Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 224

B.11 R − 1

γ,z R − 1

β,x R − 1

α,z

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ s γ 0 1 0 0 c α s α 0

R − 1

γ,z R − 1 β,x R − 1

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

α,z =

− s γ c γ 0

001

0 c β s β − s α c α 0

001

0 − s β c β

⎡ ⎤

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

⎣ ⎦

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

−

s β s α s β c α c β

⎡
⎣

⎤
⎦

001
0

R − 1

90 ° ,z R − 1 90 ° ,x R − 1 90 ° ,z =

10
100

−

⎡ ⎤ ⎡ ⎤

001
0

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

10
100

−

⎡ ⎤

01010101
00

⎣ ⎦ .

= 1

00001111

− 1 − 100 − 1 −

This rotation sequence is illustrated in Fig. B.10 (a)-(d), where the axis of rota-
tion is

T

[ 202 ] and the angle of rotation 180°.

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

90 ° ,z R − 1 90 ° ,x R − 1

Fig. B.10

90 ° ,z