An /spl epsiv/ arithmetic for removing degeneracies

Abstract

Symbolic perturbation by infinitely small values removes degeneracies in geometric algorithms and enables programmers to handle only generic cases: there are a few such cases, whereas there are an overwhelming number of degenerate cases. Current perturbation schemes have limitations. To overcome them, the paper proposes to use an /spl epsiv/-arithmetic, i.e. to represent in an explicit way infinitely small numbers and to define arithmetic operations (+,-,*,/,<,=) on them.<>