Degree Reduction Of Interval And Disk Q-Bézier Curves

In order to guarantee the stability of numerical computation and the accuracy of the calculation results,the interval and disk algorithms have been widely applied in the field of curves and surfaces modeling design.In this thesis,we apply interval and disk algorit-hms to q-Bézier curves to get interval q-Bézier curves and disk q-Bézier curves,and discuss the problem of their degree reduction.Different modeling systems have different limits on the degree of polynomial parametric curve.In order to achieve the data conver-sion and transfer between different degrees curves,we use low degree curve to describe or approximate higher degree curve under certain error requirement.So the research on degree reduction of curve is of great significance,and has been concerned by many scho-lars in recent years.The main work of this thesis includes the following three parts:In the first part,interval q-Bézier curves are presented using a generalized Bernstein basis and the problem of degree reduction approximation of them is studied.We propose three different methods,that is to say,perturbation method,constrained best uniform approximation method based on Chebyshev polynomials and best uniform approximation method.The explicit representation of bounding error of each method is derived.The merit and demerit of these method are discussed by several numerical examples.In the second part,we study the degree reduction of disk q-Bézier curves.First of all,the degree reduction approximation to the center curves of the original disk q-Bézier curves are found using best uniform approximation methods.The center curves of the degree reduced disk q-Bézier curves are obtained.Then the radius of the degree reduced disk q-Bézier curve is computed by using perturbation method.Finally,the bounding errors for the degree reduction algorithm are analyzed.In the third part,a family of disk rational q-Bézier curves can be obtained by changing the value of parameter q.The based properties of this kind of rational curves are discussed.De Casteljau type algorithm of disk rational q-Bézier curves is also considered.The quadratic disk rational q-Bézier curve can be used to represent accurately conic section.