Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 225

B.12 R − 1

γ,z R − 1

β,y R − 1

α,x

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ s γ 0
− s γ c γ 0
001

c β 0 − s β 1 0 0

R − 1

γ,z R − 1

β,y R − 1

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

α,x =

01 0 0 c α s α

s β 0 c β 0 − s α c α

⎡ ⎤

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

⎣ ⎦

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

s β − c β s α c β c α

⎡ ⎤

001
0

R − 1

90 ° ,z R − 1 90 ° ,y R − 1

⎣ ⎦

90 ° ,x =

10
100

−

⎡ ⎤ ⎡ ⎤

001
0

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

10
100

−

⎡ ⎤

01010101
00

⎣ ⎦ .

= 1

00001111

− 1 − 100 − 1 −

This rotation sequence is illustrated in Fig. B.11 (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 ° ,y R − 1

Fig. B.11

90 ° ,x