[{"date_published":"2015-01-01T00:00:00Z","page":"257 - 267","publication":"Visualization and Processing of Higher Order Descriptors for Multi-Valued Data","citation":{"chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. https://doi.org/10.1007/978-3-319-15090-1_13.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer, 2015, pp. 257–267.","mla":"Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:10.1007/978-3-319-15090-1_13.","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature,” in Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., vol. 40, I. Hotz and T. Schultz, Eds. Springer, 2015, pp. 257–267.","apa":"Zobel, V., Reininghaus, J., & Hotz, I. (2015). Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In I. Hotz & T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (1st ed., Vol. 40, pp. 257–267). Springer. https://doi.org/10.1007/978-3-319-15090-1_13","ista":"Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization, vol. 40, 257–267.","ama":"Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Vol 40. 1st ed. Springer; 2015:257-267. doi:10.1007/978-3-319-15090-1_13"},"day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"None","status":"public","title":"Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature","intvolume":" 40","_id":"1531","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece."}],"alternative_title":["Mathematics and Visualization"],"type":"book_chapter","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-15090-1_13","quality_controlled":"1","month":"01","publication_identifier":{"isbn":["978-3-319-15089-5"]},"date_created":"2018-12-11T11:52:33Z","date_updated":"2022-06-10T09:50:14Z","volume":40,"author":[{"full_name":"Zobel, Valentin","first_name":"Valentin","last_name":"Zobel"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"}],"edition":"1","publication_status":"published","department":[{"_id":"HeEd"}],"editor":[{"last_name":"Hotz","first_name":"Ingrid","full_name":"Hotz, Ingrid"},{"full_name":"Schultz, Thomas","last_name":"Schultz","first_name":"Thomas"}],"publisher":"Springer","year":"2015","publist_id":"5640"},{"publist_id":"5616","ec_funded":1,"volume":14,"date_updated":"2021-01-12T06:51:34Z","date_created":"2018-12-11T11:52:42Z","author":[{"full_name":"Knipl, Diána","first_name":"Diána","last_name":"Knipl"},{"first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"},{"first_name":"Gergely","last_name":"Röst","full_name":"Röst, Gergely"}],"department":[{"_id":"HeEd"}],"publisher":"Society for Industrial and Applied Mathematics ","publication_status":"published","year":"2015","acknowledgement":"Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559 in the framework of the EPIDELAY project.","publication_identifier":{"eissn":["1536-0040"]},"month":"01","language":[{"iso":"eng"}],"doi":"10.1137/140993934","project":[{"name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033"}],"quality_controlled":"1","oa":1,"main_file_link":[{"url":"http://discovery.ucl.ac.uk/1473750/1/99393.pdf","open_access":"1"}],"issue":"2","abstract":[{"text":"We show that incorporating spatial dispersal of individuals into a simple vaccination epidemic model may give rise to a model that exhibits rich dynamical behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as a basis, we describe the spread of an infectious disease in a population split into two regions. In each subpopulation, both forward and backward bifurcations can occur. This implies that for disconnected regions the two-patch system may admit several steady states. We consider traveling between the regions and investigate the impact of spatial dispersal of individuals on the model dynamics. We establish conditions for the existence of multiple nontrivial steady states in the system, and we study the structure of the equilibria. The mathematical analysis reveals an unusually rich dynamical behavior, not normally found in the simple epidemic models. In addition to the disease-free equilibrium, eight endemic equilibria emerge from backward transcritical and saddle-node bifurcation points, forming an interesting bifurcation diagram. Stability of steady states, their bifurcations, and the global dynamics are investigated with analytical tools, numerical simulations, and rigorous set-oriented numerical computations.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","intvolume":" 14","ddc":["510"],"status":"public","title":"Rich bifurcation structure in a two patch vaccination model","_id":"1555","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","day":"01","scopus_import":1,"date_published":"2015-01-01T00:00:00Z","page":"980 - 1017","article_type":"original","citation":{"mla":"Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, Society for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:10.1137/140993934.","short":"D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems 14 (2015) 980–1017.","chicago":"Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics , 2015. https://doi.org/10.1137/140993934.","ama":"Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 2015;14(2):980-1017. doi:10.1137/140993934","ista":"Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017.","apa":"Knipl, D., Pilarczyk, P., & Röst, G. (2015). Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140993934","ieee":"D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two patch vaccination model,” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015."},"publication":"SIAM Journal on Applied Dynamical Systems"},{"month":"02","day":"05","scopus_import":1,"conference":{"end_date":"2014-09-25","location":"Timisoara, Romania","start_date":"2014-09-22","name":"SYNASC: Symbolic and Numeric Algorithms for Scientific Computing"},"doi":"10.1109/SYNASC.2014.81","date_published":"2015-02-05T00:00:00Z","language":[{"iso":"eng"}],"publication":"Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","citation":{"chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.” In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 7034731. IEEE, 2015. https://doi.org/10.1109/SYNASC.2014.81.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731.","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731, doi:10.1109/SYNASC.2014.81.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., & Malkova, D. (2015). The classification of endoscopy images with persistent homology. In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (p. 7034731). Timisoara, Romania: IEEE. https://doi.org/10.1109/SYNASC.2014.81","ieee":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The classification of endoscopy images with persistent homology,” in Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 2015, p. 7034731.","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification of endoscopy images with persistent homology. Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC: Symbolic and Numeric Algorithms for Scientific Computing, 7034731.","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification of endoscopy images with persistent homology. In: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE; 2015:7034731. doi:10.1109/SYNASC.2014.81"},"quality_controlled":"1","page":"7034731","abstract":[{"lang":"eng","text":"Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI) magnifying endoscopy (ME) images of the stomach, we combine methods from image processing, computational topology, and machine learning to classify patterns into normal, tubular, vessel. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions."}],"publist_id":"5603","type":"conference","author":[{"full_name":"Dunaeva, Olga","last_name":"Dunaeva","first_name":"Olga"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Lukyanov, Anton","first_name":"Anton","last_name":"Lukyanov"},{"full_name":"Machin, Michael","last_name":"Machin","first_name":"Michael"},{"first_name":"Daria","last_name":"Malkova","full_name":"Malkova, Daria"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"1289"}]},"date_updated":"2023-02-21T16:57:29Z","date_created":"2018-12-11T11:52:46Z","oa_version":"None","_id":"1568","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2015","acknowledgement":"This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research.","status":"public","publication_status":"published","title":"The classification of endoscopy images with persistent homology","department":[{"_id":"HeEd"}],"publisher":"IEEE"},{"publist_id":"5604","abstract":[{"lang":"eng","text":"My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the three-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations."}],"type":"conference","alternative_title":["LNCS"],"author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"}],"volume":9411,"oa_version":"None","date_updated":"2022-01-28T08:25:00Z","date_created":"2018-12-11T11:52:46Z","_id":"1567","year":"2015","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","intvolume":" 9411","title":"Shape, homology, persistence, and stability","status":"public","publication_status":"published","article_processing_charge":"No","day":"01","month":"01","scopus_import":"1","date_published":"2015-01-01T00:00:00Z","conference":{"location":"Los Angeles, CA, United States","start_date":"2015-09-24","end_date":"2015-09-26","name":"GD: Graph Drawing and Network Visualization"},"language":[{"iso":"eng"}],"citation":{"ista":"Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.","ieee":"H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd International Symposium, Los Angeles, CA, United States, 2015, vol. 9411.","apa":"Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer Nature.","ama":"Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International Symposium. Vol 9411. Springer Nature; 2015.","chicago":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In 23rd International Symposium, Vol. 9411. Springer Nature, 2015.","mla":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” 23rd International Symposium, vol. 9411, Springer Nature, 2015.","short":"H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015."},"publication":"23rd International Symposium","quality_controlled":"1"},{"_id":"1563","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015","title":"An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds","publication_status":"published","status":"public","department":[{"_id":"HeEd"}],"publisher":"Juliusz Schauder Center for Nonlinear Studies","intvolume":" 45","author":[{"full_name":"Graff, Grzegorz","first_name":"Grzegorz","last_name":"Graff"},{"full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2021-01-12T06:51:37Z","date_created":"2018-12-11T11:52:44Z","oa_version":"None","volume":45,"type":"journal_article","abstract":[{"text":"For a given self-map $f$ of $M$, a closed smooth connected and simply-connected manifold of dimension $m\\geq 4$, we provide an algorithm for estimating the values of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic points in the smooth homotopy class of $f$. Our results are based on the combinatorial scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at {\\tt http://www.pawelpilarczyk.com/combtop/}.","lang":"eng"}],"issue":"1","publist_id":"5608","publication":"Topological Methods in Nonlinear Analysis","citation":{"chicago":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies, 2015. https://doi.org/10.12775/TMNA.2015.014.","short":"G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286.","mla":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:10.12775/TMNA.2015.014.","apa":"Graff, G., & Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies. https://doi.org/10.12775/TMNA.2015.014","ieee":"G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds,” Topological Methods in Nonlinear Analysis, vol. 45, no. 1. Juliusz Schauder Center for Nonlinear Studies, pp. 273–286, 2015.","ista":"Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 45(1), 273–286.","ama":"Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 2015;45(1):273-286. doi:10.12775/TMNA.2015.014"},"quality_controlled":"1","page":"273 - 286","date_published":"2015-03-01T00:00:00Z","doi":"10.12775/TMNA.2015.014","language":[{"iso":"eng"}],"scopus_import":1,"month":"03","day":"01"},{"day":"01","month":"08","scopus_import":1,"date_published":"2015-08-01T00:00:00Z","doi":"10.1016/j.comgeo.2015.04.001","language":[{"iso":"eng"}],"citation":{"chicago":"Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001.","short":"T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.","mla":"Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:10.1016/j.comgeo.2015.04.001.","apa":"Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001","ieee":"T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier, pp. 507–519, 2015.","ista":"Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.","ama":"Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001"},"publication":"Computational Geometry","page":"507 - 519","quality_controlled":"1","issue":"7","publist_id":"5593","abstract":[{"text":"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.","lang":"eng"}],"type":"journal_article","author":[{"full_name":"Cao, Thanhtung","first_name":"Thanhtung","last_name":"Cao"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Tan, Tiowseng","last_name":"Tan","first_name":"Tiowseng"}],"volume":48,"oa_version":"None","date_updated":"2021-01-12T06:51:43Z","date_created":"2018-12-11T11:52:49Z","acknowledgement":"The research of the second author is partially supported by NSF under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n","_id":"1578","year":"2015","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Elsevier","department":[{"_id":"HeEd"}],"intvolume":" 48","publication_status":"published","title":"Triangulations from topologically correct digital Voronoi diagrams","status":"public"},{"month":"07","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","doi":"10.1016/j.comgeo.2015.01.004","language":[{"iso":"eng"}],"publist_id":"5587","file_date_updated":"2020-07-14T12:45:03Z","license":"https://creativecommons.org/licenses/by/4.0/","year":"2015","department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","related_material":{"record":[{"relation":"other","status":"public","id":"1582"}]},"author":[{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"first_name":"Dominik","last_name":"Kaaser","full_name":"Kaaser, Dominik"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"}],"volume":48,"date_created":"2018-12-11T11:52:51Z","date_updated":"2023-02-23T10:05:22Z","scopus_import":1,"has_accepted_license":"1","day":"01","citation":{"apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(5), 429–442.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.","mla":"Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004."},"publication":"Computational Geometry: Theory and Applications","page":"429 - 442","date_published":"2015-07-01T00:00:00Z","type":"journal_article","issue":"5","abstract":[{"text":"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. 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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.","lang":"eng"}],"type":"journal_article","date_published":"2015-02-01T00:00:00Z","page":"120 - 133","citation":{"ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. 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Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon."}],"issue":"2","type":"journal_article","date_published":"2015-02-01T00:00:00Z","publication":"Information Processing Letters","citation":{"mla":"Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 115(2), 243–247.","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” Information Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021"},"page":"243 - 247","day":"01","has_accepted_license":"1","scopus_import":1},{"scopus_import":"1","article_processing_charge":"No","day":"27","citation":{"ama":"Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28","ista":"Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347.","apa":"Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., & Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28","ieee":"O. Aichholzer et al., “Representing directed trees as straight skeletons,” in Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–347.","mla":"Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:10.1007/978-3-319-27261-0_28.","short":"O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.","chicago":"Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28."},"publication":"Graph Drawing and Network Visualization","page":"335 - 347","date_published":"2015-11-27T00:00:00Z","type":"book_chapter","alternative_title":["LNCS"],"abstract":[{"lang":"eng","text":"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."}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"1590","intvolume":" 9411","title":"Representing directed trees as straight skeletons","status":"public","oa_version":"Preprint","publication_identifier":{"isbn":["978-3-319-27260-3"],"eisbn":["978-3-319-27261-0"]},"month":"11","main_file_link":[{"url":"http://arxiv.org/abs/1508.01076","open_access":"1"}],"oa":1,"quality_controlled":"1","doi":"10.1007/978-3-319-27261-0_28","conference":{"location":"Los Angeles, CA, United States","start_date":"2015-09-24","end_date":"2015-09-26","name":"GD: International Symposium on Graph Drawing"},"language":[{"iso":"eng"}],"publist_id":"5581","year":"2015","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"last_name":"Hackl","first_name":"Thomas","full_name":"Hackl, Thomas"},{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"},{"full_name":"Vogtenhuber, Birgit","first_name":"Birgit","last_name":"Vogtenhuber"}],"volume":9411,"date_updated":"2022-01-28T09:10:37Z","date_created":"2018-12-11T11:52:54Z"}]