Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 214

⎡ ⎤

c β 0 − s β

R − 1

⎣ ⎦

rotate the frame β about the y -axis

β,y =

01 0

s β 0 c β

⎡ ⎤

c γ s γ 0

R − 1

⎣ ⎦

rotate the frame γ about the z -axis

γ,z =

− s γ c γ 0

001

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.