An Axiomatic Approach to Robust Geometric Programs

Creating robust geometric programs, i.e., programs that handle degenerate configurations correctly, is a difficult problem, especially if the underlying geometric primitives are implemented in floating point arithmetic. This paper presents an axiomatic method for constructing programs built on imprecise primitives and for analyzing their accuracy. We demonstrate the power of this approach by analyzing as a case study a non-trivial plane sweep algorithm for the computation of the closest-pair among a set of points.