Planar G2 Hermite interpolation with some fair, C-shaped curves

摘要

G2 Hermite data consists of two points, two unit tangent vectors at those points, and two signed curvatures at those points. The planar G2 Hermite interpolation problem is to find a planar curve matching planar G2 Hermite data. In this paper, a C-shaped interpolating curve made of one or two spirals is sought. Such a curve is considered fair because it comprises a small number of spirals. The C-shaped curve used here is made by joining a circular arc and a conic in a G2 manner. A curve of this type that matches given G2 Hermite data can be found by solving a quadratic equation. The new curve is compared to the cubic Bézier curve and to a curve made from a G2 join of a pair of quadratics. The new curve covers a much larger range of the G2 Hermite data that can be matched by a C-shaped curve of one or two spirals than those curves cover.