A Shape Preserving Class of Two-Frequency Trigonometric B-Spline Curves

Albrecht, Gudrun ; Mainar, Esmeralda (Universidad de Zaragoza) ; Peña, Juan Manuel (Universidad de Zaragoza) ; Rubio, Beatriz (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.3390/sym15112041

Año: 2023

Publicado en: Symmetry 15, 11 (2023), 2041 [17 pp.]
ISSN: 2073-8994

Factor impacto JCR: 2.2 (2023)

Categ. JCR: MULTIDISCIPLINARY SCIENCES rank: 50 / 134 = 0.373 (2023) - Q2 - T2

Factor impacto CITESCORE: 5.4 - Computer Science (miscellaneous) (Q1) - Mathematics (all) (Q1) - Physics and Astronomy (miscellaneous) (Q1) - Chemistry (miscellaneous) (Q2)

Factor impacto SCIMAGO: 0.485 - Chemistry (miscellaneous) (Q2) - Physics and Astronomy (miscellaneous) (Q2) - Mathematics (miscellaneous) (Q2) - Computer Science (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/CICYT/BFM2000–1253
Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-23R
Financiación: info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)