Curvature bounds for planar B-spline curve segments (Q1114317)

The authors discuss the introduction of a piecewise bound on the curvature of a planar cubic B-spline curve segment, which has its extreme values at the zeros of a quintic polynomial. The largest extreme value and its location is found computationally by repeated subdivision of the Bézier representation of the B-spline curve segment. An algorithm (in Pascal on MacIntosh Plus PC) to determine an upper bound of planar cubic B-spline curve segment is presented. In several examples the developed algorithm with a method based on a simple linear search of discrete values of the curvature function on a uniform partition of the curve parameter is assessed. It is illustrated that the developed method is to be preferred.