Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 209

A.10 R γ,z R β,x R α,y

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ − s γ 0 10 0 c α 0 s α

01 0

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

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

0 0 1 0 s β c β − s α 0 c α

⎡ ⎤

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

⎣ ⎦

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

− c β s α s β c β c α

⎡ ⎤

− 100

001
010

⎣ ⎦

R 90 ° ,z R 90 ° ,x R 90 ° ,y =

⎡ ⎤ ⎡ ⎤

− 100

001
010

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

⎡ ⎤

0000 1

01010101
00110011

− 1 − 1 − 1 −

⎣ ⎦ .

=

This rotation sequence is illustrated in Fig. A.9 (a)-(d), where the axis of rotation

T

is [ 022 ] and the angle of rotation 180°.

Fig. A.9 Four views of the unit cube before and during the three rotations R 90 ° ,z R 90 ° ,x R 90 ° ,y