Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 201

A.2 R γ,x R β,y R α,x

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

10 0 c β 0 s β

01 0

10 0

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

R γ,x R β,y R α,x = 0 c γ − s γ 0 c α − s α

0 s γ c γ − s β 0 c β 0 s α c α

⎡ ⎤

c β s β s α s β c α

⎣ ⎦

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

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

⎡ ⎤

01 0

⎣ ⎦

R 90 ° ,x R 90 ° ,y R 90 ° ,x = 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. A.1 (a)-(d), where the axis of rotation

T

is [ 220 ] and the angle of rotation 180°.

Fig. A.1 Four views of the unit cube before and during the three rotations R 90 ° ,x R 90 ° ,y R 90 ° ,x