@article{1578, abstract = {We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations.}, author = {Cao, Thanhtung and Edelsbrunner, Herbert and Tan, Tiowseng}, journal = {Computational Geometry}, number = {7}, pages = {507 -- 519}, publisher = {Elsevier}, title = {{Triangulations from topologically correct digital Voronoi diagrams}}, doi = {10.1016/j.comgeo.2015.04.001}, volume = {48}, year = {2015}, } @article{1584, abstract = {We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.}, author = {Biedl, Therese and Held, Martin and Huber, Stefan and Kaaser, Dominik and Palfrader, Peter}, journal = {Computational Geometry: Theory and Applications}, number = {5}, pages = {429 -- 442}, publisher = {Elsevier}, title = {{Reprint of: Weighted straight skeletons in the plane}}, doi = {10.1016/j.comgeo.2015.01.004}, volume = {48}, year = {2015}, } @article{1582, abstract = {We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.}, author = {Biedl, Therese and Held, Martin and Huber, Stefan and Kaaser, Dominik and Palfrader, Peter}, journal = {Computational Geometry: Theory and Applications}, number = {2}, pages = {120 -- 133}, publisher = {Elsevier}, title = {{Weighted straight skeletons in the plane}}, doi = {10.1016/j.comgeo.2014.08.006}, volume = {48}, year = {2015}, } @article{1583, abstract = {We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon.}, author = {Biedl, Therese and Held, Martin and Huber, Stefan and Kaaser, Dominik and Palfrader, Peter}, journal = {Information Processing Letters}, number = {2}, pages = {243 -- 247}, publisher = {Elsevier}, title = {{A simple algorithm for computing positively weighted straight skeletons of monotone polygons}}, doi = {10.1016/j.ipl.2014.09.021}, volume = {115}, year = {2015}, } @inbook{1590, abstract = {The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.}, author = {Aichholzer, Oswin and Biedl, Therese and Hackl, Thomas and Held, Martin and Huber, Stefan and Palfrader, Peter and Vogtenhuber, Birgit}, booktitle = {Graph Drawing and Network Visualization}, isbn = {978-3-319-27260-3}, location = {Los Angeles, CA, United States}, pages = {335 -- 347}, publisher = {Springer Nature}, title = {{Representing directed trees as straight skeletons}}, doi = {10.1007/978-3-319-27261-0_28}, volume = {9411}, year = {2015}, }