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<dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:invenio="http://invenio-software.org/elements/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><dc:identifier>doi:10.3390/sym15112041</dc:identifier><dc:language>eng</dc:language><dc:creator>Albrecht, Gudrun</dc:creator><dc:creator>Mainar, Esmeralda</dc:creator><dc:creator>Peña, Juan Manuel</dc:creator><dc:creator>Rubio, Beatriz</dc:creator><dc:title>A Shape Preserving Class of Two-Frequency Trigonometric B-Spline Curves</dc:title><dc:identifier>ART-2023-135860</dc:identifier><dc:description>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.</dc:description><dc:date>2023</dc:date><dc:source>http://zaguan.unizar.es/record/129645</dc:source><dc:doi>10.3390/sym15112041</dc:doi><dc:identifier>http://zaguan.unizar.es/record/129645</dc:identifier><dc:identifier>oai:zaguan.unizar.es:129645</dc:identifier><dc:relation>info:eu-repo/grantAgreement/ES/CICYT/BFM2000–1253</dc:relation><dc:relation>info:eu-repo/grantAgreement/ES/DGA/E41-23R</dc:relation><dc:relation>info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00</dc:relation><dc:relation>info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T</dc:relation><dc:identifier.citation>Symmetry 15, 11 (2023), 2041 [17 pp.]</dc:identifier.citation><dc:rights>by</dc:rights><dc:rights>http://creativecommons.org/licenses/by/3.0/es/</dc:rights><dc:rights>info:eu-repo/semantics/openAccess</dc:rights></dc:dc>

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