Exact Numerical Perturbation ∗

We present our exact numerical perturbation technique for eliminating degeneracies occurring in geometric modeling processes. Consider a geometric modeler that performs a set of geometric operations (e.g. CSG-based Boolean operations). We would like to make the geometric modeler “robust” with respect to degeneracies, meaning that it will not crash. Our approach achieves many of the same results as symbolic perturbation, but requires very little algorithmic adjustment. Our perturbation technique differs significantly from the other methods (such as fixed-precision perturbation) in the following ways: First, exact computation is used in order to avoid problems caused by numerical errors. Unlike the methods using fixed precision arithmetic or interval arithmetic, there is no need to keep track of errors ∗This work funded in part by NSF awards DMS-0138446 and CCR-0220047