray*} \textrm{Axis} = '\textit{x}': & & \textrm{HomMat2DSlant} = \textrm{HomMat2D} \cdot \mvHomMatrixTwoDElements{\cos(\textrm{Theta}) & 0 & 0 \\ \sin(\textrm{Theta}) & 1 & 0} \\*[0.3cm] \textrm{Axis} = '\textit{y}': & & \textrm{HomMat2DSlant} = \textrm{HomMat2D} \cdot \mvHomMatrixTwoDElements{1 & - \sin(\textrm{Theta}) & 0 \\ 0 & \cos(\textrm{Theta}) & 0} \\ \end{eqnarray*}\]

The fixed point of the transformation is the origin of the local coordinate system, i.e., this point remains unchanged when transformed using HomMat2DSlanthomMat2DSlanthom_mat_2dslant.

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 (Rowrowrow,Columncolumncolumn). 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🔗

HomMat2DhomMat2Dhom_mat_2d (input_control) hom_mat2d → (real)HTuple (double)HHomMat2D, HTuple (double)Sequence[float]Htuple (double)

Input transformation matrix.

Thetathetatheta (input_control) angle.rad → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Union[float, int]Htuple (double / Hlong)

Slant angle.

Default: 0.780.78
Suggested values: 0.1, 0.2, 0.3, 0.4, 0.78, 1.57, 3.140.1, 0.2, 0.3, 0.4, 0.78, 1.57, 3.14
Value range: 0 ≤ Theta ≤ 6.28318530718

Axisaxisaxis (input_control) string → (string)HTuple (HString)HTuple (string)strHtuple (char*)

Coordinate axis that is slanted.

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

HomMat2DSlanthomMat2DSlanthom_mat_2dslant (output_control) hom_mat2d → (real)HTuple (double)HHomMat2D, HTuple (double)Sequence[float]Htuple (double)

Output transformation matrix.

Result🔗

If the parameters are valid, the operator hom_mat2d_slant_localHomMat2dSlantLocal returns 2 (H_MSG_TRUE). If necessary, an exception is raised.

Combinations with other operators🔗

Combinations

Possible predecessors

hom_mat2d_identityHomMat2dIdentity, hom_mat2d_translate_localHomMat2dTranslateLocal, hom_mat2d_scale_localHomMat2dScaleLocal, hom_mat2d_rotate_localHomMat2dRotateLocal, hom_mat2d_slant_localHomMat2dSlantLocal, hom_mat2d_reflectHomMat2dReflect

Possible successors

hom_mat2d_translate_localHomMat2dTranslateLocal, hom_mat2d_scale_localHomMat2dScaleLocal, hom_mat2d_rotate_localHomMat2dRotateLocal, hom_mat2d_slant_localHomMat2dSlantLocal, hom_mat2d_reflect_localHomMat2dReflectLocal

See also

hom_mat2d_slantHomMat2dSlant

Module🔗

Foundation