Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 221

B.8 R − 1

γ,y R − 1

β,z R − 1

α,x

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ 0 − s γ c β s β 0 1 0 0

R − 1

γ,y R − 1 β,z R − 1

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

α,x =

01 0 − s β c β 0

001

0 c α s α

s γ 0 c γ 0 − s α c α

⎡
⎣

⎤
⎦

(s γ s α +

−

s γ c α +

c γ c β c γ s β c α )( c γ s β s α )

= − s β c β c α c β s α

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

⎡ ⎤

010

R − 1

90 ° ,y R − 1 90 ° ,z R − 1

⎣ ⎦

90 ° ,x =

− 100

001

⎡ ⎤ ⎡ ⎤

010 00001111

00110011
01010101

⎣ ⎦ ⎣ ⎦

− 100

001

⎡ ⎤

00110011
0000

⎣ ⎦ .

= 1

01010101

− 1 − 1 − 1 −

This rotation sequence is illustrated in Fig. B.7 (a)-(d), where the axis of rotation

T

is [ 220 ] and the angle of rotation 180°.

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

90 ° ,y R − 1 90 ° ,z R − 1

Fig. B.7

90 ° ,x