Piecewise rational rotation-minimizing motions via data stream interpolation
<|reference_start|>Piecewise rational rotation-minimizing motions via data stream interpolation: When a moving frame defined along a space curve is required to keep an axis aligned with the tangent direction of motion, the use of rotation-minimizing frames (RMF) avoids unnecessary rotations in the normal plane. The construction of rigid body motions using a specific subset of quintic curves with rational RMFs (RRMFs) is here considered. In particular, a novel geometric characterization of such subset enables the design of a local algorithm to interpolate an assigned stream of positions, together with an initial frame orientation. To achieve this, the translational part of the motion is described by a parametric $G^1$ spline curve whose segments are quintic RRMFs, with a globally continuous piecewise rational rotation-minimizing frame. A selection of numerical experiments illustrates the performances of the proposed method on synthetic and arbitrary data streams.<|reference_end|>
@article{giannelli2024piecewise,
    title={Piecewise rational rotation-minimizing motions via data stream
  interpolation},
    author={Carlotta Giannelli, Lorenzo Sacco, Alessandra Sestini, Zbynv{e}k
  v{S}'ir},
    journal={arXiv preprint arXiv:2405.14229},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14229},
    primaryClass={math.NA cs.NA}
}