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

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)224-238
Number of pages15
JournalGraphical Models
Volume76
Issue number4
DOIs
Publication statusPublished - 2014 Jan 1
Externally publishedYes

Fingerprint

Property of line
Parametric Surfaces
Differential Geometry
Visualization
Curvature
Geometry
Derivatives
Line
Shipbuilding
Binormal vector
Torsional stress
Unit tangent vector
Tangent vector
Higher order derivative
Twist
Torsion
Derivative
Computing
Evaluate

Keywords

  • Curvature
  • Line heating
  • Lines of curvature
  • Plate development
  • Torsion

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation
  • Geometry and Topology
  • Computer Graphics and Computer-Aided Design

Cite this

Differential geometry properties of lines of curvature of parametric surfaces and their visualization. / Joo, Han Kyul; Yazaki, Tatsuya; Takezawa, Masahito; Maekawa, Takashi.

In: Graphical Models, Vol. 76, No. 4, 01.01.2014, p. 224-238.

Research output: Contribution to journalArticle

Joo, Han Kyul ; Yazaki, Tatsuya ; Takezawa, Masahito ; Maekawa, Takashi. / Differential geometry properties of lines of curvature of parametric surfaces and their visualization. In: Graphical Models. 2014 ; Vol. 76, No. 4. pp. 224-238.
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