Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 204

A.5 R γ,x R β,z R α,y

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

10 0 c β − s β 0 c α 0 s α

01 0

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

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

0 s γ c γ 0 0 1 − s α 0 c α

⎡ ⎤

−

c β c α s β c β s α

⎣ ⎦

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

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

⎡ ⎤

0 10

100
001

−

⎣ ⎦

R 90 ° ,x R 90 ° ,z R 90 ° ,y =

⎡ ⎤ ⎡ ⎤

0 10

100
001

− 00001111

00110011
01010101

⎣ ⎦ ⎣ ⎦

⎡ ⎤

00 1

00001111
01010101

− 1 − 100 − 1 −

⎣ ⎦ .

=

This rotation sequence is illustrated in Fig. A.4 (a)-(d), where the axis of rotation

T

is [ 002 ] and the angle of rotation 90°.

Fig. A.4 Four views of the unit cube before and during the three rotations R 90 ° ,x R 90 ° ,z R 90 ° ,y