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3. Affine transformations in three dimensions

Everything works exactly the same: For x$ = (x,y,z)$, $ \hat{\mbox{\bf x}}$ is $ (x,y,z,1)$. The extended matrix of an affine transformation $ T:$   R$ ^3 \rightarrow$   R$ ^3$ is $ 4 \times 4$.



Application 3.1 . Rotations in R$ ^3$ about axes that do not go through the origin.



Application 3.2 . Reflections in R$ ^3$ in plane mirrors that do not go through the origin.




Kirby A. Baker 2002-01-16