Mostrar el registro sencillo del ítem
dc.contributor.author | Marinelli, K. | es_ES |
dc.contributor.author | Peters, T. J. | es_ES |
dc.date.accessioned | 2019-04-04T10:13:01Z | |
dc.date.available | 2019-04-04T10:13:01Z | |
dc.date.issued | 2019-04-01 | |
dc.identifier.issn | 1576-9402 | |
dc.identifier.uri | http://hdl.handle.net/10251/118975 | |
dc.description.abstract | [EN] Previously, numerical evidence was presented of a self-intersecting Bezier curve having the unknot for its control polygon. This numerical demonstration resolved open questions in scientic visualization, but did not provide a formal proof of self-intersection. An example with a formal existence proof is given, even while the exact self-intersection point remains undetermined. | es_ES |
dc.description.sponsorship | The authors acknowledge, with appreciation, the contributions of •D. Marsh, for software that generated experimental visualizations and related computations, •the reviewers, for singularly comprehensive and constructive comments,and •the editors, for their keen insight and informed perspective in selecting those reviewers. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Universitat Politècnica de València | |
dc.relation.ispartof | Applied General Topology | |
dc.rights | Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) | es_ES |
dc.subject | Knot theory | es_ES |
dc.subject | Isotopy | es_ES |
dc.subject | Parametric curve | es_ES |
dc.title | Exact computation for existence of a knot counterexample | es_ES |
dc.type | Artículo | es_ES |
dc.date.updated | 2019-04-04T06:30:09Z | |
dc.identifier.doi | 10.4995/agt.2019.10928 | |
dc.rights.accessRights | Abierto | es_ES |
dc.description.bibliographicCitation | Marinelli, K.; Peters, TJ. (2019). Exact computation for existence of a knot counterexample. Applied General Topology. 20(1):251-264. https://doi.org/10.4995/agt.2019.10928 | es_ES |
dc.description.accrualMethod | SWORD | es_ES |
dc.relation.publisherversion | https://doi.org/10.4995/agt.2019.10928 | es_ES |
dc.description.upvformatpinicio | 251 | es_ES |
dc.description.upvformatpfin | 264 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 20 | |
dc.description.issue | 1 | |
dc.identifier.eissn | 1989-4147 | |
dc.description.references | Cybergloves. http://www.cyberglovesystems.com/cyberglove-iii/ | es_ES |
dc.description.references | ManusVR. https://manus-vr.com/ | es_ES |
dc.description.references | Virtual motion labs. http://www.virtualmotionlabs.com/ | es_ES |
dc.description.references | N. Amenta, T. J. Peters and A. C. Russell, Computational topology: Ambient isotopic approximation of 2-manifolds, Theoretical Computer Science 305 (2003), 3-15. https://doi.org/10.1016/s0304-3975(02)00691-6 | es_ES |
dc.description.references | L. E. Andersson, S. M. Dorney, T. J. Peters and N. F. Stewart, Polyhedral perturbations that preserve topological form, CAGD 12, no. 8 (1995), 785-799. https://doi.org/10.1016/0167-8396(94)00039-7 | es_ES |
dc.description.references | L. E. Andersson, T. J. Peters and N. F. Stewart, Selfintersection of composite curves and surfaces, CAGD 15 (1998), 507-527. | es_ES |
dc.description.references | M. A. Armstrong, Basic Topology, Springer, New York, 1983. | es_ES |
dc.description.references | R. H. Bing, The Geometric Topology of 3-Manifolds, American Mathematical Society, Providence, RI, 1983. | es_ES |
dc.description.references | J. Bisceglio, T. J. Peters, J. A. Roulier and C. H. Sequin, Unknots with highly knotted control polygons, CAGD 28, no. 3 (2011), 212-214. https://doi.org/10.1016/j.cagd.2011.01.001 | es_ES |
dc.description.references | F. Chazal and D. Cohen-Steiner, A condition for isotopic approximation, Graphical Models 67, no. 5 (2005), 390-404. https://doi.org/10.1016/j.gmod.2005.01.005 | es_ES |
dc.description.references | T. Culver, J. Keyser and D. Manocha, Exact computation of the medial axis of a polyhedron, Computer Aided Geometric Design 21, no. 1 (2004), 65-98. https://doi.org/10.1016/j.cagd.2003.07.008 | es_ES |
dc.description.references | T. Etiene, L. G. Nonato, C. E. Scheidegger, J. Tierny, T.J. Peters, V. Pascucci, R. M.Kirby and C. T. Silva, Topology verification for isosurface extraction, IEEE Trans. Vis. Comput. Graph. 18, no. 6 (2012), 952-965. https://doi.org/10.1109/tvcg.2011.109 | es_ES |
dc.description.references | G. E. Farin, Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide, Academic Press, Inc., 1996. | es_ES |
dc.description.references | J. D. Foley, A. van Dam, S. K. Feiner and J. F. Hughes, Computer Graphics: Principles and Practice (2Nd Ed.), Addison-Wesley Longman Publishing Co., Inc., Boston, MA,USA, 1990. | es_ES |
dc.description.references | D. Jiang and N. F. Stewart, Backward error analysis in computational geometry, Springer Berlin Heidelberg, Berlin, Heidelberg, 2006, pp.50-59. | es_ES |
dc.description.references | K. E. Jordan, J. Li, T. J. Peters and J. A. Roulier, Isotopic equivalence from Bézier curve subdivision for application to high performance computing, CAGD 31 (2014), 642-655. https://doi.org/10.1016/j.cagd.2014.07.002 | es_ES |
dc.description.references | K. E. Jordan, L. E. Miller, E. L. F. Moore, T. J. Peters and A. Russell, Modeling time and topology for animation and visualization with examples on parametric geometry, Theoretical Computer Science 405 (2008), 41-49. https://doi.org/10.1016/j.tcs.2008.06.023 | es_ES |
dc.description.references | L. Kettner, K. Mehlhorn, S. Pion, S. Schirra and C. Yap, Classroom examples of robustness problems in geometric computations, Computational Geometry 40, no. 1 (2008),61-78. https://doi.org/10.1016/j.comgeo.2007.06.003 | es_ES |
dc.description.references | R. M. Kirby and C. T. Silva, The need for verifiable visualization, IEEE Computer Graphics and Applications September/October (2008), 1-9. | es_ES |
dc.description.references | J. M. Lane and R. F. Riesenfeld, A theoretical development for the computer generation and display of piecewise polynomial surfaces, IEEE, PAMI-2no. 1, January 1980. | es_ES |
dc.description.references | J. Li and T. J. Peters, Isotopic convergence theorem, Journal of Knot Theory and Its Ramifications 22, no. 3 (2013). https://doi.org/10.1142/s0218216513500120 | es_ES |
dc.description.references | J. Li, T. J. Peters, D. Marsh and K. E. Jordan, Computational topology counter examples with 3D visualization of Bézier curves, Applied General Topology 13, no. 2 (2012), 115-134. https://doi.org/10.4995/agt.2012.1624 | es_ES |
dc.description.references | G. McGill, Molecular movies coming to a lecture near you, Cell 133, no. 7 (2008), 1127-1132. https://doi.org/10.1016/j.cell.2008.06.013 | es_ES |
dc.description.references | J. Munkres, Topology, Prentice Hall, 2nd edition, 1999. | es_ES |
dc.description.references | M. Neagu, E. Calcoen and B. Lacolle, Bézier curves: topological convergence of the control polygon, 6th Int. Conf. on Mathematical Methods for Curves and Surfaces, Vanderbilt (2000), pp. 347-354. | es_ES |
dc.description.references | J. Peters and X. Wu, On the optimality of piecewise linear max-norm enclosures based on SLEFES, International Conference on Curves and Surfaces, Saint-Malo, France, 2002. | es_ES |
dc.description.references | L. Piegl and W. Tiller, The NURBS Book, Springer, New York, 1997. | es_ES |
dc.description.references | C. H. Sequin, Spline knots and their control polygons with differing knottedness, http://www.eecs.berkeley.edu/Pubs/TechRpts/2009/EECS-2009-152.html | es_ES |
dc.description.references | M. Wertheim and K. Millett, Where the wild things are: An interview with Ken Millett, Cabinet 20, 2006. | es_ES |