Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 212

A.13 R γ,z R β,y R α,z

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ − s γ 0 c β 0 s β

01 0
− s β

c α − s α 0

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

R γ,z R β,y R α,z =

s γ c γ 0 s α c α 0

0 0 1 0 c β 0 0 1

⎡ ⎤

( − s γ s α + c γ c β c α ) − s γ c α − c γ c β s α ) γ s β
(c γ s α + s γ c β c α )

⎣ ⎦

= (c γ c α − s γ c β s α ) γ s β

− s β c α s β s α c β

⎡ ⎤

− 100

001
010

⎣ ⎦

R 90 ° ,z R 90 ° ,y R 90 ° ,z =

⎡ ⎤ ⎡ ⎤

− 100

001
010

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

⎡ ⎤

0000 1

01010101
00110011

− 1 − 1 − 1 −

⎣ ⎦ .

=

This rotation sequence is illustrated in Fig. A.12 (a)-(d), where the axis of rota-
tion is

T

[ 022 ] and the angle of rotation 180°.

Fig. A.12 Four views of the unit cube before and during the three rotations R 90 ° ,z R 90 ° ,y R 90 ° ,z