Robustness of k-gon Voronoi diagram construction

Abstract

In this paper, we present a plane sweep algorithm for constructing the Voronoi diagram of a set of non-crossing line segments in 2D space using a distance metric induced by a regular k-gon and study the robustness of the algorithm. Following the algorithmic degree model [G. Liotta, F.P. Preparata, R. Tamassia, Robust proximity queries: an illustration of degree-driven algorithm design, SIAM J. Comput. 28 (3) (1998) 864–889], we show that the Voronoi diagram of a set of arbitrarily oriented segments can be constructed with degree 14 for certain k-gon metrics (e.g., k = 6 , 8 , 12 ). For rectilinear segments or segments with slope +1 or −1, the degree reduces to 2. The algorithm is easy to implement and finds applications in VLSI layout.