Planar curve interpolation by piecewise conics of arbitrary type

Five points in general position inR ² 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 2n+1≥5 of points inR ², if they can be interpolated at all by a smooth curve with nonvanishing curvature, will have a uniqueGC ² 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 ?(h ⁵), whereh is the maximal distance of adjacent data pointsf(t _i ) sampled from a smooth and regular planar curvef with nonvanishing curvature. Two algorithms for the construction of the interpolant are suggested, and some examples are presented.