On Convergence of the Control Polygons Series of C-Bezier Curves

摘要

The C-Bezier curve is introduced to CAD/CAM to deal with circular arcs, cylinders, and cones. It can precisely represent these conic curves in a Bezier-like way. A conjecture in [Chen and Wang'2003] is that the sequence of control polygons associated with the C-Bezier representation of a curve converges to the curve itself as the curve degree n goes to infinity. In this paper we prove this conjecture.