Shape analysis of cubic trigonometric Bézier curves with a shape parameter

Abstract For the cubic trigonometric polynomial curves with a shape parameter (TB curves, for short), the effects of the shape parameter on the TB curve are made clear, the shape features of the TB curve are analyzed. The necessary and sufficient conditions are derived for these curves having single or double inflection points, a loop or a cusp, or be locally or globally convex. The results are summarized in a shape diagram of TB curves, which is useful when using TB curves for curve and surface modeling. Furthermore the influences of shape parameter on the shape diagram and the ability for adjusting the shape of the curve are shown by graph examples, respectively.