Add a rotation to a homogeneous 3D transformation matrix.

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 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. It is performed relative to the global (i.e., fixed) coordinate system; this corresponds to the following chain of transformation matrices:

Axis = 'x':

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


Axis = 'z':

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

Axis = [x,y,z]: 

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

                   / 1 0 0 +Px \   /        0 \   / 1 0 0 -Px \ 
  HomMat3DRotate = | 0 1 0 +Py | * |   R    0 | * | 0 1 0 -Py | * HomMat3D
                   | 0 0 1 +Pz |   |        0 |   | 0 0 1 -Pz |
                   \ 0 0 0  1  /   \ 0 0 0  1 /   \ 0 0 0  1  /   

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

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].

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

hom_mat3d_rotate is reentrant and processed without parallelization.

hom_mat3d_identity, hom_mat3d_translate, hom_mat3d_scale, hom_mat3d_rotate

hom_mat3d_translate, hom_mat3d_scale, hom_mat3d_rotate

hom_mat3d_invert, hom_mat3d_identity, hom_mat3d_rotate_local, pose_to_hom_mat3d, hom_mat3d_to_pose, hom_mat3d_compose

Foundation