Robust Geometric Computation

Geometric algorithms are often composed of a set of basic geometric predicates and constructions, also called primitives. Correctness of an algorithm is usually proved under the assumption that all primitives return the correct result. This is in sharp contrast to the naive, but common strategy of implementing such primitives with fixed-precision floating-point arithmetic. The disastrous effects of this gap between theory and practice have been witnessed in various areas using geometric algorithms, like computer-aided design or computational fluid dynamics.