Interpolating splines of biarcs from a sequence of planar points

An algorithm for the numerical computation of a spline of biarcs that interpolates a given set of ordered planar points is presented. Biarcs are G1 curves composed of two arcs of circle that may degenerate to line segments. The tangents at each point are free variables, which are optimised to minimise three different targets, namely: the total length of the spline, the integral of the absolute value of the curvature, the integral of the square of the curvature. Indeed other targets are possible. Conditions for the existence of the spline are given in terms of admissible point sequences and numerical experiments validate the proposed method.