Approximating Cornu spirals by arc splines

While modeling planar parametric curves, it is desirable to approximate them efficiently by arc splines with fewest segments within the prescribed tolerance. Planar arc splines are ideal for describing the path of a numerically controlled cutting machine because they are easy to offset. In this paper, we derive a vector solution to interpolate a G1-continuous biarc curve between a given pair of points with specified start, joint and end tangents. Using this solution as the underlying idea, we present an efficient algorithm for approximating a Cornu spiral with a sequence of arcs within the prescribed maximum deviation. The method is simple and generic and can be applied to other types of planar parametric curves as well.