Controlled Perturbation of sets of line segments in ℝ2 with smart processing order

Controlled Perturbation is a framework for perturbing geometric sets to make the processes that use them more robust for fixed-precision manipulation. We present a Controlled Perturbation scheme for sets of line segments in IR (CPLS, for short). CPLS iteratively perturbs the endpoints of the line segments to eliminate potential degeneracies that may cause round-off errors when using fixed-precision arithmetic. We implemented CPLS and provide experimental results. In the core of this work, we present a novel method for decreasing the perturbation magnitude. The main idea behind our method is that different endpoint processing orders yield different perturbation quality. We devise several heuristics for deciding smart endpoint processing to decrease the perturbation. We implemented and experimented with them. Our experiments show a significant decrease in the perturbation magnitude.