A smooth, obstacle-avoiding curve

An algorithm for finding a smooth, obstacle-avoiding curve in the plane can be quite complicated. The process usually involves finding one or more feasible polyline paths, choosing a desirable path (for example the shortest path), and smoothing the polyline path to give a curve that avoids the obstacles. This paper is concerned with the last stage in the process; it assumes the existence of an obstacle-avoiding polyline path. A method is given to replace that polyline path by a G2 cubic spline curve that also avoids the obstacles. The advantages of this method are the simplicity of the smooth, obstacle-avoiding curve, and the simplicity of the algorithm that finds the obstacle-avoiding curve.