Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 223

B.10 R − 1

γ,z R − 1

β,x R − 1

α,y

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ s γ 0 1 0 0 c α 0 − s α

R − 1

γ,z R − 1

β,x R − 1

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

α,y =

− s γ c γ 0

001

0 c β s β 01 0

0 − s β c β s α 0 c α

⎡ ⎤

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

⎣ ⎦

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

c β s α − s β c β c α

⎡ ⎤

100
001
0

R − 1

90 ° ,z R − 1 90 ° ,x R − 1

⎣ ⎦

90 ° ,y =

− 10

⎡ ⎤ ⎡ ⎤

100
001
0

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

−

10

⎡ ⎤

00001111
01010101
00

⎣ ⎦ .

=

− 1 − 100 − 1 − 1

This rotation sequence is illustrated in Fig. B.9 (a)-(d), where the axis of rotation

T

is [ 200 ] and the angle of rotation 90°.

Four views of the frame before and during the three rotations R − 1

90 ° ,z R − 1 90 ° ,x R − 1

Fig. B.9

90 ° ,y