Computer Aided Engineering Design

TRANSFORMATIONS AND PROJECTIONS 31

Figure 2.8 Reflection about an arbitrary line

In Eq. (2.10), TPQ represents translation from point P to Q. The above procedure is not unique in that
the steps (b), (c) and (d) above can be altered so that L is made to coincide with the x-axis by rotating
it through an angle α, reflection is performed about the x-axis, and the line is rotated back by –α.

2.2.7 Reflection through a Point

A point P (x,y, 1) when reflected through the origin is written as P (x,y*, 1) = (−x,−y, 1) or

x

y

x

y

x

y

x

fo y

*

*

1

=

• 
  


• 
  

  1

  
  

=

–1 0 0

0–10

0011

=

1

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R (2.11)

For reflection of an object about a point Pr, we would require to shift Pr to the origin, perform the
above reflection and then transform Pr back to its original position.

D

L

S

x

(a) Original position

O

y

y

x

(b) Translating D to O

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y

(d) Reflection about the y-axis

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y

(c) Rotating L to coincide with the y-axis

x

y

(e) Rotating L back to the position in (b) (f) Translating L to its original position

x

y

S

L

D

S*