Transformation Pipeline

The entire transformation pipeline that defines either a shape transformation or a group transformation is represented by the matrix T, defined at the end of this subsection.

Scaling and translation are produced by the following matrix:

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The following matrix translates the bounding box to the origin in preparation for rotation and flipping:

.

Rotation and flipping are produced by the following matrix:

.

The entire transformation pipeline for one step in the group hierarchy is represented by the matrix