Symbolic treatment of geometric degeneracies

Abstract

Many descriptions of algorithms in computational geometry exclude degeneracies by fiat . Practitioners are left to their own devices for dealing with degeneracies when implementing such algorithms. Since degeneracies tend to be numerous and hard to enumerate exhaustively, this is often a reason against implementing such algorithms. This paper proposes a symbolic scheme for treating degeneracies. Our method is simple to use, and is applicable to a variety of problems in computational geometry. Implementation, limitations and wider issues are discussed.