Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 210

A.11 R γ,z R β,x R α,z

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ − s γ 0 10 0 c α − s α 0

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

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

0 0 1 0 s β c β 0 0 1

⎡ ⎤

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

⎣ ⎦

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

s β s α s β c α c β

⎡ ⎤

001
0

⎣ ⎦

R 90 ° ,z R 90 ° ,x R 90 ° ,z = 10

100

−

⎡ ⎤ ⎡ ⎤

001
0

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

10
100

−

⎡ ⎤

01010101
00

⎣ ⎦ .

= 1

00001111

− 1 − 100 − 1 −

This rotation sequence is illustrated in Fig. A.10 (a)-(d), where the axis of rota-
tion is

T

[ 202 ] and the angle of rotation 180°.

Fig. A.10 Four views of the unit cube before and during the three rotations R 90 ° ,z R 90 ° ,x R 90 ° ,z