Admissible regions for rational cubic spirals matching G2G2 Hermite data

This paper finds reachable regions for a single segment of parametric rational cubic Bézier spiral matching G2G2 Hermite data. First we derive spiral conditions for rational cubics and then we use a free parameter to find the admissible region for a spiral segment with respect to the curvatures at its endpoints under the fixed positional and tangential end conditions. Spirals are curves of constant sign monotone curvature and therefore have the advantage that the minimum and maximum curvatures are at their endpoints only.

Research highlights
► Admissible regions for the spiral segments matching G2G2 Hermite conditions are derived.
► Use of a single free parameter in our method rather than two has a benefit because the designers have fewer entities to deal with.
► Our method is stable and there is no fear of spiking phenomenon of non-monotone curvature.