[Hill:224-225. Foley & van
Dam: p.208-210, 217-222] Find the transformation that rotates by an
angle theta about a point P(x,y):
Let's choose to describe all transformations w.r.t. a fixed set of axes:
translate P to origin: trans(-2,-3,0)
perform rotation: rot(z,90)
translate P back: trans(2,3,0)
T =
trans(2,3,0) rot(z,90) trans(-2,-3,0)
Rotation about an arbitrary axis
Hill: 239-241
translate axis k to origin: trans(-P0)
rotate about x-axis to bring axis k' to lie in xz plane:
rot(x,alpha) The amount of rotation is determined by looking at
the projection on the yz plane. Alpha need not actually be calculated; it's
sine and cosine can be evaluated directly.
rotate about y-axis to align axis k'' with z-axis: rot(y,-beta).
As in the previous step, we need not actually calculate beta.
