Smoothing Arc Splines by Cubic Curves

Abstract

Arc splines are planar, tangent continuous, piecewise curves made of circular arcs and straight line segments. They are important in manufacturing industries because of their use in the cutting paths for numerically controlled cutting machinery, highway route and robot paths. This paper considers how to smooth three kinds of G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> biarc models: the C-, S-, and J-shaped, by replacing their parts by a single G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> cubic Bezier function. All kinds of transition curves have just one inflection point in their curvature. Use of a single curve rather than two functions has the benefit because designers and implementers have fewer entities to be concerned.