Operators

# hom_mat2d_scale_local (Operator)

## Name

hom_mat2d_scale_local — Add a scaling to a homogeneous 2D transformation matrix.

## Signature

hom_mat2d_scale_local( : : HomMat2D, Sx, Sy : HomMat2DScale)

## Description

hom_mat2d_scale_local 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 2×2 scaling matrix S. In contrast to hom_mat2d_scale, it is performed relative to the local coordinate system, i.e., the coordinate system described by HomMat2D; this corresponds to the following chain of transformation matrices:

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

S = | Sx 0 |
| 0 Sy |
```

The fixed point of the transformation is the origin of the local coordinate system, i.e., this point remains unchanged when transformed using HomMat2DScale.

## 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 (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  /
```

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.

## Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Processed without parallelization.

## Parameters

HomMat2D (input_control)  hom_mat2d (real)

Input transformation matrix.

Sx (input_control)  number (real / integer)

Scale factor along the x-axis.

Default value: 2

Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 16

Restriction: Sx != 0

Sy (input_control)  number (real / integer)

Scale factor along the y-axis.

Default value: 2

Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 16

Restriction: Sy != 0

HomMat2DScale (output_control)  hom_mat2d (real)

Output transformation matrix.

## Result

hom_mat2d_scale_local returns 2 (H_MSG_TRUE) if both scale factors are not 0. If necessary, an exception is raised.