Fast Detection of the Geometric Form of Two-Dimensional Cubic Bezier Curves

摘要

This paper presents an algorithm that determines, from the control points of a cubic two-dimensional Bezier curve, the geometric form of the curve (arch, single inflection, two inflections, cusp, loop, or the degenerate forms straight line or point). The algorithm is based on a case analysis of the signs of the determinants of the control-point triples. Source code is available on the web site listed at the end of this paper.