hom_mat3d_scaleT_hom_mat3d_scalehom_mat3d_scaleHomMat3dScaleHomMat3dScale (Operator)

Name

hom_mat3d_scaleT_hom_mat3d_scalehom_mat3d_scaleHomMat3dScaleHomMat3dScale — Add a scaling to a homogeneous 3D transformation matrix.

Signature

Description

hom_mat3d_scalehom_mat3d_scalehom_mat3d_scaleHomMat3dScaleHomMat3dScale adds a scaling by the scale factors SxSxSxSxsx, SySySySysy, and SzSzSzSzsz to the homogeneous 3D transformation matrix HomMat3DHomMat3DHomMat3DHomMat3DhomMat3D and returns the resulting matrix in HomMat3DScaleHomMat3DScaleHomMat3DScaleHomMat3DScalehomMat3DScale. 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 (PxPxPxPxpx,PyPyPyPypy,PzPzPzPzpz) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat3DScaleHomMat3DScaleHomMat3DScaleHomMat3DScalehomMat3DScale. 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 HomMat3DHomMat3DHomMat3DHomMat3DhomMat3D, use hom_mat3d_scale_localhom_mat3d_scale_localhom_mat3d_scale_localHomMat3dScaleLocalHomMat3dScaleLocal.

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].

Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Processed without parallelization.

Parameters

Result

hom_mat3d_scalehom_mat3d_scalehom_mat3d_scaleHomMat3dScaleHomMat3dScale returns 2 (H_MSG_TRUE) if all three scale factors are not 0. If necessary, an exception is raised.

Possible Predecessors

hom_mat3d_identityhom_mat3d_identityhom_mat3d_identityHomMat3dIdentityHomMat3dIdentity, hom_mat3d_translatehom_mat3d_translatehom_mat3d_translateHomMat3dTranslateHomMat3dTranslate, hom_mat3d_scalehom_mat3d_scalehom_mat3d_scaleHomMat3dScaleHomMat3dScale, hom_mat3d_rotatehom_mat3d_rotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotate

Possible Successors

hom_mat3d_translatehom_mat3d_translatehom_mat3d_translateHomMat3dTranslateHomMat3dTranslate, hom_mat3d_scalehom_mat3d_scalehom_mat3d_scaleHomMat3dScaleHomMat3dScale, hom_mat3d_rotatehom_mat3d_rotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotate

See also

hom_mat3d_inverthom_mat3d_inverthom_mat3d_invertHomMat3dInvertHomMat3dInvert, hom_mat3d_identityhom_mat3d_identityhom_mat3d_identityHomMat3dIdentityHomMat3dIdentity, hom_mat3d_scale_localhom_mat3d_scale_localhom_mat3d_scale_localHomMat3dScaleLocalHomMat3dScaleLocal, pose_to_hom_mat3dpose_to_hom_mat3dpose_to_hom_mat3dPoseToHomMat3dPoseToHomMat3d, hom_mat3d_to_posehom_mat3d_to_posehom_mat3d_to_poseHomMat3dToPoseHomMat3dToPose, hom_mat3d_composehom_mat3d_composehom_mat3d_composeHomMat3dComposeHomMat3dCompose

Module

Foundation