Shape modelling by Bézier-type cubic trigonometric curves with a shape parameter over the space Ω = span {1, sin ݐ, cos ݐ, sinଶ cosଶ ,ݐ sinଷ ,ݐ cosଷ ,ݐ ݐ {is studied in this paper and the corresponding cubic trigonometric Bézier surfaces are defined. These curves not only inherit most properties of the usual cubic Bézier curves with the Bernstein basis in the polynomial space, but also enjoy some other advantageous properties for shape modelling. The shape parameter provides freedom in terms of design and shape control of the curve. Thus we can construct smooth curves of almost any shape. The shape of the curve can be adjusted by altering the values of shape parameter while the control polygon is kept unchanged. These curves can be used as an efficient model for geometric design in the fields of CAGD.
