Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 215

B.2 R − 1

γ,x R − 1

β,y R − 1

α,x

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

1 0 0 c β 0 − s β 1 0 0

R − 1

γ,x R − 1

β,y R − 1

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

α,x =

0 c γ s γ 01 0 0 c α s α

0 − s γ c γ s β 0 c β 0 − s α c α

⎡ ⎤

c β s β s α − s β c α

⎣ ⎦

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

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

⎡
⎣

⎤
⎦

01 0

R − 1

90 ° ,x R − 1 90 ° ,y R − 1 90 ° ,x =

10 0

00 − 1

⎡ ⎤ ⎡ ⎤

01 0 00001111

00110011
01010101

⎣ ⎦ ⎣ ⎦

10 0

00 − 1

⎡ ⎤

00110011
00001111
0

⎣ ⎦ .

=

− 10 − 10 − 10 − 1

This rotation sequence is illustrated in Fig. B.1 (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 ° ,x R − 1 90 ° ,y R − 1

Fig. B.1

90 ° ,x