Add a scaling to a homogeneous 2D transformation matrix.

hom_mat2d_scale adds a scaling by the scale factors Sx and Sy to the homogeneous 2D transformation matrix HomMat2D and returns the resulting matrix in HomMat2DScale. 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 (Px,Py) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat2DScale. 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 HomMat2D, use hom_mat2d_scale_local.

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 (Row,Column). 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  /

hom_mat2d_scale returns 2 (H_MSG_TRUE) if both scale factors are not 0. If necessary, an exception is raised.

hom_mat2d_scale is reentrant and processed without parallelization.

hom_mat2d_identity, hom_mat2d_translate, hom_mat2d_scale, hom_mat2d_rotate, hom_mat2d_slant

hom_mat2d_translate, hom_mat2d_scale, hom_mat2d_rotate, hom_mat2d_slant

hom_mat2d_scale_local

Foundation