G2∕C1 Hermite interpolation by planar PH B-spline curves with shape parameter. (November 2021)

• Record Type: Journal Article
• Authors: Albrecht, Gudrun; Beccari, Carolina Vittoria; Romani, Lucia
• Is Part Of: Applied mathematics letters. Volume 121(2021)
• Publication Date: 2021-11
• Subjects: Planar B-spline curve -- Pythagorean-Hodograph -- Hermite interpolation -- Shape parameter; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107452
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We solve the problem of G 2 ∕ C 1 Hermite interpolation (i.e. interpolation of prescribed boundary points as well as first derivatives and curvatures at these points) by planar quintic Pythagorean Hodograph B-spline curves with one free interior knot which acts as a shape parameter. We present conditions on the data ensuring the existence of solutions. Finally, we illustrate the influence of the interior knot on the shape of the resulting interpolant and on the values of the absolute rotation index or the bending energy.