一种新的自适应多分辨率细分曲面的表示法

摘要

For the problems having existed in adaptive subdivision methods,this paper proposed a new representation for adaptive multiresolution subdivision surface. Combining the features of topological subdivision mesh, used two-dimensional map to define the formalization of half-edge data structures, and introduced a kind of concept of hypermaps. Extension of half-edges for the representation of multiresolution subdivision surfaces was educed in the universal theoretical frame of hypermaps and discussed its application on adaptive subdivision. Results indicate that the structure is universal, and supports a variety of subdivision schemes. Moreover, topological cracks in the mesh are avoided during the adaptive subdivision.%针对已有自适应细分方法中存在的问题,提出了一种新的自适应多分辨率细分曲面的表示方法.该方法结合拓扑细分的特点,运用二维组合映射对半边数据结构进行形式化定义,并引出超映射的概念.在超映射这个通用的理论框架中引出了半边结构在多分辨率上的扩展,并对其在自适应细分方法中的应用进行了讨论.结果表明这种结构具有普适性,支持多种细分方法,允许在网格的任何多分辨率层次上及时有效地导航,并且在自适应细分过程中避免了拓扑裂缝的产生.