A controlled clothoid spline

A clothoid has the property that its curvature varies linearly with arclength. This is a useful feature for the path of a vehicle whose turning radius is controlled as a linear function of the distance travelled. Highways, railways and the paths of car-like robots may be composed of straight line segments, clothoid segments and circular arcs. Control polylines are used in computer aided design and computer aided geometric design applications to guide composite curves during the design phase. This article examines the use of a control polyline to guide a curve composed of segments of clothoids, straight lines, and circular arcs.