Shape Control of Cubic H-Bezier Curve by Moving Control Point ?

This paper considers the shape control of the cubic H-Bezier curve, which can represent hyperbolas and catenaries accurately. We flx all the control points while let one vary. The locus of the moving control point that yields a cusp on the cubic H-Bezier curve is a planar curve; The tangent surface of the planar curve is the locus of the positions of the moving control point that yield in∞ection points. The positions of the moving control point that yield a loop lie on a plane. We provide the comparison on the singularity of cubic Bezier, cubic rational Bezier, C-Bezier and H-Bezier curves. The approach and results may have signiflcant application in shape classiflcation and control of parametric curves.