非流形曲面Loop细分研究

工业产品几何造型技术的发展要求，以及代数拓扑学复形等概念引入到几何造型中，因此产生了非流形几何造型理论。参数曲面造型所表示的物体复杂性受到限制，细分造型计算简单，可以表达任意拓扑关系，目前在图形学中已得到广泛研究并在三维建模、计算机动画中得到广泛应用。本文介绍了扩展实现Loop细分算法，使之能应用于非流形曲面，并相应提出了一种简易的基于三角形控制网格的数据结构。

Research about Loop Subdivision for Non-manifold Surface

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being.The complicacy of object represented by parameter surface model is limited, but subdivision surface model is simple and can represent any topology relation, so it is widely used in computer graphics and animation at present. In this paper, we describe a subdivision algorithm that makes it possible to model nonmanifold surface,which is the extension of Loop subdivision scheme,and a corresponding data structure which is simple and bases on triangle control mesh.