Planar Curve Interpolation by Piecewise Conics of Arbitrary Type

: Five points in general position in IR 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 in IR 2 , if they can be interpolated at all by a smooth curve with nonvanishing curvature, will have a unique GC 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 O(h 5 ), where h is the maximal distance of adjacent data points f(t i ) 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. Keywords: Geometric rational curve interpolation, shape preservation, convexity, parametric splines, conics, approximat..