Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 205

A.6 R γ,y R β,x R α,y

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ 0 s γ
01 0
− s γ

10 0 c α 0 s α

01 0
− s α

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

R γ,y R β,x R α,y =

0 c β − s β

0 c γ 0 s β c β 0 c α

⎡ ⎤

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

⎣ ⎦

= s β s α c β − s β c α

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

⎡ ⎤

01 0

⎣ ⎦

R 90 ° ,y R 90 ° ,x R 90 ° ,y = 10 0

00 − 1

⎡ ⎤ ⎡ ⎤

01 0 00001111

00110011
01010101

⎣ ⎦ ⎣ ⎦

10 0

00 − 1

⎡ ⎤

00110011
00001111
0

⎣ ⎦ .

=

− 10 − 10 − 10 − 1

This rotation sequence is illustrated in Fig. A.5 (a)-(d), where the axis of rotation

T

[ ]

is 220 and the angle of rotation 180°.

Fig. A.5 Four views of the unit cube before and during the three rotations R 90 ° ,y R 90 ° ,x R 90 ° ,y