Applying a General Analysis Method for Controlled Perturbation

that case problems arise for evaluation results close to zero. The basic idea of controlled perturbation is to modify the input data slightly to
get rid of those problems. Another benefit of this approach is the elimination of degenerate situations, which simplifies the implementation.
One is interested in how much the input has to be perturbed, depending on the floating-point precision and the actual expression.
Estimations on the maximum perturbation bound have been conducted for several geometric algorithms. It turned out that for algorithms with
complex geometric predicates these analyses are often complicated and laborious. Now there is a general method for analyzing controlled
perturbation algorithms. We apply this method exemplarily on two problems to see how it performs. The first problem is computing circle
arrangements. It turns out that the analysis of this problem is strongly simplified. The second problem is computing a Voronoi diagram of line
segments. This hasn't been done so far and now it can be done quite easily