The method offers a free choice of a tangent direction, two derivatives, and a curvature at each interpolation point. This flexibility can be achieved by constructing two cubic seoments for each adjacent pair of vertices. The method is also compared with other local schemes for curve construction.
procedural interpolation, cubic splines, curvature continuity
In Reference 1, a procedural method has been introduced for the construction of Gl-continuous interpolating splines with local and global shape parameters. However, it is often very important to have not only tangentdirection continuity, but continuity of curvature (G z) as well. The authors' aim is to build a natural G 2 extension of that method, and, at the same time, to maintain pleasing behavior, simple B6zier representation, and freedom of selection of various shape parameters.
Many techniques for constructing curvature-continuous splines have been proposed 2-4. In a recent development, quintic splines with shape parameters were introduced 5,6. Indeed, quintic B6zier curves are well suited for G 2 local interpolation, because the first and the last inner control points can be used to define derivatives, while the inner pair of control points defines (indirectly) the curvatures at the vertices. For cubic B6zier curves, however, the curvature at the end of the segment depends on both interior control points. Therefore, it is impossible to achieve G 2 continuity without sacrificing the freedom of choosing the Bbzier points. An interesting compromise, proposed by de Boor et al. 7, allows a free choice of the