Research On Approximate Degree Reduction Of Bezier Curves With Shape Parameter With Constraints Of Geometric Continuity

Firstly, wo briefly expound the development history of Computer AidedGeometric Design and the research background of this paper, especially reviewdetailedly of definition and properties on Bézier curves and Bézier curves withshape parameter,and several main degree reduction methods of Bézier curves.Secondly,we introduce detailedly algorithms for degree reduction withconstraints of geometric continuity Bézier curves,we refer to the existing method ofdegree reduction with C3–continuity with endpoints Bézier curves in L2-norm, givealgorithms for the degree reduction of Bézier curves with G3-continuity inL2-norm,and we correct the reducted curves,then we get more effectivenessreduction curves,This method realizes G3-continuity with endpoints by simple andstable method,and achieves near optimal uniform approximation inL∞-norm.Lastly, in the basis of summary the existing research results on several maindegree reduction methods of Bézier curves,we consider a method about themulti-degree reduction of Bézier curve with shape parameter with G1-continuitywith endpoints. In addition wo conclude the thesis and mention the future work.