The nature and meaning of perturbations in geometric computing

Abstract

This note addresses some fundamental questions concerning perturbations as they are used in computational geometry: How does one define them? What does it mean to compute with them? How can one compute with them? Is it sensible to use them? We define perturbations to be curves, point out that computing with them amounts to computing with limits. and (re)derive some methods of computing with such limits automatically. In principle a line can always be used as a perturbation curve. We discuss a generic method for choosing such a line that is applicable in many situations.