hom_mat3d

hom_mat3d_scale ( : : HomMat3D, Sx, Sy, Sz, Px, Py, Pz : HomMat3DScale )

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  /

To perform the transformation in the local coordinate system, i.e., the one described by HomMat3D, use hom_mat3d_scale_local.

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.

`Sx` (input_control)	number `->` real / integer
Scale factor along the x-axis.
Default value: 2
Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 112
Restriction: `Sx != 0`

`Sy` (input_control)	number `->` real / integer
Scale factor along the y-axis.
Default value: 2
Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 112
Restriction: `Sy != 0`

`Sz` (input_control)	number `->` real / integer
Scale factor along the z-axis.
Default value: 2
Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 112
Restriction: `Sz != 0`

`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

`HomMat3DScale` (output_control)	hom_mat3d-array `->` real
Output transformation matrix.

Result

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

Parallelization Information

hom_mat3d_scale is reentrant and processed without parallelization.

Possible Predecessors

hom_mat3d_identity, hom_mat3d_translate, hom_mat3d_scale, hom_mat3d_rotate

Possible Successors

hom_mat3d_translate, hom_mat3d_scale, hom_mat3d_rotate

Module

Foundation