The cubic trigonometric Bézier curve with two shape parameters

Abstract A cubic trigonometric Bezier curve analogous to the cubic Bezier curve, with two shape parameters, is presented in this work. The shape of the curve can be adjusted by altering the values of shape parameters while the control polygon is kept unchanged. With the shape parameters, the cubic trigonometric Bezier curves can be made close to the cubic Bezier curves or closer to the given control polygon than the cubic Bezier curves. The ellipses can be represented exactly using cubic trigonometric Bezier curves.