Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 222

B.9 R − 1

γ,y R − 1

β,z R − 1

α,y

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ 0 − s γ c β s β 0 c α 0 − s α

R − 1

γ,y R − 1

β,z R − 1

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

α,y =

01 0 − s β c β 0

001

01 0

s γ 0 c γ s α 0 c α

⎡ ⎤

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

⎣ ⎦

= − s β c α c β s β s α

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

⎡ ⎤

− 100

001
010

R − 1

90 ° ,y R − 1 90 ° ,z R − 1

⎣ ⎦

90 ° ,y =

⎡ ⎤ ⎡ ⎤

− 100

001
010

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

⎡ ⎤

0000 1

01010101
00110011

− 1 − 1 − 1 −

⎣ ⎦ .

=

This rotation sequence is illustrated in Fig. B.8 (a)-(d), where the axis of rotation

T

is [ 022 ] 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.8

90 ° ,y