Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 202

A.3 R γ,x R β,y R α,z

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

10 0 c β 0 s β

01 0

c α − s α 0

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

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

0 s γ c γ − s β 0 c β 0 0 1

⎡ ⎤

c β c α − c β s α s β

⎣ ⎦

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

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

⎡ ⎤

001
0

⎣ ⎦

R 90 ° ,x R 90 ° ,y R 90 ° ,z = 10

100

−

⎡ ⎤ ⎡ ⎤

001
0

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

10
100

−

⎡ ⎤

01010101
00

⎣ ⎦ .

= 1

00001111

− 1 − 100 − 1 −

This rotation sequence is illustrated in Fig. A.2 (a)-(d), where the axis of rotation

T

is [ 202 ] and the angle of rotation 180°.

Fig. A.2 Four views of the unit cube before and during the three rotations R 90 ° ,x R 90 ° ,y R 90 ° ,z