Nonparametric Bézier Representation of Polynomial Transition Curves
Publication: Journal of Surveying Engineering
Volume 144, Issue 2
Abstract
In a series of papers in this journal, polynomial solutions of transition curves are introduced for road design, constructed as graphs of polynomial functions. These curves admit a simple expression in nonparametric Bézier form, which facilitates their implementation into commercial software and data exchange. Furthermore, in this Bézier representation, few compact formulas describe all possible cases, and the boundary conditions defining the curves translate into intuitive geometric arrangements of the control points. This is illustrated with several examples, including cases where, at the endpoints, zero curvature and smoothness of the curvature diagram are required. The authors also consider an alternative using a nonparametric B-spline curve of lower degree, but at the cost of a more complex model. Quartic splines, at a minimum, are required to ensure a continuous change of lateral acceleration along the transition.
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Acknowledgments
This research was supported by the Spanish Ministerio de Economía y Competitividad (Plan Nacional de I + D + i), under Research Grant DPI2015-65472-R, cofinanced by the European Regional Development Fund (ERDF). The authors are grateful to a reviewer for suggestions, which improved the quality of this article.
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Published In
Journal of Surveying Engineering
Volume 144 • Issue 2 • May 2018
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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, http://creativecommons.org/licenses/by/4.0/.
History
Received: Jun 14, 2017
Accepted: Nov 28, 2017
Published online: Jan 24, 2018
Published in print: May 1, 2018
Discussion open until: Jun 24, 2018
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