Add a scaling to a homogeneous 3D transformation matrix.

hom_mat3d_scale adds a scaling by the scale factors Sx, Sy, and Sz to the homogeneous 3D transformation matrix HomMat3D and returns the resulting matrix in HomMat3DScale. The scaling is described by a 3x3 scaling matrix S. It is performed relative to the global (i.e., fixed) coordinate system; this corresponds to the following chain of transformation matrices:

                  /        0 \                     / Sx 0  0  \
  HomMat3DScale = |   S    0 | * HomMat3D      S = | 0  Sy 0  | 
                  |        0 |                     \ 0  0  Sz /
                  \ 0 0 0  1 /

The point (Px,Py,Pz) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat3DScale. 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 scaling 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 \ 
  HomMat3DScale = | 0 1 0 +Py | * |   S    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  /   

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].

hom_mat3d_scale returns 2 (H_MSG_TRUE) if all three scale factors are not 0. If necessary, an exception is raised.

hom_mat3d_scale 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

Basic operators