hom_mat3d_rotate

hom_mat3d_rotate_local ( : : HomMat3D, Phi, Axis : HomMat3DRotate )

Add a rotation to a homogeneous 3D transformation matrix.

hom_mat3d_rotate_local 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 by specified by passing the strings 'x', 'y', or 'z', or by passing a vector [x,y,z] as a tuple.

The rotation is decribed by a 3x3 rotation matrix R. In contrast to hom_mat3d_rotate, it is performed relative to the local coordinate system, i.e., the coordinate system described by HomMat3D; this corresponds to the following chain of transformation matrices:

Axis = 'x':

                              /        0 \          / 1    0         0     \
  HomMat3DRotate = HomMat3D * |  Rx    0 |     Rx = | 0 cos(Phi) -sin(Phi) |
                              |        0 |          \ 0 sin(Phi)  cos(Phi) /
                              \ 0 0 0  1 / 


Axis = 'y':

                              /        0 \          /  cos(Phi) 0 sin(Phi) \
  HomMat3DRotate = HomMat3D * |  Ry    0 |     Ry = |     0     1    0     |
                              |        0 |          \ -sin(Phi) 0 cos(Phi) /
                              \ 0 0 0  1 / 


Axis = 'z':

                              /        0 \          / cos(Phi) -sin(Phi) 0 \ 
  HomMat3DRotate = HomMat3D * |  Rz    0 |     Rz = | sin(Phi)  cos(Phi) 0 | 
                              |        0 |          \    0         0     1 /
                              \ 0 0 0  1 / 

Axis = [x,y,z]: 

                              /        0 \
  HomMat3DRotate = HomMat3D * |  Ra    0 |
                              |        0 |
                              \ 0 0 0  1 /

                       T                  T
               Ra = u*u + cos(Phi)*( I-u*u ) + sin(Phi)*S

                      Axis       / x' \
               u  = --------  =  | y' |
                    ||Axis||     \ z' /

                   / 1 0 0 \         /  0  -z'  y' \
               I = | 0 1 0 |     S = |  z'  0  -x' |
                   \ 0 0 1 /         \ -y'  x'  0  /

The fixed point of the transformation is the origin of the local coordinate system, i.e., this point remains unchanged when transformed using HomMat3DRotate.

Attention

Note that homogeneous matrices are stored row-by-row as a tuple; the last row is not stored because it is identical for all homogeneous matrices that describe an affine transformation. For example, the homogeneous matrix

    / ra rb rc td \
    | re rf rg th |
    | ri rj rk tl |
    \ 0  0  0  1  /

is stored as the tuple [ra, rb, rc, td, re, rf, rg, th, ri, rj, rk, tl].

Parameters

`HomMat3D` (input_control)	hom_mat3d-array `->` 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'

`HomMat3DRotate` (output_control)	hom_mat3d-array `->` real
Output transformation matrix.

Result

If the parameters are valid, the operator hom_mat3d_rotate_local returns 2 (H_MSG_TRUE). If necessary, an exception is raised.

Parallelization Information

hom_mat3d_rotate_local is reentrant and processed without parallelization.

Possible Predecessors

hom_mat3d_identity, hom_mat3d_translate_local, hom_mat3d_scale_local, hom_mat3d_rotate_local

Possible Successors

hom_mat3d_translate_local, hom_mat3d_scale_local, hom_mat3d_rotate_local

Module

Foundation