Construction And Application Of Combined Subdivision Scheme

The subdivision method is a very popular and effective geometric modeling tool.This thesis focuses on the study of subdivision curves,constructs the static fusion type and dynamic fusion type curve subdivision formats,and analyzes the nature of the format.The main research results of this thesis are:The first chapter introduces the research background and significance of the subdivision method in detail.And it makes arrangements for the content and chapters of this thesisThe second chapter is based on the binary B-spline,from the geometric meaning,by adding the offset vector,the double-seven-order B-spline format is modified to obtain the parameterized fusion five-point double fusion type The subdivision format,and found that some existing double subdivision formats are special cases of the format of this chapter,using Laurent polynomial to analyze the Ck continuity of the format of this chapter.Finally,through numerical examples,it can be found that the subdivision method in this chapter can not only generate a limit curve with higher continuity,but also have better shape retention than some existing double subdivision methods.The third Chapter constructs a class of masked asymmetric fusion five-point triple subdivision format,and strictly analyzes the important properties of the fusion subdivision format.Numerical examples show that the format of this chapter can generate a limit curve that is smooth and keeps closer to the initial polygon shape.In the fourth chapter,we construct a dynamic double fusion type subdivision format based on the relationship between the dynamic interpolation subdivision method and the hyperbolic function.Numerical examples show that the conical curve can be generated by the dynamic fusion subdivision method in this chapter.In the fifth chapter,we summarize the full text and looks forward to some work that can be done in the future.