hom_mat3d_scaleT_hom_mat3d_scaleHomMat3dScaleHomMat3dScalehom_mat3d_scale (Operator)

Name

hom_mat3d_scaleT_hom_mat3d_scaleHomMat3dScaleHomMat3dScalehom_mat3d_scale — Add a scaling to a homogeneous 3D transformation matrix.

Signature

Description

hom_mat3d_scalehom_mat3d_scaleHomMat3dScaleHomMat3dScaleHomMat3dScalehom_mat3d_scale adds a scaling by the scale factors SxSxSxSxsxsx, SySySySysysy, and SzSzSzSzszsz to the homogeneous 3D transformation matrix HomMat3DHomMat3DHomMat3DHomMat3DhomMat3Dhom_mat_3d and returns the resulting matrix in HomMat3DScaleHomMat3DScaleHomMat3DScaleHomMat3DScalehomMat3DScalehom_mat_3dscale. The scaling is described by a 3×3 scaling matrix S. It is performed relative to the global (i.e., fixed) coordinate system; this corresponds to the following chain of transformation matrices:

The point (PxPxPxPxpxpx,PyPyPyPypypy,PzPzPzPzpzpz) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat3DScaleHomMat3DScaleHomMat3DScaleHomMat3DScalehomMat3DScalehom_mat_3dscale. 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:

To perform the transformation in the local coordinate system, i.e., the one described by HomMat3DHomMat3DHomMat3DHomMat3DhomMat3Dhom_mat_3d, use hom_mat3d_scale_localhom_mat3d_scale_localHomMat3dScaleLocalHomMat3dScaleLocalHomMat3dScaleLocalhom_mat3d_scale_local.

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 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

• 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_scaleHomMat3dScaleHomMat3dScaleHomMat3dScalehom_mat3d_scale returns TRUE if all three scale factors are not 0. If necessary, an exception is raised.

Possible Predecessors

hom_mat3d_identityhom_mat3d_identityHomMat3dIdentityHomMat3dIdentityHomMat3dIdentityhom_mat3d_identity, hom_mat3d_translatehom_mat3d_translateHomMat3dTranslateHomMat3dTranslateHomMat3dTranslatehom_mat3d_translate, hom_mat3d_scalehom_mat3d_scaleHomMat3dScaleHomMat3dScaleHomMat3dScalehom_mat3d_scale, hom_mat3d_rotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotateHomMat3dRotatehom_mat3d_rotate

Possible Successors

hom_mat3d_translatehom_mat3d_translateHomMat3dTranslateHomMat3dTranslateHomMat3dTranslatehom_mat3d_translate, hom_mat3d_scalehom_mat3d_scaleHomMat3dScaleHomMat3dScaleHomMat3dScalehom_mat3d_scale, hom_mat3d_rotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotateHomMat3dRotatehom_mat3d_rotate

See also

hom_mat3d_inverthom_mat3d_invertHomMat3dInvertHomMat3dInvertHomMat3dInverthom_mat3d_invert, hom_mat3d_identityhom_mat3d_identityHomMat3dIdentityHomMat3dIdentityHomMat3dIdentityhom_mat3d_identity, hom_mat3d_scale_localhom_mat3d_scale_localHomMat3dScaleLocalHomMat3dScaleLocalHomMat3dScaleLocalhom_mat3d_scale_local, pose_to_hom_mat3dpose_to_hom_mat3dPoseToHomMat3dPoseToHomMat3dPoseToHomMat3dpose_to_hom_mat3d, hom_mat3d_to_posehom_mat3d_to_poseHomMat3dToPoseHomMat3dToPoseHomMat3dToPosehom_mat3d_to_pose, hom_mat3d_composehom_mat3d_composeHomMat3dComposeHomMat3dComposeHomMat3dComposehom_mat3d_compose

Module

Foundation