Controlled Perturbation of Arrangements of Line Segments in IR with Smart Processing Order∗

Controlled Perturbation is a framework for perturbing geometric arrangements to make them more robust for further manipulation. The idea is to slightly perturb the arrangement to make it more robust for finite precision arithmetic. We present a Controlled Perturbation scheme for arrangements of line segments in IR (CPAL for short). CPAL perturbs the endpoints of the arrangement to eliminate degeneracies that may cause errors when using finite-precision arithmetic. We describe and analyze all degeneracies. While eliminating the degeneracies, CPAL also preserves the edges of the arrangement (two adjacent endpoints remain adjacent). We implemented CPAL and provide experimental results. In the core of this work, we present a novel technique to significantly decrease the perturbation magnitude of Controlled Perturbation algorithms. The idea is to determine a smart order for processing the endpoints. We developed and implemented our method and performed experiments to evaluate its efficiency. Our experiments show that this method is very effective in decreasing the perturbation magnitude.