Subdivision Curves And Surfaces Of Two-parameter Constructor Study

Subdivide Scheme is a very important method of computer aided geometric design ,is a method for discrete modelling of curves and surfaces, is a method ofgenereting curves and surfaces or other geometric figure directly by computer based on initial datas .With the development of computer graphics and geometric modeling, subdivide scheme has been widely and deeply studied ,at present ,many subdivide schemes have appeared such as Chaikin method,4-point interpolatory subdivision scheme,de Boor method and Catmull-Clark skill.Based on these subdivide schemes ,this thesis studies a new class of two-parameters subdivision surfaces and subdivision curves.The two-parameters subdivision curves. Interpolatory subdivision curves and approximation subdivision curves are discussed in the two-parameters subdivision curves. A new algorithm to design adjustable subdivision curves using two control parameters is presented in the two subdivision scheme. A kind of subdivision curves can be constructed by changing one of the parameters. Meanwhile , the shapes of the subdivision curves can be adjusted by using the another control parameter. The convergence and continuity of the subdivision scheme are analyzed. Some examples of the curve design are given to demonstrate the freedom and efficiency of the algorithm. The two-parameters subdivision surfaces. A new algorithm to design adjustable subdivision surfaces using two control parameters is presented in this paper. A kind of subdivision surfaces can be constructed by changing one of the parameters. Meanwhile , the shapes of the subdivision surfaces can be adjusted by using the another control parameter.Some wxamples of the curve design are given to demonstrate the freedom and efficiency of the algorithm.