New generalized blended trigonometric Bézier curves with one shape parameter

Abstract

This paper introduces a new basis for generalized blended trigonometric (GBT) B?zier curves along with one shape parameter. The recursive technique is adopted to formulate the basis for higher order GBT-B?zier curves. The curves are better approximated using the proposed basis than the traditional Bernstein basis. New basis functions and curves satisfy all the properties followed by classical B?zier curves. The shape of these curves can be adjusted by changing the values of the parameter, keeping the control polygon unchanged. This adds to the flexibility of new GBT-B?zier curves. Appropriate conditions for parametric (C0,C1,C2 and C3) and geometric (G0, G1, G2 and G3) continuities to compose two or more GBT-B?zier curves have been worked upon. Applications of the proposed GBT-B?zier curves are discussed with different formations.