hom_mat2d_scale_localT_hom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocalhom_mat2d_scale_local (Operator)

Name

hom_mat2d_scale_localT_hom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocalhom_mat2d_scale_local — Add a scaling to a homogeneous 2D transformation matrix.

Signature

Description

hom_mat2d_scale_localhom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocalHomMat2dScaleLocalhom_mat2d_scale_local adds a scaling by the scale factors SxSxSxSxsxsx and SySySySysysy to the homogeneous 2D transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DhomMat2Dhom_mat_2d and returns the resulting matrix in HomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScalehomMat2DScalehom_mat_2dscale. The scaling is described by a 2×2 scaling matrix S. In contrast to hom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScaleHomMat2dScalehom_mat2d_scale, it is performed relative to the local coordinate system, i.e., the coordinate system described by HomMat2DHomMat2DHomMat2DHomMat2DhomMat2Dhom_mat_2d; this corresponds to the following chain of transformation matrices:

The fixed point of the transformation is the origin of the local coordinate system, i.e., this point remains unchanged when transformed using HomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScalehomMat2DScalehom_mat_2dscale.

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

• 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_scale_localhom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocalHomMat2dScaleLocalhom_mat2d_scale_local returns TRUE if both scale factors are not 0. If necessary, an exception is raised.

Possible Predecessors

hom_mat2d_identityhom_mat2d_identityHomMat2dIdentityHomMat2dIdentityHomMat2dIdentityhom_mat2d_identity, hom_mat2d_translate_localhom_mat2d_translate_localHomMat2dTranslateLocalHomMat2dTranslateLocalHomMat2dTranslateLocalhom_mat2d_translate_local, hom_mat2d_scale_localhom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocalHomMat2dScaleLocalhom_mat2d_scale_local, hom_mat2d_rotate_localhom_mat2d_rotate_localHomMat2dRotateLocalHomMat2dRotateLocalHomMat2dRotateLocalhom_mat2d_rotate_local, hom_mat2d_slant_localhom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocalHomMat2dSlantLocalhom_mat2d_slant_local, hom_mat2d_reflect_localhom_mat2d_reflect_localHomMat2dReflectLocalHomMat2dReflectLocalHomMat2dReflectLocalhom_mat2d_reflect_local

Possible Successors

hom_mat2d_translate_localhom_mat2d_translate_localHomMat2dTranslateLocalHomMat2dTranslateLocalHomMat2dTranslateLocalhom_mat2d_translate_local, hom_mat2d_scale_localhom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocalHomMat2dScaleLocalhom_mat2d_scale_local, hom_mat2d_rotate_localhom_mat2d_rotate_localHomMat2dRotateLocalHomMat2dRotateLocalHomMat2dRotateLocalhom_mat2d_rotate_local, hom_mat2d_slant_localhom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocalHomMat2dSlantLocalhom_mat2d_slant_local, hom_mat2d_reflect_localhom_mat2d_reflect_localHomMat2dReflectLocalHomMat2dReflectLocalHomMat2dReflectLocalhom_mat2d_reflect_local

See also

hom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScaleHomMat2dScalehom_mat2d_scale

Module

Foundation