Approximation of Curves by a Measure of Shape

摘要

Based on the support function, a well-known tool in the theory of convex sets, a new measure of a "distance" between two planar parametric curves is introduced and its main properties are established. The measure is invariant under affine transformations and depends not only on the position vectors but Also on the tangent vectors of the curves. An algorithm to compute the optimal Bezier approximant to A given curve is derived.