A note on finding clothoids

Authors:
D. S. Meek;D. J. Walton
Affiliations:
Department of Computer Science, University of Manitoba, Winnipeg, Man., Canada R3T 2N2;Department of Computer Science, University of Manitoba, Winnipeg, Man., Canada R3T 2N2
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

The clothoid is a spiral that is used as transition curve in highway and railway route design. Although its defining formulas are transcendental functions, recent work has shown that it can be used fairly easily on small computers. A single nonlinear equation must be solved in each of four common arrangements of the clothoid. The purpose of this work is to give starting intervals for which Newton's root finding method applied to those equations is guaranteed to converge.