An arc spline approximation to a clothoid

  • Authors:

  • D. S. Meek;D. J. Walton

  • Affiliations:

  • Department of Computer Science, University of Manitoba, Winnipeg, Canada, R3T 2N2;Department of Computer Science, University of Manitoba, Winnipeg, Canada, R3T 2N2

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2004

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Abstract

The clothoid is a spiral used in highway and railway route design. Clothoids are transcendental functions and so have been approximated by polynomials, by power series and continued fractions, and by rational functions. Here the clothoid is approximated by an arc spline. The chief advantage in doing so is that arc splines are very easy to lay out and to offset. Examples show that the approximation is of extremely high accuracy. It is proved that if the arc spline has n arcs, then the error in the approximation is of order O(1/n2).