A FAST STRAIGHT-SKELETON ALGORITHM BASED ON GENERALIZED MOTORCYCLE GRAPHS

Abstract

This paper deals with the fast computation of straight skeletons of planar straight-line graphs (PSLGs) at an industrial-strength level. We discuss both the theoretical foundations of our algorithm and the engineering aspects of our implementation Bone. Our investigation starts with an analysis of the triangulation-based algorithm by Aichholzer and Aurenhammer and we prove the existence of flip-event-free Steiner triangulations. This result motivates a careful generalization of motorcycle graphs such that their intimate geometric connection to straight skeletons is maintained. Based on the generalized motorcycle graph, we devise a non-procedural characterization of straight skeletons of PSLGs and we discuss how to obtain a discretized version of a straight skeleton by means of graphics rendering. Most importantly, this generalization allows us to present a fast and easy-to-implement straight-skeleton algorithm.We implemented our algorithm in C++ based on floating-point arithmetic. Extensive benchmarks with our code Bone demonstrate an [Formula: see text] time complexity and [Formula: see text] memory footprint on 22 300 datasets of diverse characteristics. This is a linear factor better than the implementation provided by CGAL 4.0, which shows an [Formula: see text] time complexity and an [Formula: see text] memory footprint; the CGAL code has been the only fully-functional straight-skeleton code so far. In particular, on datasets with ten thousand vertices, Bone requires about 0.2–0.6 seconds instead of 4–7 minutes consumed by the CGAL code, and Bone uses only 20 MB heap memory instead of several gigabytes. We conclude our paper with a discussion of the engineering aspects and principles that make Bone reliable enough to compute the straight skeleton of datasets comprising a few million vertices on a desktop computer.