Composite Frame Rotation Sequences - Rotation Transforms for Computer Graphics - page 220

B.7 R − 1

γ,y R − 1

β,x R − 1

α,z

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ 0 − s γ 1 0 0 c α s α 0

R − 1

γ,y R − 1

β,x R − 1

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

α,z =

01 0 0 c β s β − s α c α 0

001 s γ 0 c γ 0 − s β c β

⎡ ⎤

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

⎣ ⎦

= − c β s α c β c α s β

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

⎡ ⎤

− 100

001
010

R − 1

90 ° ,y R − 1 90 ° ,x R − 1

⎣ ⎦

90 ° ,z =

⎡ ⎤ ⎡ ⎤

− 100

001
010

00001111
00110011
01010101

⎣ ⎦ ⎣ ⎦

⎡ ⎤

0000 1

01010101
00110011

− 1 − 1 − 1 −

⎣ ⎦ .

=

This rotation sequence is illustrated in Fig. B.6 (a)-(d), where the axis of rotation

T

is [ 022 ] 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.6

90 ° ,z