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Zbl 0756.65005
Meek, D.S.; Walton, D.J.
Clothoid spline transition spirals. (English)
[J] Math. Comput. 59, No.199, 117-133 (1992). ISSN 0025-5718; ISSN 1088-6842/e

A piecewise defined planar curve, consisting of straight line segments, circular arcs and clothoid segments, which is twice continuously differentiable with respect to arc length is called a clothoid spline, as circles and straight lines can be considered limiting forms of clothoids [see {\it E. Mehlum}, Non-linear splines in Computer Aided Geometric Design, Eds. R. E. Barnhill and R. F. Riesenfield, Academic Press, New York, 173-207 (1974)]. Such splines are used in the route design of the centre lines of highways and railways [see {\it K. G. Baass}, Transportation Forum 1, 47-52 (1984)].\par The authors study the problem of finding a clothoid spline transition spiral which joins two given points and matches given curvature 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 [cf. {\it D. S. Meek} and {\it R. S. D. Thomas}, Comput. Aided Geom. Des. 8, No. 2, 163-174 (1991)].
[H.P.Dikshit (Jabalpur)]

MSC 2000:: *65D05 Interpolation (numerical methods)
65D07 Splines (numerical methods)
41A15 Spline approximation
65D17 Computer aided design (modeling of curves and surfaces)
41A05 Interpolation

Keywords: clothoid spline; centre lines of highways and railways; clothoid spline transition spiral; algorithms

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