An Improvement Subdivision Schemes For Subdivision Curve

Computer Aided Geometric Design is one of the important areas of aercomputerapplications. Subdivision is one of the basic methods for Computer Aided Geometric Design,as well as subdivision is one important technology in curves and surfaces modeling.Subdivision has been widely used in Computer Aided Geometric Design and ComputerGraphics.A class of subdivision schemes with a improved cut angle method is discussed inthis Thesis, Constructed in the subdivision with the format in the geometric meaning of theparameters, the parameters can effectively control, regulate the limit shape of the curve, thecurve increased the freedom of design, make up one-parameter sub-limit curve shape formatdisadvantage of lack of control; And in this thesis we also based on the introduction of thismethod tensor parameters, proposed to reproduce conic subdivision.This thesis is structuredas follows:Firstly, We has outlined the importance of segmentation methodsAnd this paper are alsointroduced some important approximation subdivision, interpolation subdivision scheme, andsome new methods. Also on the reproduce of existing conic subdivision methods aresummarizedSecondly, We improves based on the format original two-parameter subdivision, and geta new subdivision format.The two parameters of this subdivision format are greater range on[0,1].Thus, geometric meaning of parameters is not only more obvious, but also increasedcurve of degree of freedom. These papers also study the convergence of the format of thissubdivision, summed up the importance of the geometric nature of the limit curve. And usethis method to construct the shapes of the curves.Finally, We introduce tensor parameters based on the improved the format and propose asubdivision method of reproduce conic. This method not only to maintain the convergence oforiginal format and the geometric properties of the limit curve, while able to reproduceconic.At last, we use this method by selecting the appropriate parameters and the initialpolygon to reproduce circle, ellipse, parabola, hyperbola, respectively.