Fair Path Planning with a Single Cubic Spiral Segment

Spirals are curves of monotone curvature with constant sign and therefore such curves are free from singularities (loops, cusps), inflection points, and local curvature extrema. These properties make the study of spiral segments an interesting problem both in practical and aesthetic applications. An important issue in this paper is to design spiral transitions preserving G² Hermite conditions. This paper aims to improve the existing methods of a C-shaped transition between two circles with a single cubic spiral segment.