Planar G~2 Hermite interpolation with some fair, C-shaped curves

摘要

G~2 Hermite data consists of two points, two unit tangent vectors, and two signed curvatures at those points. The planar G~2 Hermite interpolation problem is to find a planar curve matching planar G~2 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 are and a conic in a G~2 manner. A curve of this type that matches given G~2 Hermite data can be found by solving a quadratic equation. The new curve is compared to the cubic Bezier curve and to a curve made from a G~2 join of a pair of quadratics. The new curve covers a much larger range of the G~2 Hermite data that can be matched by a C-shaped curve of one or two spirals than those curves cover.