Poisson Curve And Surface Subdivision Technology Research

With the prevalence and progressively broad application of computer technology, Subdivision method has recently become a focus of study in geometric modeling, computer aided geometric design and computer graphics in the world. Subdivision allows to generate smooth curves and surfaces by applying simple refinement rules to the given control polygon and control mesh. Subdivision method has become a powerful tool in computer aided geometric design and computer graphics recently. Poisson curves and surfaces have some excellent geometric and algebraic properties, but some special curves and surfaces, common transcendental curves and surfaces are represented as Poisson curves and surfaces accurately. This thesis studies modeling of subdivision scheme for Poisson curves and surfaces.At first, this thesis briefly introduces creative thoughts, history, character and models of subdivision algorithm, but we introduce typical subdivision curves and surfaces in detail. According to subdivision models, in this thesis we study approximating subdivision models.Secondly, this thesis studies a subdivision for Bézier curves based on de Casteljau algorithm. In 1962 French engineer Bézier developed a kind of special parametric polynomial curves, this curves have numerous remarkable geometric features. In 1963 de Casteljau presented a subdivision for Bézier curves. Sta|¨rk and Chang gen-zhe gave its proof respectively. De Casteljau algorithm is both an evaluation and a subdivision procedure. This algorithm defines a Bézier curve. According to subdivision formula of Bernstein basis functionWe get a subdivision algorithm for Bézier curves.Thirdly, some properties of a Poisson curve are similar to those of a Bézier curve. For example, they are characterized by their control polygons, and their shape can be modified intuitively by moving their control points, but Poisson basis is a...