Clothoid spline transition spirals

Meek, D. S.; Walton, D. J.

doi:10.1090/S0025-5718-1992-1134736-8

Clothoid spline transition spirals

Authors: D. S. Meek and D. J. Walton
Journal: Math. Comp. 59 (1992), 117-133
MSC: Primary 65D07; Secondary 41A15
DOI: https://doi.org/10.1090/S0025-5718-1992-1134736-8
MathSciNet review: 1134736
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Abstract: Highway and railway designers use clothoid splines (planar ${G^2}$ curves consisting of straight line segments, circular arcs, and clothoid segments) as center lines in route location. This paper considers the problem of finding a clothoid spline transition spiral which joins two given points and matches given curvatures and unit tangents at the two points. Conditions are given for the existence and uniqueness of the clothoid spline transition spirals, and algorithms for finding them are outlined.

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