Research On Generating Subdivision Surface And Applying To Surface Modeling

Along with the great progress in 3D data measurement device and the popularization of complex surface modeling, recursive subdivision has been a research focus in the world over the past 20 years in computer aided geometric design and computer graphics. However most subdivision schemes don't take the limit surface's convergence to some user-definded position parameters into account. So subdivision surfaces are always applied in computer animation and artware shape design, not in reverse engineering in which the position-setting constrains are appended to the result surfaces, precision machine design and medical image reconstruction.Just in order to change the puzzle and passive situation mentioned above, we are devoted to the applied research of the generation of subdivision surfaces that can interpolate multiple given curves and possess sharp features, and its application in the field of surface modeling and surface design. This paper summarizes our theoretical research results and algorithms that have high actual practicable values. The main contents include the construction of subdivision surfaces satisfying the constrain of curves interpolation based on Catmull-Clark subdivision scheme, the interpolated curves are uniform B-spline; the construction of subdivision surfaces interpolating NURBS curves based on non-uniform rational Catmull-Clark (NURCC) subdivision scheme; generation of sharp features on subdivision surfaces; application of subdivision surfaces in the traditional surface design method - skinning.After reviewing the classification and history of curve and surface modeling, we present a systematic survey of recursive subdivision including its origin, research history, research results and application in many aspects in resent years.It is an essential tool and purpose in surface modeling to interpolate the given curves. So we present a new method of subdivision surface modeling. This method not only maintains the intrinsic property of Catmull-Clark subdivision surface, but also makes this kind of surface have a new function of interpolating multi-predefined B-spline curves. It overcomes some limitation of Catmull-Clark subdivision scheme and widens its application range, which brings subdivision surfaces from animation design and artistic modeling to mechanical products design. The main innovation of our method is that we only need construct polygonal mesh possessing simple symmetricproperties on both sides of control polygon edges of interpolated curves, and don't need modify the subdivision rules near the interpolation curves during the process of subdivision. Thus the subdivision rules are simple. The process is convergent and the limit surface is C everywhere except a finite number of points. Our method can deal with the interpolation of single uniform B-spline curve and a mesh of nonintersecting or intersecting uniform B-spline curves.Since NURBS curves possess stronger ability than uniform B-spline curves in shape representation, we give a method of generating non-uniform subdivision surface modeling by improving NURCC surface proposed by Sederberg et al.. This method can interpolate predefined NURBS curves based on NURCC surface while maintain NURCC surface's basic function of the controllability of the continuous order. Its accomplishment is simple and intuitional. The main innovation of this method is that we only need construct a symmetric zonal mesh for each interpolated curve respectively and write appropriate knot spacings for mesh edges. Then applying NURCC rules to the initial control polygonal mesh consisting of those symmetric zonal meshes can generate a surface that satisfies interpolation constrains. Basing on NURCC scheme we can construct surfaces that can interpolate NURBS curves and have different local continuous order. Our method enables subdivision surfaces to be used in the field of complex shape design of industry products.From the angle of mesh topology, we present a method of sharp features generation on subdivision surfaces. By topology modificatio...