Differential geometry properties of lines of curvature of parametric surfaces and their visualization

Han Kyul Joo, Tatsuya Yazaki, Masahito Takezawa, Takashi Maekawa

研究成果: Article査読

8 被引用数 (Scopus)

抄録

We present algorithms for computing the differential geometry properties of lines of curvature of parametric surfaces. We derive a unit tangent vector, curvature vector, binormal vector, torsion, and algorithms to evaluate their higher-order derivatives of lines of curvature of parametric surfaces. Among these quantities, it is shown that the curvature and its first derivative of the lines of curvature lend a hand for the formation of curved plates in shipbuilding. We also visualize the twist of lines of curvature, which enables us to observe how much the osculating plane of the line of curvature turns about the tangent vector.

本文言語English
ページ(範囲)224-238
ページ数15
ジャーナルGraphical Models
76
4
DOI
出版ステータスPublished - 2014 7
外部発表はい

ASJC Scopus subject areas

  • ソフトウェア
  • モデリングとシミュレーション
  • 幾何学とトポロジー
  • 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

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