hom_mat3d_rotateT_hom_mat3d_rotateHomMat3dRotateHomMat3dRotate (Operator)

Name

hom_mat3d_rotateT_hom_mat3d_rotateHomMat3dRotateHomMat3dRotate — Add a rotation to a homogeneous 3D transformation matrix.

Signature

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

hom_mat3d_rotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotateHomMat3dRotate adds a rotation by the angle PhiPhiPhiPhiphi around the axis passed in the parameter AxisAxisAxisAxisaxis to the homogeneous 3D transformation matrix HomMat3DHomMat3DHomMat3DHomMat3DhomMat3D and returns the resulting matrix in HomMat3DRotateHomMat3DRotateHomMat3DRotateHomMat3DRotatehomMat3DRotate. 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:

AxisAxisAxisAxisaxis = 'x'"x""x""x""x":

AxisAxisAxisAxisaxis = 'y'"y""y""y""y":

AxisAxisAxisAxisaxis = 'z'"z""z""z""z":

AxisAxisAxisAxisaxis = [x,y,z]:

The point (PxPxPxPxpx,PyPyPyPypy,PzPzPzPzpz) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat3DRotateHomMat3DRotateHomMat3DRotateHomMat3DRotatehomMat3DRotate. 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 HomMat3DHomMat3DHomMat3DHomMat3DhomMat3D, use hom_mat3d_rotate_localhom_mat3d_rotate_localHomMat3dRotateLocalHomMat3dRotateLocalHomMat3dRotateLocal.

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).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters

HomMat3DHomMat3DHomMat3DHomMat3DhomMat3D (input_control) hom_mat3d → (real)

Input transformation matrix.

PhiPhiPhiPhiphi (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 Phi Phi Phi phi ≤ 6.28318530718

AxisAxisAxisAxisaxis (input_control) string(-array) → (string / real / integer)

Axis, to be rotated around.

Default value: 'x' "x" "x" "x" "x"

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

PxPxPxPxpx (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

PyPyPyPypy (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

PzPzPzPzpz (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

HomMat3DRotateHomMat3DRotateHomMat3DRotateHomMat3DRotatehomMat3DRotate (output_control) hom_mat3d → (real)

Output transformation matrix.

Result

If the parameters are valid, the operator hom_mat3d_rotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotateHomMat3dRotate returns 2 (H_MSG_TRUE). If necessary, an exception is raised.