Approximation of logarithmic spirals

Christoph Baumgarten, Gerald Farin

Research output: Contribution to journalArticle

25 Scopus citations

Abstract

The radius of curvature of a logarithmic spiral is proportional to its arc length, a property that is desirable for the design of aesthetic curves. We describe a method for approximating logarithmic spiral segments by rational cubic spline curves. This approach provides the tools for the construction of planar spline curves whose curvature radius plot is continuous and close to piecewise linear. A number of examples illustrate the approximation method.

Original languageEnglish (US)
Pages (from-to)515-532
Number of pages18
JournalComputer Aided Geometric Design
Volume14
Issue number6
DOIs
StatePublished - Aug 1997

Keywords

  • Approximation
  • Logarithmic spirals
  • Rational cubic spline curves
  • Shape optimization

ASJC Scopus subject areas

  • Modeling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design

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