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Before the transformation, the set of eight vertices (1, 2, …, 8) in their homogeneous coordinates is written as

Using the given scales along the x, y, z axes, the scaling matrix Eq. (2.6) is given as

Therefore, the set of vertices of the object after scaling transformation can be found as

A 3D reflection refers to a transformation of mirroring an object about a specified plane. A reflection transformation matrix can be treated as a special case of a scaling matrix, where the scale of the corresponding axis of the reflected coordinate is set as a negative value of −1. Note that the axis for the reflection is aligned with the normal reflecting or mirroring plane. Therefore, the reflection coordination transformations about YZ, XZ, and XY planes are expressed by [T]_{RE_YZ}, [T]_{RE_XZ}, and [T]_{RE_XZ}, respectively, as follows:

(2.7)