Abstract
G 2 Hermite data consists of two points, two unit tangent vectors at those points, 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 arc 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 Bézier 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.
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