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

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 curved 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 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 scan be matched by a C-shaped curve of one or two spirals than those curves cover. (C) 2002 Elsevier Science B.V. All rights reserved.