Robust Geometric Computation

Authored by: Chee K. Yap

Discrete and Computational Geometry

Print publication date:  April  2004
Online publication date:  April  2004

Print ISBN: 9781584883012
eBook ISBN: 9781420035315
Adobe ISBN:

10.1201/9781420035315.ch41

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Abstract

Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising from numerical errors. Section 41.1 provides background on these problems. Although nonrobustness is already an issue in “purely numerical” computation, the problem is compounded in “geometric computation.” In Section 41.2 we characterize such computations. Researchers trying to create robust geometric software have tried two approaches: making fixed-precision computation robust (Section 41.3), and making the exact approach viable (Section 41.4). Another source of nonrobustness is the phenomenon of degenerate inputs. General methods for treating degenerate inputs are described in Section 41.5.

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