Smoothing an arc spline

Are splines are G(1) continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an are spline is known and controlled at all but a finite number of points, and that the offset curve of an are spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which to cut and are used by highway route planners as a natural curve along which to plan the centre line of a road. In this paper, it is shown how to increase the smoothness of a planar arc spline by replacing parts of it and thus to create a G(2) continuous curve. The replacement parts are low-degree NURBS curves: cubic B ezier curves and quadratic rational Bezier curves. (c) 2005 Elsevier Ltd. All rights reserved.