# hom_mat2d_rotate_local (Operator)

## Name

`hom_mat2d_rotate_local` — Add a rotation to a homogeneous 2D transformation matrix.

## Signature

`hom_mat2d_rotate_local( : : HomMat2D, Phi : HomMat2DRotate)`

## Description

`hom_mat2d_rotate_local` adds a rotation by the angle `Phi` to the homogeneous 2D transformation matrix `HomMat2D` and returns the resulting matrix in `HomMat2DRotate`. The rotation is described by a 2×2 rotation matrix R. In contrast to `hom_mat2d_rotate`, 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:

The fixed point of the transformation is the origin of the local coordinate system, i.e., this point remains unchanged when transformed using `HomMat2DRotate`.

## 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 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).
• Processed without parallelization.

## Parameters

`HomMat2D` (input_control)  hom_mat2d `→` (real)

Input transformation matrix.

`Phi` (input_control)  angle.rad `→` (real / integer)

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 ≤ 6.28318530718```

`HomMat2DRotate` (output_control)  hom_mat2d `→` (real)

Output transformation matrix.

## Result

If the parameters are valid, the operator `hom_mat2d_rotate_local` returns 2 (H_MSG_TRUE). If necessary, an exception is raised.

## Possible Predecessors

`hom_mat2d_identity`, `hom_mat2d_translate_local`, `hom_mat2d_scale_local`, `hom_mat2d_rotate_local`, `hom_mat2d_slant_local`, `hom_mat2d_reflect_local`

## Possible Successors

`hom_mat2d_translate_local`, `hom_mat2d_scale_local`, `hom_mat2d_rotate_local`, `hom_mat2d_slant_local`, `hom_mat2d_reflect_local`

`hom_mat2d_rotate`