Admissible regions for rational cubic spirals matching G2 Hermite data

This paper finds reachable regions for a single segment of parametric rational cubic Bezier spiral matching G^2 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.

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