hom_mat3d_scale_localHomMat3dScaleLocalHomMat3dScaleLocalhom_mat3d_scale_localT_hom_mat3d_scale_local🔗

Short description🔗

hom_mat3d_scale_localHomMat3dScaleLocalHomMat3dScaleLocalhom_mat3d_scale_localT_hom_mat3d_scale_local — Add a scaling to a homogeneous 3D transformation matrix.

Signature🔗

hom_mat3d_scale_local( hom_mat3d HomMat3D, number Sx, number Sy, number Sz, out hom_mat3d HomMat3DScale )

Description🔗

hom_mat3d_scale_localHomMat3dScaleLocal adds a scaling by the scale factors Sxsxsx, Sysysy, and Szszsz to the homogeneous 3D transformation matrix HomMat3DhomMat3Dhom_mat_3d and returns the resulting matrix in HomMat3DScalehomMat3DScalehom_mat_3dscale. The scaling is described by a 3×3 scaling matrix S. In contrast to hom_mat3d_scaleHomMat3dScale, it is performed relative to the local coordinate system, i.e., the coordinate system described by HomMat3DhomMat3Dhom_mat_3d; this corresponds to the following chain of transformation matrices:

\[\begin{eqnarray*} \textrm{HomMat3DScale} = \textrm{HomMat3D} \cdot \mvHomMatrixThreeDRotTrans{\mvScalingMatrixVar{}{}} {\mvVectorThreeDPlain{0}{0}{0}} \qquad \mvScalingMatrixVar{}{} = \mvMatrix{ \textrm{Sx} & 0 & 0 \\ 0 & \textrm{Sy} & 0 \\ 0 & 0 & \textrm{Sz}} \end{eqnarray*}\]

The fixed point of the transformation is the origin of the local coordinate system, i.e., this point remains unchanged when transformed using HomMat3DScalehomMat3DScalehom_mat_3dscale.

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 \(\mvHomMatrixThreeDElements{ ra & rb & rc & td \\ re & rf & rg & th \\ ri & rj & rk & tl}\) 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🔗

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🔗

HomMat3DhomMat3Dhom_mat_3d (input_control) hom_mat3d → (real)HTuple (double)HHomMat3D, HTuple (double)Sequence[float]Htuple (double)

Input transformation matrix.

Sxsxsx (input_control) number → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Union[float, int]Htuple (double / Hlong)

Scale factor along the x-axis.

Default: 22
Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 1120.125, 0.25, 0.5, 1, 2, 4, 8, 112
Restriction: Sx != 0

Sysysy (input_control) number → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Union[float, int]Htuple (double / Hlong)

Scale factor along the y-axis.

Default: 22
Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 1120.125, 0.25, 0.5, 1, 2, 4, 8, 112
Restriction: Sy != 0

Szszsz (input_control) number → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Union[float, int]Htuple (double / Hlong)

Scale factor along the z-axis.

Default: 22
Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 1120.125, 0.25, 0.5, 1, 2, 4, 8, 112
Restriction: Sz != 0

HomMat3DScalehomMat3DScalehom_mat_3dscale (output_control) hom_mat3d → (real)HTuple (double)HHomMat3D, HTuple (double)Sequence[float]Htuple (double)

Output transformation matrix.

Result🔗

hom_mat3d_scale_localHomMat3dScaleLocal returns 2 (H_MSG_TRUE) if all three scale factors are not 0. If necessary, an exception is raised.

Combinations with other operators🔗

Combinations

Possible predecessors

hom_mat3d_identityHomMat3dIdentity, hom_mat3d_translate_localHomMat3dTranslateLocal, hom_mat3d_scale_localHomMat3dScaleLocal, hom_mat3d_rotate_localHomMat3dRotateLocal

Possible successors

hom_mat3d_translate_localHomMat3dTranslateLocal, hom_mat3d_scale_localHomMat3dScaleLocal, hom_mat3d_rotate_localHomMat3dRotateLocal

Module🔗

Foundation