Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 211

A.12 R γ,z R β,y R α,x

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ − s γ 0 c β 0 s β

01 0

10 0

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

R γ,z R β,y R α,x = s γ c γ 0 0 c α − s α

0 0 1 − s β 0 c β 0 s α c α

⎡ ⎤

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

⎣ ⎦

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

− s β c β s α c β c α

⎡ ⎤

001
010

⎣ ⎦

R 90 ° ,z R 90 ° ,y R 90 ° ,x =

− 100

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

001
010

00001111
00110011
01010101 − 100

⎡ ⎤

01010101
00110011
0000

⎣ ⎦ .

=

− 1 − 1 − 1 − 1

This rotation sequence is illustrated in Fig. A.11 (a)-(d), where the axis of rota-
tion is

T

[ 020 ] and the angle of rotation 90°.

Fig. A.11 Four views of the unit cube before and during the three rotations R 90 ° ,z R 90 ° ,y R 90 ° ,x