Five-point Subdivison Scheme With Two Parameters

Subdivision allows to generate smooth curves and surface by applying simplerefinement rules to the given control polygon and control mesh. Subdivisionmethod can greatly improve the speed of calculation, generation and display ofcurve and surface. In recent years, with the prevalence and progressively broadapplication of computer technology, subdivision scheme has become a focus ofstudy in computer aided geometric design and computer graphics. After reviewingthe general situation and history of subdivision, the author introduces the theoryinvolved in the study of curve subdivision. At the same time, we introduce a4-pointbinary subdivision of Dyn and4-point ternary subdivision of Hassan.This thesis extends the4-point interpolating subdivision scheme of Hassan,and presents a five point interpolating ternary subdivision scheme with twoparametersω,μ. The sufficient conditions of the uniform convergence propertyandC~Kcontinuity properties of the five-point ternary subdivision scheme with twoparameters were proved. By adjusting these two parametersω,μappropriately,this subdivision curve can satisfy the uniform convergence property, andC~1orC~2continuity property. Using the presented scheme, one can model not only smoothinterpolating subdivision curves, but also the fractal curves. Some examples of thecurve design were given to show the efficiency of the proposed subdivision scheme.