Abstract: The shape features of a class of Bézier curve with two shape parameters are analyzed by
using the method based on the theory of envelope and topological mapping. Investigate effects of the
shape parameter on the curve shape. Necessary and sufficient conditions are derived for this curve
having one or two inflection points, a loop or a cusp, or be locally or globally convex. Those conditions
are completely characterized by the relative position of the edge vectors of the control polygon.
Furthermore we discussed the influences of shape parameter on the shape diagram and the ability for
adjusting the shape of the curve.

Key words: Bézier curve, singular points, inflection points, curve shape, shape parameter