Quintic trigonometric Bézier curve with two shape parameters

Abstract

The fifth degree of trigonometric Bézier curve called quintic with two shapes parameter is presented in this paper. Shape parameters provide more control on the shape of the curve compared to the ordinary Bézier curve. This technique is one of the crucial parts in constructing curves and surfaces because the presence of shape parameters will allow the curve to be more flexible without changing its control points. Furthermore, by changing the value of shape parameters, the curve still preserves its geometrical features thus makes it more convenient rather than altering the control points. But, to interpolate curves from one point to another or surface patches, we need to satisfy certain continuity constraints to ensure the smoothness not just parametrically but also geometrically.