000129645 001__ 129645
000129645 005__ 20241125101132.0
000129645 0247_ $$2doi$$a10.3390/sym15112041
000129645 0248_ $$2sideral$$a135860
000129645 037__ $$aART-2023-135860
000129645 041__ $$aeng
000129645 100__ $$aAlbrecht, Gudrun
000129645 245__ $$aA Shape Preserving Class of Two-Frequency Trigonometric B-Spline Curves
000129645 260__ $$c2023
000129645 5060_ $$aAccess copy available to the general public$$fUnrestricted
000129645 5203_ $$aThis 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.
000129645 536__ $$9info:eu-repo/grantAgreement/ES/CICYT/BFM2000–1253$$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00$$9info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T
000129645 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000129645 590__ $$a2.2$$b2023
000129645 592__ $$a0.485$$b2023
000129645 591__ $$aMULTIDISCIPLINARY SCIENCES$$b50 / 134 = 0.373$$c2023$$dQ2$$eT2
000129645 593__ $$aChemistry (miscellaneous)$$c2023$$dQ2
000129645 593__ $$aPhysics and Astronomy (miscellaneous)$$c2023$$dQ2
000129645 593__ $$aMathematics (miscellaneous)$$c2023$$dQ2
000129645 593__ $$aComputer Science (miscellaneous)$$c2023$$dQ2
000129645 594__ $$a5.4$$b2023
000129645 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000129645 700__ $$0(orcid)0000-0002-1101-6230$$aMainar, Esmeralda$$uUniversidad de Zaragoza
000129645 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, Juan Manuel$$uUniversidad de Zaragoza
000129645 700__ $$0(orcid)0000-0001-9130-0794$$aRubio, Beatriz$$uUniversidad de Zaragoza
000129645 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000129645 773__ $$g15, 11 (2023), 2041 [17 pp.]$$pSymmetry (Basel)$$tSymmetry$$x2073-8994
000129645 8564_ $$s1321107$$uhttps://zaguan.unizar.es/record/129645/files/texto_completo.pdf$$yVersión publicada
000129645 8564_ $$s2421286$$uhttps://zaguan.unizar.es/record/129645/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000129645 909CO $$ooai:zaguan.unizar.es:129645$$particulos$$pdriver
000129645 951__ $$a2024-11-22-11:59:18
000129645 980__ $$aARTICLE