doi:10.3390/sym15112041engAlbrecht, GudrunMainar, EsmeraldaPeña, Juan ManuelRubio, BeatrizA Shape Preserving Class of Two-Frequency Trigonometric B-Spline CurvesART-2023-135860This 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.2023http://zaguan.unizar.es/record/12964510.3390/sym15112041http://zaguan.unizar.es/record/129645oai:zaguan.unizar.es:129645info:eu-repo/grantAgreement/ES/CICYT/BFM2000–1253info:eu-repo/grantAgreement/ES/DGA/E41-23Rinfo:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-TSymmetry 15, 11 (2023), 2041 [17 pp.]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess