A Generalized Cubic Exponential B-Spline Scheme with Shape Control

Abstract EN

In this paper, a generalized cubic exponential B-spline scheme is presented, which can generate different kinds of curves, including the conics.

Such a scheme is obtained by generalizing the cubic exponential B-spline scheme based on an iteration from the generation of exponential polynomials and a suitable function with two parameters μ and ν.

By changing the values of μ and ν, the sensitivity of the shape of the subdivision curve to the initial control value v0 can be changed and different kinds of curves can then be obtained by adjusting the value of v0.

For this new scheme, we show that, with any admissible choice of μ and ν, it owns the same smoothness order and support as the cubic exponential B-spline scheme.

Besides, based on a different iteration and another suitable function, we construct a similar nonstationary scheme to generate more curves with different shapes and show the role of iterations and suitably chosen functions in the construction and analysis of such schemes.

Several examples are given to illustrate the performance of our new schemes.