Planar G2 transition curves composed of cubic Bézier spiral segments

Authors:
D. J. Walton;D. S. Meek;J. M. Ali
Affiliations:
Department of Computer Science and St. Paul's College, University of Manitoba, 70 Dysart Road, Winnipeg, Manitoba, Canada R3T 2M6;Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2;School of Mathematical Sciences, The University of Science Malaysia, 11800 Minden, Penang, Malaysia
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

In curve and surface design it is often desirable to have a planar transition curve, composed of at most two spiral segments, between two circles. The purpose may be practical, e.g., in highway design, or aesthetic. Cubic Bézier curves are commonly used in curve and surface design because they are of low degree, are easily evaluated, and allow inflection points. This paper generalizes earlier results on planar cubic Bézier spiral segments which were proposed as transition curve elements, and examines techniques for curve design using the new results.