Uniform Stationary Univariate Subdivision Schemes And Its Continuity

Subdivision—curve and surface modeling method of discretization, is the method which according to initial data to directly generate curves and surfaces or other geometric shapes by computer, it have been appreciated in many fields such as computer graphics, computer aided geometric design and computer animation due to its efficient subdivision schemes. Uniform stationary univariate subdivision scheme is a foundation and simple kind of subdivision, it has symmetry, stability and easy to control. So far among the research results of uniform stationary univariate subdivision, there are even-point binary or ternary interpolatory subdivision schemes and approximating subdivision schemes, but with odd number of control points, researches only about three-point. So, odd-point subdivision schemes have much research space.In this paper, we mainly introduce the definition and natures of uniform subdivision schemes, show the conditions for C k-continuity of subdivision schemes. We also take a summary about several classical subdivision schemes and construct the five-point and seven-point interpolating schemes and approximating schemes. Using the conditions for C k- continuity, the continuity and accuracy of the schemes are presented. Compared with even-point interpolating schemes, the interpolating schemes of this paper have higher accuracy, at the same time, compared with the interpolating schemes, the approximating schemes of us have many improvement in the continuity.