Point-tangent/point-normal B-spline curve interpolation by geometric algorithms

Shu ichi Gofuku, Shigefumi Tamura, Takashi Maekawa

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

We introduce a novel method to interpolate a set of data points as well as unit tangent vectors or unit normal vectors at the data points by means of a B-spline curve interpolation technique using geometric algorithms. The advantages of our algorithm are that it has a compact representation, it does not require the magnitudes of the tangent vectors or normal vectors, and it has C2 continuity. We compare our method with the conventional curve interpolation methods, namely, the standard point interpolation method, the method introduced by Piegl and Tiller, which interpolates points as well as the first derivatives at every point, and the piecewise cubic Hermite interpolation method. Examples are provided to demonstrate the effectiveness of the proposed algorithms.

Original languageEnglish
Pages (from-to)412-422
Number of pages11
JournalCAD Computer Aided Design
Volume41
Issue number6
DOIs
Publication statusPublished - 2009 Jun 1
Externally publishedYes

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Splines
Interpolation
Derivatives

Keywords

  • B-spline curve
  • Geometric algorithm
  • Interpolation
  • Point-normal interpolation
  • Point-tangent interpolation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

Cite this

Point-tangent/point-normal B-spline curve interpolation by geometric algorithms. / Gofuku, Shu ichi; Tamura, Shigefumi; Maekawa, Takashi.

In: CAD Computer Aided Design, Vol. 41, No. 6, 01.06.2009, p. 412-422.

Research output: Contribution to journalArticle

Gofuku, Shu ichi ; Tamura, Shigefumi ; Maekawa, Takashi. / Point-tangent/point-normal B-spline curve interpolation by geometric algorithms. In: CAD Computer Aided Design. 2009 ; Vol. 41, No. 6. pp. 412-422.
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