A natural question that arises is whether it is possible
to find a better path, with fewer discontinuities in the curva-
ture, using the guidance of these control points (or polygon).
More precisely, we first partition the path at any cusps, into
forward and reverse segments, and process each segment
separately. Actually, it is convenient to reverse the state-
ment and ask a more general question: given this control
polygon, is it possible to get a collision free path with better
curvature (by better, we mean bigger and/or more continu-
ous curvature)?