New Generalized Blended Trigonometric B\'{e}zier curves with one shape parameter

Abstract

In this paper, new basis for generalized blended trigonometric (GBT) B\'{e}zier curves has been introduced along with one shape parameter. Recursive technique is adopted to formulate basis for higher order GBT B\'{e}zier curves. The curves are better approximated by using the proposed basis as compared to the traditional Bernstein basis. New basis functions and curves satisfy all the properties followed by classical B\'{e}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\'{e}zier curves. Appropriate conditions for parametric ($C^{0}, C^{1}, C^{2}$ and $C^{3}$) and geometric ($G^{0}$, $G^{1}$, $G^{2}$ and $G^{3}$) continuities to compose two or more GBT B\'{e}zier curves have been worked upon. Applications of the proposed GBT B\'{e}zier curves are discussed with different formations.