Subdivision Surfaces Modeling

This thesis studies modeling and application of subdivision surfaces.Subdivision method has become an important tool in computer graphics recently.To extend application areas (especially in the area of CAD) more widely, however, many problems have to be solved. We list some common schemes that modeling surfaces, and we point to its history background and exist reasons, at the last, we show the foundation of mathematic of subdivision technology which we have discussed it is a generalize of B-spline, and we have analysis continuity of two schemes. Since the subdivision technology is new tool for modeling surface, following chapters, we have posted two schemes that interpolating surfaces in this paper.The construction of an adjustable smooth surface interpolating a mesh of arbitrary topological type is an important problem in many graphics applications. The paper presents a modification of the control mesh and a subsequent Doo-Sabin subdivision. The method has the following features: First it can adjust extremely surface according to a scalar and can interpolate some or all vertices of a mesh with arbitrary topology, thus make the new method itself suitable for interactive free-form shape design. Second the whole complexity is O(k), where k is the number of the vertices. At the end of this chapter we have discussed shape adjust which is different subdivision surface.The construction of an adjustable surfaces curve interpolating is an important task in many graphics applications. An algorithm with multi-features for curves interpolating on the adjustable surface was proposed. The parameters of the sameness of the result surfaces were introduced, and the curves were defined. The control mesh was modified topologically, and the mesh to be interpolated. Under the condition of satisfying curves interpolating, some similarities between result surface and control mesh had been made and two-side adjustable parameters were updated. It used the predefined curvature to adjust the bended degree of the curves and created the curvature control formula. The result shows it is available to the curve interpolating adjustable surfaces and the extremely surfaces are diverse.