Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 206

A.7 R γ,y R β,x R α,z

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ 0 s γ
01 0
− s γ

10 0 c α − s α 0

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

R γ,y R β,x R α,z =

0 c β − s β s α c α 0

0 c γ 0 s β c β 0 0 1

⎡ ⎤

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

⎣ ⎦

= c β c α − s β

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

⎡ ⎤

10 0

⎣ ⎦

R 90 ° ,y R 90 ° ,x R 90 ° ,z = 00 − 1

01 0

⎡ ⎤ ⎡ ⎤

10 0 00001111

00110011
01010101

⎣ ⎦ ⎣ ⎦

00 − 1

01 0

⎡ ⎤

00001111
0

⎣ ⎦ .

= 1

00110011

− 10 − 10 − 10 −

This rotation sequence is illustrated in Fig. A.6 (a)-(d), where the axis of rotation

T

[ ]

is 200 and the angle of rotation 90°.

Fig. A.6 Four views of the unit cube before and during the three rotations R 90 ° ,y R 90 ° ,x R 90 ° ,z