Planar curve interpolation by piecewise conics of arbitrary type.

Five points in general position in R always lie on a unique conic, and three points plus two tangents also have a unique interpolating conic, the type of which depends on the data. These well-known facts from projective geometry are generalized: an odd number 2 n+1≥5 of points in R, if they can be interpolated at all by a smooth curve with nonvanishing curvature, will have a unique GC interpolant consisting of pieces of conics of varying type. This interpolation process reproduces conics of arbitrary type and preserves strict convexity. Under weak additional assumptions its approximation order is ϑ( h), where h is the maximal distance of adjacent data points f(t) sampled from a smooth and regular planar curve f with nonvanishing curvature. Two algorithms for the construction of the interpolant are suggested, and some examples are presented. [ABSTRACT FROM AUTHOR]