A new four-point binary subdivision scheme with convexity preservation
Subdivision method has become a powerful tool to create curves and surfaces geometric modeling because of its efficiency and simplicity.In order to enrich the methods of curve and surface modeling,a new four-point binary approximating subdivision scheme with a parameter is proposed through quadratic combination.By choice of appropriate parameters,some ex-isting subdivision schemes such as the cubic B-spline scheme,the quartic B-spline scheme and the quintic B-spline scheme can be obtained,as well as some new approximating subdivision schemes.It is shown that the result curves are different continuity with different parameters.The range of the parameter for the property of convexity preservation of the limiting curves is also pro-vided.Experimental results demonstrate the efficiency and flexibility of the scheme.