hom_mat2d_scaleT_hom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScale (Operator)

Name

hom_mat2d_scaleT_hom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScale — Add a scaling to a homogeneous 2D transformation matrix.

Signature

Description

hom_mat2d_scalehom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScale adds a scaling by the scale factors SxSxSxSxsx and SySySySysy to the homogeneous 2D transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D and returns the resulting matrix in HomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScalehomMat2DScale. The scaling is described by a 2x2 scaling matrix S. It is performed relative to the global (i.e., fixed) coordinate system; this corresponds to the following chain of transformation matrices:

                  / Sx 0  0 \
  HomMat2DScale = | 0  Sy 0 | * HomMat2D
                  \ 0  0  1 /

       S = | Sx 0 |
           | 0 Sy |

The point (PxPxPxPxpx,PyPyPyPypy) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScalehomMat2DScale. 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 scaling 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 \   / Sx 0  0 \   / 1 0 -Px \
  HomMat2DScale = | 0 1 +Py | * | 0  Sy 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_scale_localhom_mat2d_scale_localhom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocal.

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

Result

hom_mat2d_scalehom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScale returns 2 (H_MSG_TRUE) if both scale factors are not 0. If necessary, an exception is raised.

Possible Predecessors

hom_mat2d_identityhom_mat2d_identityhom_mat2d_identityHomMat2dIdentityHomMat2dIdentity, hom_mat2d_translatehom_mat2d_translatehom_mat2d_translateHomMat2dTranslateHomMat2dTranslate, hom_mat2d_scalehom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScale, hom_mat2d_rotatehom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate, hom_mat2d_slanthom_mat2d_slanthom_mat2d_slantHomMat2dSlantHomMat2dSlant

Possible Successors

hom_mat2d_translatehom_mat2d_translatehom_mat2d_translateHomMat2dTranslateHomMat2dTranslate, hom_mat2d_scalehom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScale, hom_mat2d_rotatehom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate, hom_mat2d_slanthom_mat2d_slanthom_mat2d_slantHomMat2dSlantHomMat2dSlant

See also

hom_mat2d_scale_localhom_mat2d_scale_localhom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocal

Module

Foundation