Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 219

B.6 R − 1

γ,y R − 1

β,x R − 1

α,y

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ 0 − s γ 1 0 0 c α 0 − s α

R − 1

γ,y R − 1

β,x R − 1

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

α,y =

01 0 0 c β s β 01 0

s γ 0 c γ 0 − s β c β s α 0 c α

⎡ ⎤

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

⎣ ⎦

= s β s α c β s β c α

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

⎡ ⎤

01 0

R − 1

90 ° ,y R − 1 90 ° ,x R − 1

⎣ ⎦

90 ° ,y =

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.5 (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 ° ,x R − 1

Fig. B.5

90 ° ,y