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

This paper considers the shape control of the cubic H-Bézier curve, which can represent hyperbolas and catenaries accurately. We fix all the control points while let one vary. The locus of the moving control point that yields a cusp on the cubic H-Bézier 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 inflection 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 Bézier, cubic rational Bézier, C-Bézier and H-Bézier curves. The approach and results may have significant application in shape classification and control of parametric curves.