Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 200

⎡ ⎤

10 0

⎣ ⎦

rotate α about the x -axis R α,x = 0 c α − s α

0 s α c α

⎡ ⎤

c β 0 s β
01 0

⎣ ⎦

rotate β about the y -axis R β,y =

− s β 0 c β

⎡ ⎤

c γ − s γ 0

⎣ ⎦

rotate γ about the z -axis R γ,z = s γ c γ 0

0 0 1

where c α = sin α ,etc.

Remember that the right-most transform is applied first and the left-most trans-
form last. In terms of angles, the sequence is always α , β , γ .
For each composite transform you can verify that when α

cos α and s α =

= β = γ = 0 the result

is the identity transform I .
We now examine the twelve combinations in turn.