G2 Transition curve using Quartic Bezier Curve

TL;DR

This paper introduces a novel method for constructing transition curves using quartic Bezier spirals, enhancing flexibility and approximation accuracy for S-shape and C-shape contact curves between circles.

Contribution

It presents a new family of quartic Bezier spiral curves with increased degrees of freedom, simplifying construction and extending application scope for transition curves.

Findings

More flexible curve design options.

Simplified construction process.

Extended application area for transition curves.

Abstract

A method to construct transition curves using a family of the quartic Bezier spiral is described. The transition curves discussed are S-shape and C-shape of contact, between two separated circles. A spiral is a curve of monotone increasing or monotone decreasing curvature of one sign. Thus, a spiral cannot have an inflection point or curvature extreme. The family of quartic Bezier spiral form which is introduced has more degrees of freedom and will give a better approximation. It is proved that the methods of constructing transition curves can be simplified by the transformation process and the ratio of two radii has no restriction, which extends the application area, and it gives a family of transition curves that allow more flexible curve designs.