G 2 Planar Cubic Transition Between Two Circles

Abstract

Meek and Walton [2] have examined the shapes of G 2 planar single cubic transition S- and C-shaped curves connecting two circles. We show that use of another parameter makes their analysis more complete and easier to read. We presented a very short algorithm with less restrictive ratio of the larger to the smaller radii of the given circular arcs. It is more comfortable for practical applications. Our compact algorithm also guarantee the absence of interior curvature extrema for an S-shaped transition curve and one curvature extrema for C-shaped transition curve. Transition curves of monotonically increasing or decreasing curvature between circles also play an important role in the design of highways and railways.