Operators

# hom_mat3d_rotate (Operator)

## Name

hom_mat3d_rotate — Add a rotation to a homogeneous 3D transformation matrix.

## Signature

hom_mat3d_rotate( : : HomMat3D, Phi, Axis, Px, Py, Pz : HomMat3DRotate)

## Description

hom_mat3d_rotate adds a rotation by the angle Phi around the axis passed in the parameter Axis to the homogeneous 3D transformation matrix HomMat3D and returns the resulting matrix in HomMat3DRotate. The axis can be specified by passing the strings 'x', 'y', or 'z', or by passing a vector [x,y,z] as a tuple.

The rotation is described by a 3×3 rotation matrix R. It is performed relative to the global (i.e., fixed) coordinate system; this corresponds to the following chain of transformation matrices:

Axis = 'x':

Axis = 'y':

Axis = 'z':

Axis = [x,y,z]:

The point (Px,Py,Pz) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat3DRotate. 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 rotation is added, and finally a translation that moves the fixed point back to its original position. This corresponds to the following chain of transformations:

To perform the transformation in the local coordinate system, i.e., the one described by HomMat3D, use hom_mat3d_rotate_local.

## Attention

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, rc, td, re, rf, rg, th, ri, rj, rk, tl]. However, it is also possible to process full 4×4 matrices, which represent a projective 4D transformation.

## Execution Information

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

## Parameters

HomMat3D (input_control)  hom_mat3d (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

Axis (input_control)  string(-array) (string / real / integer)

Axis, to be rotated around.

Default value: 'x'

Suggested values: 'x', 'y', 'z'

Px (input_control)  point3d.x (real / integer)

Fixed point of the transformation (x coordinate).

Default value: 0

Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024

Py (input_control)  point3d.y (real / integer)

Fixed point of the transformation (y coordinate).

Default value: 0

Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024

Pz (input_control)  point3d.z (real / integer)

Fixed point of the transformation (z coordinate).

Default value: 0

Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024

HomMat3DRotate (output_control)  hom_mat3d (real)

Output transformation matrix.

## Result

If the parameters are valid, the operator hom_mat3d_rotate returns 2 (H_MSG_TRUE). If necessary, an exception is raised.