Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Straight Skeletons for General Polygonal Figures in the Plane
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Heuristics for the Generation of Random Polygons
Proceedings of the 8th Canadian Conference on Computational Geometry
Motorcycle Graphs and Straight Skeletons
Algorithmica
Linear axis for planar straight line graphs
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Motorcycle graphs: Stochastic properties motivate an efficient yet simple implementation
Journal of Experimental Algorithmics (JEA)
Generating realistic roofs over a rectilinear polygon
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
On computing straight skeletons by means of kinetic triangulations
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
A faster algorithm for computing motorcycle graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We study straight skeletons and make both theoretical and practical contributions which support new approaches to the computation of straight skeletons of arbitrary planar straight-line graphs (PSLGs). We start with an adequate extension of the concept of motorcycle graphs to PSLGs, with motorcycles starting at the reflex vertices of a PSLG, which allows us to generalize well-known results on the relation between the straight skeleton and the motorcycle graph to arbitrary PSLGs: the edges of the motorcycle graph cover a specific subset of the edges of the straight skeleton, and they form the basis of 3D slabs such that the projection of the lower envelope of those slabs to the plane forms the straight skeleton. As an immediate application we sketch how to use a graphics hardware for computing (approximate) straight skeletons of PSLGs. Further, we present and analyze a novel wavefront-type algorithm which bridges the current gap between the theory and practice of straight-skeleton computations. Our algorithm handles arbitrary PSLGs, is easy to implement, and is fast enough to handle complex data: it can be expected to run in O(n log n) time in practice for an n-vertex PSLG; its worst-case complexity is O(n2 log n). Extensive experimental results confirm an average runtime of 20 n log n µs on a standard PC for virtually all of our 13500 datasets of different characteristics. As also confirmed by our experiments, this constitutes an average gain in performance by a multiplicative factor of n, or at least one to two orders of magnitude, relative to the speed of the implementation provided by CGAL for closed polygons.