hom_mat2d_rotateHomMat2dRotateHomMat2dRotatehom_mat2d_rotateT_hom_mat2d_rotate🔗

Short description🔗

hom_mat2d_rotateHomMat2dRotateHomMat2dRotatehom_mat2d_rotateT_hom_mat2d_rotate — Add a rotation to a homogeneous 2D transformation matrix.

Signature🔗

hom_mat2d_rotate( hom_mat2d HomMat2D, angle.rad Phi, point.x Px, point.y Py, out hom_mat2d HomMat2DRotate )

Description🔗

hom_mat2d_rotateHomMat2dRotate adds a rotation by the angle Phiphiphi to the homogeneous 2D transformation matrix HomMat2DhomMat2Dhom_mat_2d and returns the resulting matrix in HomMat2DRotatehomMat2DRotatehom_mat_2drotate. 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:

\[\begin{eqnarray*} \textrm{HomMat2DRotate} = \mvHomMatrixTwoDRotTrans{\mvRotationMatrixVar{}{}} {\mvVectorTwoDPlain{0}{0}} \cdot \textrm{HomMat2D} \qquad \mvRotationMatrixVar{}{} \: = \: \mvMatrix{\cos(\textrm{Phi}) & - \sin(\textrm{Phi}) \\ \sin(\textrm{Phi}) & \cos(\textrm{Phi})} \end{eqnarray*}\]

The point (Pxpxpx,Pypypy) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat2DRotatehomMat2DRotatehom_mat_2drotate. 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:

\[\begin{eqnarray*} \textrm{HomMat2DRotate} = \mvHomMatrixTwoDElements{1 & 0 & + \textrm{Px} \\ 0 & 1 & + \textrm{Py}} \cdot \mvHomMatrixTwoDRotTrans{\mvRotationMatrixVar{}{}} {\mvVectorTwoDPlain{0}{0}} \cdot \mvHomMatrixTwoDElements{1 & 0 & - \textrm{Px} \\ 0 & 1 & - \textrm{Py}} \cdot \textrm{HomMat2D} \end{eqnarray*}\]

To perform the transformation in the local coordinate system, i.e., the one described by HomMat2DhomMat2Dhom_mat_2d, use hom_mat2d_rotate_localHomMat2dRotateLocal.

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.

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

Rotation 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 ≤ Phi ≤ 6.28318530718

Pxpxpx (input_control) point.x → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Union[float, int]Htuple (double / Hlong)

Fixed point of the transformation (x coordinate).

Default: 00
Suggested values: 0, 16, 32, 64, 128, 256, 512, 10240, 16, 32, 64, 128, 256, 512, 1024

Pypypy (input_control) point.y → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Union[float, int]Htuple (double / Hlong)

Fixed point of the transformation (y coordinate).

Default: 00
Suggested values: 0, 16, 32, 64, 128, 256, 512, 10240, 16, 32, 64, 128, 256, 512, 1024

HomMat2DRotatehomMat2DRotatehom_mat_2drotate (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_rotateHomMat2dRotate returns 2 (H_MSG_TRUE). If necessary, an exception is raised.

Combinations with other operators🔗

Combinations

Possible predecessors

hom_mat2d_identityHomMat2dIdentity, hom_mat2d_translateHomMat2dTranslate, hom_mat2d_scaleHomMat2dScale, hom_mat2d_rotateHomMat2dRotate, hom_mat2d_slantHomMat2dSlant, hom_mat2d_reflectHomMat2dReflect

Possible successors

hom_mat2d_translateHomMat2dTranslate, hom_mat2d_scaleHomMat2dScale, hom_mat2d_rotateHomMat2dRotate, hom_mat2d_slantHomMat2dSlant, hom_mat2d_reflectHomMat2dReflect

Module🔗

Foundation