Accurate High-Order Derivatives of Geodesic Paths on Smooth Surfaces

Felix Scholz*, Takashi Maekawa

*この研究の対応する著者

研究成果: Article査読

抄録

We propose a new approach for the accurate numerical computation of high-order derivatives along geodesic curves on surfaces. The method is based on the observation that for geodesics the Darboux frame and the Frenet–Serret frame are locally equal up to a constant rotation around the tangent. It computes derivatives of arbitrary order from the result of the numerical method employed for computing the geodesic. Since it does not rely on finite difference approximations, no additional discretization errors are introduced. Applications of the method include motion planning of autonomous vehicles and geometric modeling with developable surfaces.

本文言語English
論文番号103082
ジャーナルCAD Computer Aided Design
140
DOI
出版ステータスPublished - 2021 11

ASJC Scopus subject areas

  • コンピュータ サイエンスの応用
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 産業および生産工学

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