Interpolation of two-dimensional curves with Euler spirals

Abstract

We propose an algorithm for the interpolation of two-dimensional curves using Euler spirals. The method uses a lower order reconstruction to approximate solution derivatives at each sample point. The computed tangents are then used to connect consecutive points with segments of Euler spirals. The resulting interpolation is G1 in regions where the curve being interpolated is smooth. The algorithm uses an adaptive stencil which allows it to construct an approximation free of oscillations near discontinuities in the function or its derivatives. The approximation is based on geometrical shapes which makes it particularly suitable for two-dimensional curves.