Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 216

B.3 R − 1

γ,x R − 1

β,y R − 1

α,z

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

1 0 0 c β 0 − s β c α s α 0

R − 1

γ,x R − 1

β,y R − 1

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

α,z =

0 c γ s γ 01 0 − s α c α 0

001 0 − s γ c γ s β 0 c β

⎡ ⎤

c β c α c β s α − s β

⎣ ⎦

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

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

⎡
⎣

⎤
⎦

−

00 1

R − 1

90 ° ,x R − 1 90 ° ,y R − 1 90 ° ,z =

01 0

10 0

⎡ ⎤ ⎡ ⎤

00 − 1 00001111

00110011
01010101

⎣ ⎦ ⎣ ⎦

01 0

10 0

⎡ ⎤

0 1

00110011
00001111

− 10 − 10 − 10 −

⎣ ⎦ .

=

This rotation sequence is illustrated in Fig. B.2 (a)-(d), where the axis of rotation

T

is [ 020 ] and the angle of rotation 90°.

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

90 ° ,x R − 1 90 ° ,y R − 1

Fig. B.2

90 ° ,z