--- _id: '1531' 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 article_processing_charge: No author: - first_name: Valentin full_name: Zobel, Valentin last_name: Zobel - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz citation: 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' 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 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. 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. 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.' 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. 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. date_created: 2018-12-11T11:52:33Z date_published: 2015-01-01T00:00:00Z date_updated: 2022-06-10T09:50:14Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-319-15090-1_13 edition: '1' editor: - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz - first_name: Thomas full_name: Schultz, Thomas last_name: Schultz intvolume: ' 40' language: - iso: eng month: '01' oa_version: None page: 257 - 267 publication: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data publication_identifier: isbn: - 978-3-319-15089-5 publication_status: published publisher: Springer publist_id: '5640' quality_controlled: '1' scopus_import: '1' status: public title: Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 40 year: '2015' ... --- _id: '1555' abstract: - lang: eng 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. 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. article_processing_charge: No article_type: original author: - first_name: Diána full_name: Knipl, Diána last_name: Knipl - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk - first_name: Gergely full_name: Röst, Gergely last_name: Röst citation: 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 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 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. 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. 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. 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. date_created: 2018-12-11T11:52:42Z date_published: 2015-01-01T00:00:00Z date_updated: 2021-01-12T06:51:34Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1137/140993934 ec_funded: 1 intvolume: ' 14' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: http://discovery.ucl.ac.uk/1473750/1/99393.pdf month: '01' oa: 1 oa_version: Published Version page: 980 - 1017 project: - _id: 255F06BE-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '622033' name: Persistent Homology - Images, Data and Maps publication: SIAM Journal on Applied Dynamical Systems publication_identifier: eissn: - 1536-0040 publication_status: published publisher: 'Society for Industrial and Applied Mathematics ' publist_id: '5616' quality_controlled: '1' scopus_import: 1 status: public title: Rich bifurcation structure in a two patch vaccination model type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2015' ... --- _id: '1568' 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. acknowledgement: This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research. author: - first_name: Olga full_name: Dunaeva, Olga last_name: Dunaeva - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Anton full_name: Lukyanov, Anton last_name: Lukyanov - first_name: Michael full_name: Machin, Michael last_name: Machin - first_name: Daria full_name: Malkova, Daria last_name: Malkova citation: 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' 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' 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. 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.' 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. 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. conference: end_date: 2014-09-25 location: Timisoara, Romania name: 'SYNASC: Symbolic and Numeric Algorithms for Scientific Computing' start_date: 2014-09-22 date_created: 2018-12-11T11:52:46Z date_published: 2015-02-05T00:00:00Z date_updated: 2023-02-21T16:57:29Z day: '05' department: - _id: HeEd doi: 10.1109/SYNASC.2014.81 language: - iso: eng month: '02' oa_version: None page: '7034731' publication: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing publication_status: published publisher: IEEE publist_id: '5603' quality_controlled: '1' related_material: record: - id: '1289' relation: later_version status: public scopus_import: 1 status: public title: The classification of endoscopy images with persistent homology type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2015' ... --- _id: '1567' 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. alternative_title: - LNCS article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International Symposium. Vol 9411. Springer Nature; 2015.' apa: 'Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer Nature.' chicago: Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In 23rd International Symposium, Vol. 9411. Springer Nature, 2015. ieee: H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd International Symposium, Los Angeles, CA, United States, 2015, vol. 9411. ista: 'Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.' 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. conference: end_date: 2015-09-26 location: Los Angeles, CA, United States name: 'GD: Graph Drawing and Network Visualization' start_date: 2015-09-24 date_created: 2018-12-11T11:52:46Z date_published: 2015-01-01T00:00:00Z date_updated: 2022-01-28T08:25:00Z day: '01' department: - _id: HeEd intvolume: ' 9411' language: - iso: eng month: '01' oa_version: None publication: 23rd International Symposium publication_status: published publisher: Springer Nature publist_id: '5604' quality_controlled: '1' scopus_import: '1' status: public title: Shape, homology, persistence, and stability type: conference user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9411 year: '2015' ... --- _id: '1563' abstract: - lang: eng 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/}. author: - first_name: Grzegorz full_name: Graff, Grzegorz last_name: Graff - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk citation: 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 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 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. 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. 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. short: G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286. date_created: 2018-12-11T11:52:44Z date_published: 2015-03-01T00:00:00Z date_updated: 2021-01-12T06:51:37Z day: '01' department: - _id: HeEd doi: 10.12775/TMNA.2015.014 intvolume: ' 45' issue: '1' language: - iso: eng month: '03' oa_version: None page: 273 - 286 publication: Topological Methods in Nonlinear Analysis publication_status: published publisher: Juliusz Schauder Center for Nonlinear Studies publist_id: '5608' quality_controlled: '1' scopus_import: 1 status: public title: An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 45 year: '2015' ... --- _id: '1578' abstract: - lang: eng 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. 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" author: - first_name: Thanhtung full_name: Cao, Thanhtung last_name: Cao - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Tiowseng full_name: Tan, Tiowseng last_name: Tan citation: 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 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 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. 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. 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. short: T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519. date_created: 2018-12-11T11:52:49Z date_published: 2015-08-01T00:00:00Z date_updated: 2021-01-12T06:51:43Z day: '01' department: - _id: HeEd doi: 10.1016/j.comgeo.2015.04.001 intvolume: ' 48' issue: '7' language: - iso: eng month: '08' oa_version: None page: 507 - 519 publication: Computational Geometry publication_status: published publisher: Elsevier publist_id: '5593' quality_controlled: '1' scopus_import: 1 status: public title: Triangulations from topologically correct digital Voronoi diagrams type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1584' abstract: - lang: eng 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. 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: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: 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' 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' 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.' 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.' 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.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.' date_created: 2018-12-11T11:52:51Z date_published: 2015-07-01T00:00:00Z date_updated: 2023-02-23T10:05:22Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2015.01.004 file: - access_level: open_access checksum: 5b33719a86f7f4c8e5dc62c1b6893f49 content_type: application/pdf creator: system date_created: 2018-12-12T10:17:36Z date_updated: 2020-07-14T12:45:03Z file_id: '5292' file_name: IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf file_size: 508379 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 48' issue: '5' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 429 - 442 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5587' pubrep_id: '475' quality_controlled: '1' related_material: record: - id: '1582' relation: other status: public scopus_import: 1 status: public title: 'Reprint of: Weighted straight skeletons in the plane' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1582' abstract: - lang: eng 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. 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: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133. doi:10.1016/j.comgeo.2014.08.006' apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006' chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.' ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.' ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(2), 120–133.' mla: 'Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:10.1016/j.comgeo.2014.08.006.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.' date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2023-02-23T10:05:27Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2014.08.006 file: - access_level: open_access checksum: c1ef67f6ec925e12f73a96b8fe285ab4 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:28Z date_updated: 2020-07-14T12:45:02Z file_id: '5215' file_name: IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf file_size: 505987 relation: main_file file_date_updated: 2020-07-14T12:45:02Z has_accepted_license: '1' intvolume: ' 48' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 120 - 133 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5589' pubrep_id: '474' quality_controlled: '1' related_material: record: - id: '1584' relation: other status: public scopus_import: 1 status: public title: Weighted straight skeletons in the plane tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1583' abstract: - lang: eng text: 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: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: 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 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 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. 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. 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. 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. date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2021-01-12T06:51:45Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.ipl.2014.09.021 file: - access_level: open_access checksum: 2779a648610c9b5c86d0b51a62816d23 content_type: application/pdf creator: system date_created: 2018-12-12T10:18:45Z date_updated: 2020-07-14T12:45:03Z file_id: '5367' file_name: IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf file_size: 270137 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 115' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 243 - 247 publication: Information Processing Letters publication_status: published publisher: Elsevier publist_id: '5588' pubrep_id: '473' quality_controlled: '1' scopus_import: 1 status: public title: A simple algorithm for computing positively weighted straight skeletons of monotone polygons tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 115 year: '2015' ... --- _id: '1590' 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.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Thomas full_name: Hackl, Thomas last_name: Hackl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber 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' 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' 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. 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. 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.' 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. conference: end_date: 2015-09-26 location: Los Angeles, CA, United States name: 'GD: International Symposium on Graph Drawing' start_date: 2015-09-24 date_created: 2018-12-11T11:52:54Z date_published: 2015-11-27T00:00:00Z date_updated: 2022-01-28T09:10:37Z day: '27' department: - _id: HeEd doi: 10.1007/978-3-319-27261-0_28 intvolume: ' 9411' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1508.01076 month: '11' oa: 1 oa_version: Preprint page: 335 - 347 publication: Graph Drawing and Network Visualization publication_identifier: eisbn: - 978-3-319-27261-0 isbn: - 978-3-319-27260-3 publication_status: published publisher: Springer Nature publist_id: '5581' quality_controlled: '1' scopus_import: '1' status: public title: Representing directed trees as straight skeletons type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9411 year: '2015' ...