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  • Construction of ▫$G^2$▫ planar Hermite interpolants with prescribed arc lengths
    Knez, Marjetka, 1978- ; Pelosi, Francesca ; Sampoli, Maria Lucia
    In this paper we address the problem of constructing ▫$G^2$▫ 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 solu- tion of the ▫$G^2$▫ 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.
    Vir: Applied mathematics and computation. - ISSN 0096-3003 (Vol. 426, art. no. 127092, Aug. 2022, 14 str.)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2022
    Jezik - angleški
    COBISS.SI-ID - 133487363

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S009630032200176X
    DOI

vir: Applied mathematics and computation. - ISSN 0096-3003 (Vol. 426, art. no. 127092, Aug. 2022, 14 str.)
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