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combined with a translation of — 6.0934 units along that same vector. Alternatively, the direction of the unit vector can be reversed by multiplying it by negative one, in which case the rotation and translation become positive. Figures 4-6 illustrate the transformation from the vantage point of this reversed unit vector.

As in the two-dimensional case, the matrix logarithm provides a method for decomposing a rigid-body transformation into a set of simultaneous elementary transformations rather than the traditional sequential transformations.

For the numerical example, the matrix logarithm is

- 0 0.2376 — 0.1771 2.0923" — 0.2376 0 0.1431 0 0

0 0

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