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6.6. Transformations 139
Figure 6.14. Rotation round an arbitrar y vector.
been obtained representing the composite transformations, it can be used in
the same way as any other transformation matrix.)
The following outlines an algorithm to construct a transformation matrix
to generate a rotation by an angle
around a vector in the direction P
1
−P
0
:
1. Translate P
0
to the origin of coordinates
2. Align rotation axis P
1
− P
0
with the x-axis.
3. Rotate by angle
round x-axis.
4. Make inverse transformation to undo the rotations of Step 2.
5. Translate origin of coordinates back to P
0
to undo the translation of
Step 1.
The full algorithm is given in Figure