Abstract
This paper presents a variant scheme of the cubic exponential B-spline scheme, which, with two parameters, can generate curves with different shapes. This variant scheme is obtained based on the iteration from the generation of exponentials and a suitably chosen function. For such a scheme, we show its C2-convergence and analyze the effect of the parameters on the shape of the generated curves and also discuss its convexity preservation. In addition, a non-uniform version of this variant scheme is derived in order to locally control the shape of the generated curves. Numerical examples are given to illustrate the performance of the new schemes in this paper.
Highlights
Subdivision can be used as an effetive tool to generate smooth curves/surfaces starting from a given set of initial control points
The interpolatory ones are usually more powerful than the approximating ones in controlling the shape of the limit curves while the approximating ones can have higher smoothness order than the interpolatory ones. Besides such non-stationary subdivision, there is another kind of non-stationary schemes, which can be seen as obtained based on some fixed point iteration
This paper presented a variant cubic exponential B-spline scheme, which can generate curves with different shapes, including the conics
Summary
Subdivision can be used as an effetive tool to generate smooth curves/surfaces starting from a given set of initial control points. The interpolatory ones are usually more powerful than the approximating ones in controlling the shape of the limit curves while the approximating ones can have higher smoothness order than the interpolatory ones Besides such non-stationary subdivision, there is another kind of non-stationary schemes, which can be seen as obtained based on some fixed point iteration. Compared with the ones obtained in the view of generating exponentials, the approximating ones based on iterations can be as powerful as the interpolatory ones in controlling the shape of the limit curves without reducing the smoothness order.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
