129645 20241125101132.0 doi 10.3390/sym15112041 sideral 135860 ART-2023-135860 eng Albrecht, Gudrun A Shape Preserving Class of Two-Frequency Trigonometric B-Spline Curves 2023 Access copy available to the general public Unrestricted This paper proposes a new approach to define two frequency trigonometric spline curves with interesting shape preserving properties. This construction requires the normalized B-basis of the space U4(Iα)=span{1,cost,sint,cos2t,sin2t} defined on compact intervals Iα=[0,α], where α is a global shape parameter. It will be shown that the normalized B-basis can be regarded as the equivalent in the trigonometric space U4(Iα) to the Bernstein polynomial basis and shares its well-known symmetry properties. In fact, the normalized B-basis functions converge to the Bernstein polynomials as α→0. As a consequence, the convergence of the obtained piecewise trigonometric curves to uniform quartic B-Spline curves will be also shown. The proposed trigonometric spline curves can be used for CAM design, trajectory-generation, data fitting on the sphere and even to define new algebraic-trigonometric Pythagorean-Hodograph curves and their piecewise counterparts allowing the resolution of C(3 Hermite interpolation problems. info:eu-repo/grantAgreement/ES/CICYT/BFM2000–1253 info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00 info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 2.2 2023 MULTIDISCIPLINARY SCIENCES 50 / 134 = 0.373 2023 Q2 T2 0.485 2023 Chemistry (miscellaneous) 2023 Q2 Physics and Astronomy (miscellaneous) 2023 Q2 Mathematics (miscellaneous) 2023 Q2 Computer Science (miscellaneous) 2023 Q2 5.4 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Mainar, Esmeralda Universidad de Zaragoza (orcid)0000-0002-1101-6230 Peña, Juan Manuel Universidad de Zaragoza (orcid)0000-0002-1340-0666 Rubio, Beatriz Universidad de Zaragoza (orcid)0000-0001-9130-0794 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 15, 11 (2023), 2041 [17 pp.] Symmetry (Basel) Symmetry 2073-8994 1321107 http://zaguan.unizar.es/record/129645/files/texto_completo.pdf Versión publicada 2421286 http://zaguan.unizar.es/record/129645/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:129645 articulos driver 2024-11-22-11:59:18 ARTICLE