具有保凸性的三点二重逼近细分格式

A New Three-Point Binary Approximating Subdivision Scheme with Convexity Preservation

为丰富细分曲线曲面造型方法,构造一种新的带参数的三点二重逼近细分格式。研究该细分格式的连续性,并利用Dyn提出的生成多项式方法给出该格式具有一致连续性和各阶连续性时相应的参数取值范围。研究该细分格式的保凸性,给出生成极限曲线具有保凸性时参数的取值范围。数值实例表明,参数的取值对于生成的极限曲线的连续性具有重要的影响,所提出的细分格式是合理有效的。

In order to enrich the modeling methods of subdivision curves and surfaces,a new three-point binary approximating subdivision scheme with a parameter is constructed.The continuity of the subdivision scheme is studied and the corresponding parameter ranges are given when the scheme has uniform continuity and each order continuity by using the generating polynomial method proposed by Dyn.At the same time,the convexity preservation of the subdivision scheme is studied.The range of the parameter for the property of convexity preservation of the limiting curves is also provided.Numerical examples show that the values of parameters have an important effect on the continuity of the generated limit curve,and the proposed subdivision scheme is reasonable and effective.