Approximation of logarithmic spirals

Christoph Baumgarten; Gerald Farin

doi:10.1016/S0167-8396(96)00043-X

Approximation of logarithmic spirals

Christoph Baumgarten, Gerald Farin

Computing and Augmented Intelligence, School of (IAFSE-SCAI)

Research output: Contribution to journal › Article › peer-review

26 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 language	English (US)
Pages (from-to)	515-532
Number of pages	18
Journal	Computer Aided Geometric Design
Volume	14
Issue number	6
DOIs	https://doi.org/10.1016/S0167-8396(96)00043-X
State	Published - 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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10.1016/S0167-8396(96)00043-X

Cite this

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title = "Approximation of logarithmic spirals",

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.",

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AB - 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.

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KW - Logarithmic spirals

KW - Rational cubic spline curves

KW - Shape optimization

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Approximation of logarithmic spirals

Abstract

Keywords

ASJC Scopus subject areas

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