hom_mat2d_rotateT_hom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate (Operator)

Name

hom_mat2d_rotateT_hom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate — Add a rotation to a homogeneous 2D transformation matrix.

Signature

hom_mat2d_rotate( : : HomMat2D, Phi, Px, Py : HomMat2DRotate)

hom_mat2d_rotatehom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate adds a rotation by the angle PhiPhiPhiPhiphi to the homogeneous 2D transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D and returns the resulting matrix in HomMat2DRotateHomMat2DRotateHomMat2DRotateHomMat2DRotatehomMat2DRotate. The rotation is described by a 2x2 rotation matrix R. It is performed relative to the global (i.e., fixed) coordinate system; this corresponds to the following chain of transformation matrices:

                   / cos(Phi) -sin(Phi) 0 \
  HomMat2DRotate = | sin(Phi)  cos(Phi) 0 | * HomMat2D
                   \    0         0     1 /

       R = | cos(Phi) -sin(Phi) |
           | sin(Phi)  cos(Phi) |

The point (PxPxPxPxpx,PyPyPyPypy) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat2DRotateHomMat2DRotateHomMat2DRotateHomMat2DRotatehomMat2DRotate. 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:

                   / 1 0 +Px \   / cos(Phi) -sin(Phi) 0 \   / 1 0 -Px \
  HomMat2DRotate = | 0 1 +Py | * | sin(Phi)  cos(Phi) 0 | * | 0 1 -Py | * HomMat2D
                   \ 0 0  1  /   \    0         0     1 /   \ 0 0  1  /

To perform the transformation in the local coordinate system, i.e., the one described by HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D, use hom_mat2d_rotate_localhom_mat2d_rotate_localhom_mat2d_rotate_localHomMat2dRotateLocalHomMat2dRotateLocal.

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.

PhiPhiPhiPhiphi (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 Phi Phi Phi phi ≤ 6.28318530718

PxPxPxPxpx (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

PyPyPyPypy (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

HomMat2DRotateHomMat2DRotateHomMat2DRotateHomMat2DRotatehomMat2DRotate (output_control) hom_mat2d-array → (real)

Output transformation matrix.

Result

If the parameters are valid, the operator hom_mat2d_rotatehom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate returns 2 (H_MSG_TRUE). If necessary, an exception is raised.