Computer Aided Engineering Design

TRANSFORMATIONS AND PROJECTIONS 43

Rfyz=

–1000

0100

0010

0001

⎡

⎣

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

The transformations are

A

B*

C*

D*

E*

F*

A B C D E F

T

yyzy

* T

= =

0.707 0 – 0.707 0

01 0 0

0.707 0 0.707 0

00 0 1

–1 0 0

–1

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥

RRf R

00

0100

0010

0001

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ×

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

0.707 0 0.707 0

0100

• 0.707 0 0.707 0
  0001

=

–2 0 0 1

–3 0 0 1

–3 2 0 1

–2 2 0 1

–2 2 1 1

–3 2 1 1

T

and the reflected object is shown in Figure 2.18.

Figure 2.18 Reflection of a wedge about a plane at 45° between (– x) and z-axis.

y

x

z

45 ° Reflecting plane

D*

C* F* E*

B*

A*

E

D

F C

B

A