Bézier Curve With A Shape Parameter And Error Estimate For Doo-Sabin Subdivision Surface

This paper is organized as following:In chapter 1 we give a brief review of the corresponding background of CAGD and introduce the main contents of the paper.In chapter 2 we firstly introduce the Bézier curve and its properties. And then we define a class of a new blending functions and a class of Bézier curves with shape parameter which make it easly to adjust the shape of curves.In chapter 3 we discuss the problem of the error estimate of Doo-Sabin subdivision surface. In this chapter we firstly introduce Doo-Sabin subdivision surface and give some notational conventions adopted in this chapter.And we secondly prove that the control mesh convergences to the limit surface at an exponential rate and give a fomula of evaluation.By using the convex hull property of Doo-Sabin subdivision surface we give the fomula of the error estimate of Doo-Sabin subdivision surface .