Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 208

A.9 R γ,y R β,z R α,y

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

−

c γ 0 s γ
01 0

c β s β 0 c α 0 s α

01 0 R γ,y R β,z R α,y = s β c β 0

− s γ 0 c γ 0 0 1 − s α 0 c α

⎡ ⎤

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

⎣ ⎦

= s β c α c β s β s α

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

⎡ ⎤

− 100

001
010

⎣ ⎦

R 90 ° ,y R 90 ° ,z R 90 ° ,y =

⎡ ⎤ ⎡ ⎤

− 100

001
010

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

⎡ ⎤

− − − −

0000 1

01010101
00110011

1 1 1

⎣ ⎦ .

=

This rotation sequence is illustrated in Fig. A.8 (a)-(d), where the axis of rotation

T

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

Fig. A.8 Four views of the unit cube before and during the three rotations R 90 ° ,y R 90 ° ,z R 90 ° ,y