Degree Reduction Of Interval And Disk Generalized Ball Curves Of Wang-Said Type

Interval algorithm and disk algorithm have the important applications in the field of curve and surface modeling design, such as intersection calculation of solid modeling design, collision detection of mechanical movement, error detection of industrial product form, etc. In this thesis, we apply interval and disk algorithms to generalized Ball curves of Wang-Said type (WSGB curves), define interval WSGB curves and disk WSGB curves, and discuss the problem of their degree reduction.We use three methods to solve the degree reduction problem of interval WSGB curves, namely, geometric method by control points perturbation directly, best uniform approximation method obtained by Chebyshev polynomial and best uniform approximation method with endpoint interpolation. Toward the problem of degree reduction of disk WSGB curves, we divide it into two steps. First, we use best uniform approximation method obtained by Chebyshev polynomial or best uniform approximation method with endpoint interpolation to reduce the degree of center curves, then use perturbation method to deal with its radius.In this thesis, we define the error of degree reduction of interval and disk WSGB cures, then derive the explicit error representations of each method, give some numerical examples and figures to demonstrate the approximation effect, and finally analyze the advantages and disadvantages of various methods.