hom_mat2d_rotateT_hom_mat2d_rotateHomMat2dRotateHomMat2dRotatehom_mat2d_rotate (Operator)

Name

hom_mat2d_rotateT_hom_mat2d_rotateHomMat2dRotateHomMat2dRotatehom_mat2d_rotate — Add a rotation to a homogeneous 2D transformation matrix.

Signature

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

Herror T_hom_mat2d_rotate(const Htuple HomMat2D, const Htuple Phi, const Htuple Px, const Htuple Py, Htuple* HomMat2DRotate)

void HomMat2dRotate(const HTuple& HomMat2D, const HTuple& Phi, const HTuple& Px, const HTuple& Py, HTuple* HomMat2DRotate)

HHomMat2D HHomMat2D::HomMat2dRotate(const HTuple& Phi, const HTuple& Px, const HTuple& Py) const

HHomMat2D HHomMat2D::HomMat2dRotate(double Phi, double Px, double Py) const

static void HOperatorSet.HomMat2dRotate(HTuple homMat2D, HTuple phi, HTuple px, HTuple py, out HTuple homMat2DRotate)

HHomMat2D HHomMat2D.HomMat2dRotate(HTuple phi, HTuple px, HTuple py)

HHomMat2D HHomMat2D.HomMat2dRotate(double phi, double px, double py)

def hom_mat2d_rotate(hom_mat_2d: Sequence[float], phi: Union[float, int], px: Union[float, int], py: Union[float, int]) -> Sequence[float]

Description

hom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotateHomMat2dRotatehom_mat2d_rotate adds a rotation by the angle PhiPhiPhiPhiphiphi to the homogeneous 2D transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DhomMat2Dhom_mat_2d and returns the resulting matrix in HomMat2DRotateHomMat2DRotateHomMat2DRotateHomMat2DRotatehomMat2DRotatehom_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:

The point (PxPxPxPxpxpx,PyPyPyPypypy) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat2DRotateHomMat2DRotateHomMat2DRotateHomMat2DRotatehomMat2DRotatehom_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:

To perform the transformation in the local coordinate system, i.e., the one described by HomMat2DHomMat2DHomMat2DHomMat2DhomMat2Dhom_mat_2d, use hom_mat2d_rotate_localhom_mat2d_rotate_localHomMat2dRotateLocalHomMat2dRotateLocalHomMat2dRotateLocalhom_mat2d_rotate_local.

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 (RowRowRowRowrowrow,ColumnColumnColumnColumncolumncolumn). 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.

Execution Information

Parameters

HomMat2DHomMat2DHomMat2DHomMat2DhomMat2Dhom_mat_2d (input_control)  hom_mat2d HHomMat2D, HTupleSequence[float]HTupleHtuple (real) (double) (double) (double)

Input transformation matrix.

PhiPhiPhiPhiphiphi (input_control)  angle.rad HTupleUnion[float, int]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

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 phi ≤ 6.28318530718

PxPxPxPxpxpx (input_control)  point.x HTupleUnion[float, int]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Fixed point of the transformation (x coordinate).

Default value: 0

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

PyPyPyPypypy (input_control)  point.y HTupleUnion[float, int]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Fixed point of the transformation (y coordinate).

Default value: 0

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

HomMat2DRotateHomMat2DRotateHomMat2DRotateHomMat2DRotatehomMat2DRotatehom_mat_2drotate (output_control)  hom_mat2d HHomMat2D, HTupleSequence[float]HTupleHtuple (real) (double) (double) (double)

Output transformation matrix.

Result

If the parameters are valid, the operator hom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotateHomMat2dRotatehom_mat2d_rotate returns 2 (H_MSG_TRUE). If necessary, an exception is raised.

Possible Predecessors

hom_mat2d_identityhom_mat2d_identityHomMat2dIdentityHomMat2dIdentityHomMat2dIdentityhom_mat2d_identity, hom_mat2d_translatehom_mat2d_translateHomMat2dTranslateHomMat2dTranslateHomMat2dTranslatehom_mat2d_translate, hom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScaleHomMat2dScalehom_mat2d_scale, hom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotateHomMat2dRotatehom_mat2d_rotate, hom_mat2d_slanthom_mat2d_slantHomMat2dSlantHomMat2dSlantHomMat2dSlanthom_mat2d_slant, hom_mat2d_reflecthom_mat2d_reflectHomMat2dReflectHomMat2dReflectHomMat2dReflecthom_mat2d_reflect

Possible Successors

hom_mat2d_translatehom_mat2d_translateHomMat2dTranslateHomMat2dTranslateHomMat2dTranslatehom_mat2d_translate, hom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScaleHomMat2dScalehom_mat2d_scale, hom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotateHomMat2dRotatehom_mat2d_rotate, hom_mat2d_slanthom_mat2d_slantHomMat2dSlantHomMat2dSlantHomMat2dSlanthom_mat2d_slant, hom_mat2d_reflecthom_mat2d_reflectHomMat2dReflectHomMat2dReflectHomMat2dReflecthom_mat2d_reflect

See also

hom_mat2d_rotate_localhom_mat2d_rotate_localHomMat2dRotateLocalHomMat2dRotateLocalHomMat2dRotateLocalhom_mat2d_rotate_local

Module

Foundation