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  • Geometric interpolation of ER frames with ▫$G^2$▫ Pythagorean-hodograph curves of degree 7
    Knez, Marjetka, 1978- ; Sampoli, Maria Lucia
    The problem of constructing a curve that interpolates given initial/final positions along with orientational frames is addressed. In more detail, the resulting interpolating curve is a PH curve of ... degree 7 and among the adaptive frames that can be associated to a spatial PH curve, we consider the Euler-Rodrigues (ER) frame. Moreover ▫$G^1$▫ continuity between frames is imposed and conditions for achieving general geometric continuity are investigated. It is also shown that our construction of ▫$G^k$▫ continuity of ER frames implies ▫$G^{k + 1}$▫ continuity of the corresponding PH curves, and hence this approach can be useful to define spline motions. Exploiting the relation between rotational matrices and quaternions on the unit sphere, geometric continuity conditions on the frames are expressed through conditions on the corresponding quaternion polynomials. This leads to a nonlinear system of equations whose solvability is investigated, and asymptotic analysis of the solutions in the case of data sampled from a smooth parametric curve and its general adapted frame is derived. It is shown that there exist PH interpolants with optimal approximation order 6, except for the case of the Frenet frame, where the approximation order is at most 4. Several numerical examples are presented, which confirm the theoretical results.
    Vir: Computer Aided Geometric Design. - ISSN 0167-8396 (Vol. 88, June 2021, art. 102001 (19 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 101600515

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S0167839621000467
    DOI

vir: Computer Aided Geometric Design. - ISSN 0167-8396 (Vol. 88, June 2021, art. 102001 (19 str.))

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