Curve Interpolation And Shape Control Of Loop Subdivision Surfaces

In order to enhance expressing ability of subdivision method and satisfy actual demand of surface shape controlling, this thesis mainly studies modeling and application of subdivision surfaces, the discussed point is how to interpolate the given curves in the subdivision surface and how to control the shape of subdivision surfaces. Firstly, we review the background, history and application of subdivision surface modeling. Secondly, for triangle mesh, we present the characteristic and classification of subdivision methods and the definition rules of some representative subdivision methods. Thirdly, we propose a method that needn't modify subdivision rules for using symmetric triangle strip-shaped mesh to generate Loop subdivision surfaces with curve interpolation constraints. The symmetric triangle strip-shaped mesh is constructed by designing symmetric triangles for both sides of the control polygon of interpolated curve. This control polygon is referred as central polygon. We can prove that the symmetric triangle strip-shaped mesh can converge to the interpolated curve. So the limited surface of the given mesh with the symmetric triangle strip-shaped mesh will contain interpolated curve. This paper provides the arithmetic of the automatic producing the symmetric triangle strip-shaped mesh. If the interpolated curves intersect at point v, we can design a full symmetric triangle mesh at point v. The method proposed in this paper will interpolate intersecting curves in the given mesh. The numbers of intersecting curves are up to six. On the basis of this method, lastly, we propose some methods that can control the shape of subdivision surfaces with the interpolated curve. They mainly base on two ideas. One, keeping the shape of the control polygon of interpolated curve, we modify the shape of the symmetric triangle strip-shaped mesh. Two, we modify the shape of the control polygon of interpolated curve. The methods including: 1. curvature...