Catmull-Clark细分曲面的形状调整

Shape Modification of Catmull-Clark Subdivision Surface

提出一种调整细分曲面形状的算法 该算法用cosα(Ck)取代C B样条的形状因子α,并将Ck 的定义区间从 [- 1 ,1 ]扩大到 [- 1 ,∞ ) ;然后用这种扩展了的C B样条来构造Catmull Clark细分曲面 ;使得生成细分曲面的形状不仅能够在C B样条的范围内可调 ,而且还能在标准的Catmull Clark细分曲面和初始的控制网格之间任意调整 该算法保留了C B样条和Catmull Clark细分曲面的主要特点 ,如精确表示圆柱体。

An adjustable Catmull Clark subdivision algorithm based on C B spline is proposed The shape parameter α in C B spline is substituted by cos? α , that is C k , and the definition interval of C k is extended to [-1,∞) in constructing the Catmull Clark subdivision surface When C k is within the interval[-1, 1], it is a common Catmull Clark surface built with C B spline, and can't reach the area between the standard Catmull Clark surface and the original control mesh However, as C k is increased to over 1, the surfaces can reach this area too This algorithm inherited nearly all properties that C B spline and Catmull Clark subdivision surface possess, such as representing cylinder, and constructing surface on meshes of arbitrary topological structure etc