Symplectifying Biarcs

TL;DR

This paper explores a purely geometric approach to biarc construction, introducing a novel method for determining the join point between two circular arcs given points and tangents.

Contribution

It presents a new geometric method for defining the join point in biarc curves, expanding the existing approaches in biarc geometry.

Findings

Introduces a novel geometric approach for biarc join point determination.

Provides a comprehensive analysis of biarc construction from a geometric perspective.

Enhances the understanding of biarc curve flexibility and design options.

Abstract

In this follow-up article to Symplectification of Circular Arcs and Arc Splines, biarc geometry is examined from a purely geometric point of view. Two given points together with their associated tangent vectors in the plane are sufficient to define two directed, consecutive circular arcs. However, there remains one degree of freedom to determine the join point of both arcs. There are various approaches to this in the literature. A novel one is presented here.