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  • Construction of ▫$G^2$▫ spatial interpolants with prescribed arc lengths
    Knez, Marjetka, 1978- ; Pelosi, Francesca ; Sampoli, Maria Lucia
    In this paper the problem of constructing spatial ▫$G^2$▫ continuous Pythagorean-hodograph (PH) spline curves, that interpolate points and frame data, and in addition have the prescribed arclength, ... is addressed. The interpolation scheme is completely local and can be directly applied for motion design applications. Each spline segment is defined as a PH biarc curve of degree 7 satisfying super-smoothness conditions at the biarc’s joint point. The biarc is expressed in a closed form with additional free parameters, where one of them is determined by the length constraint. The selection of the remaining free parameters is suggested, that allows the existence of the solution of the length interpolation equation for any prescribed length and any ratio between norms of boundary tangents. By the proposed automatic procedure for computing the frame and velocity quaternions from the first and second order derivative vectors, the paper presents a direct generalization of the construction done for planar curves to spatial ones. Several numerical examples are provided to illustrate the proposed method and to show its good performance, also when a spline construction in considered.
    Vir: Journal of computational and applied mathematics. - ISSN 0377-0427 (Vol. 441, [article no.] 115684, May 2024, 14 str.)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2024
    Jezik - angleški
    COBISS.SI-ID - 179837955

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S0377042723006271
    DOI

vir: Journal of computational and applied mathematics. - ISSN 0377-0427 (Vol. 441, [article no.] 115684, May 2024, 14 str.)
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