Shape Analysis of Quartic Bézier Curve with Shape Parameter

To investigate effects of the shape parameter on the curve shape, awe analyzed the shape features of the quartic Bézier curve with shape parameter by using the method based on the theory of envelop and topological mapping．Necessary and sufficient conditions are derived for this curve having one or two inflection points, aa loop or a cusp, aor 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．