 Construction of G2 planar Hermite interpolants with prescribed arc lengthsMarjeta Knez, Francesca Pelosi and Maria Lucia Sampoli Applied Mathematics and Computation, 2022, vol. 426, issue C Abstract: In this paper we address the problem of constructing G2 planar Pythagorean–hodograph (PH) spline curves, that interpolate points, tangent directions and curvatures, and have prescribed arc-length. The interpolation scheme is completely local. Each spline segment is defined as a PH biarc curve of degree 7, which results in having a closed form solution of the G2 interpolation equations depending on four free parameters. By fixing two of them to zero, it is proven that the length constraint can be satisfied for any data and any chosen ratio between the two boundary tangents. Length interpolation equation reduces to one algebraic equation with four solutions in general. To select the best one, the value of the bending energy is observed. Several numerical examples are provided to illustrate the obtained theoretical results and to numerically confirm that the approximation order is 5. Keywords: Pythagorean–hodograph curves; Biarc curves; Geometric Hermite interpolation; Arc–length constraint; Spline construction (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:426:y:2022:i:c:s009630032200176x DOI: 10.1016/j.amc.2022.127092 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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