Interpolation with minimal-energy splines

Abstract The problem of interpolating a sequence of points in the plane with a nonlinear spline curve of minimal energy and prescribed tangents in the endpoints is addressed. The method presented is based on the idea of representing the interpolant as a curve of a piecewise polynomial curvature function. The algorithm to determine the interpolant involves a table lookup to speed up the computation of the relevant parameters, and an optimization to minimize curvature discontinuities in the curve.