Observations About Joined Circular Arcs

摘要

There is interest in interpolating and approximating strings of points in theplane by piecewise-circular smooth curves because that representation lends itself readily to some computer-automated manufacturing processes. In particular, when interpolating a string of given consecutively distinct planar points, it is commonly assumed that these points are also the 'knots' of the interpolating piecewise-circular curve, that is, the points at which successive circular arcs connect. If an initial direction is specified, such interpolating curves are uniquely determined by the string of points. This interpolation problem becomes overdetermined, however, if directions are prescribed at all points of the string. In that case, pairs of circular arcs joined together smoothly at some