The Clothoid Computation: A Simple and Efficient Numerical Algorithm
This article has been corrected.
VIEW CORRECTIONPublication: Journal of Surveying Engineering
Volume 142, Issue 3
Abstract
The clothoid (also known as Cornu spiral or Euler spiral) is a curve that is characterized by its curvature being proportional to its length. This property makes it very useful as a transition curve when designing the layout of roads and railway tracks. This paper presents an analysis of two methods for computing the clothoid: the classical method, which is based on the use of explicit formulas obtained from Taylor expansions of sine and cosine functions, and an alternative algorithm, which is based on the numerical solution of the initial value problems giving the clothoid parametrization. This alternative method is simple and efficient, and its effectiveness is shown through its application to three classical problems of horizontal road alignment.
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Acknowledgments
The authors thank the anonymous reviewers for their helpful comments and Associate Professor Jaime Rodríguez Pereña for his suggestions. The first author also thanks the support given by Project MTM2012-30842 of M.E.C. (Spain) and FEDER.
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Published In
Journal of Surveying Engineering
Volume 142 • Issue 3 • August 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Sep 21, 2015
Accepted: Dec 3, 2015
Published online: Feb 1, 2016
Discussion open until: Jul 1, 2016
Published in print: Aug 1, 2016
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