Composite Point Rotation Sequences - Rotation Transforms for Computer Graphics - page 207

A.8 R γ,y R β,z R α,x

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

c γ 0 s γ
01 0

c β − s β 0 10 0

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

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

− s γ 0 c γ 0 0 1 0 s α c α

⎡ ⎤

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

⎣ ⎦

−

= s β c β c α c β s α

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

⎡ ⎤

01 0

⎣ ⎦

R 90 ° ,y R 90 ° ,z 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.7 (a)-(d), where the axis of rotation

T

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

Fig. A.7 Four views of the unit cube before and during the three rotations R 90 ° ,y R 90 ° ,z R 90 ° ,x