Nonlinear Projections - Transformations and Projections in Computer Graphics - page 159

4 3 2 1

1 3 4

2

Figure 4.17: Four Circles and Lines.

Exercise 4.6: Search the mathematical literature or the Internet (or just think about
this) to find another anallagmatic curve.

L

Q *

Q

P P *

O

Figure 4.18: Circular Inversion of a Line.

Here is a proof of feature 4. Figure 4.18 shows a line L that does not pass through
the origin. Consequently, there must be a perpendicular to L from the origin. The point
where this perpendicular meets L is denoted P and its projection is denoted P ∗ .We
now select another arbitrary point Q on L and denote its projection Q ∗ . It is obvious
that OP OP ∗ =1and OQ OQ ∗ =1,soweconcludethat OP/OQ ∗ = OQ/OP ∗ .This

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