Department of Computer Science, University of Maryland, College Park, College Park, MD 20742, USA.
IEEE Trans Vis Comput Graph. 2009 Nov-Dec;15(6):1603-10. doi: 10.1109/TVCG.2009.186.
Volumetric datasets are often modeled using a multiresolution approach based on a nested decomposition of the domain into a polyhedral mesh. Nested tetrahedral meshes generated through the longest edge bisection rule are commonly used to decompose regular volumetric datasets since they produce highly adaptive crack-free representations. Efficient representations for such models have been achieved by clustering the set of tetrahedra sharing a common longest edge into a structure called a diamond. The alignment and orientation of the longest edge can be used to implicitly determine the geometry of a diamond and its relations to the other diamonds within the hierarchy. We introduce the supercube as a high-level primitive within such meshes that encompasses all unique types of diamonds. A supercube is a coherent set of edges corresponding to three consecutive levels of subdivision. Diamonds are uniquely characterized by the longest edge of the tetrahedra forming them and are clustered in supercubes through the association of the longest edge of a diamond with a unique edge in a supercube. Supercubes are thus a compact and highly efficient means of associating information with a subset of the vertices, edges and tetrahedra of the meshes generated through longest edge bisection. We demonstrate the effectiveness of the supercube representation when encoding multiresolution diamond hierarchies built on a subset of the points of a regular grid. We also show how supercubes can be used to efficiently extract meshes from diamond hierarchies and to reduce the storage requirements of such variable-resolution meshes.
体数据集通常使用基于域的多分辨率方法进行建模，该方法基于将域剖分为多面体网格的嵌套分解。通过最长边二分法生成的嵌套四面体网格通常用于分解规则体数据集，因为它们生成高度自适应的无裂缝表示。通过将共享公共最长边的四面体集聚类为称为钻石的结构，可以实现此类模型的有效表示。最长边的对齐和定向可用于隐式确定钻石的几何形状及其与层次结构中其他钻石的关系。我们引入超立方体作为此类网格中的高级基元，它包含所有独特类型的钻石。超立方体是对应于三个连续细分级别的连贯边集。钻石通过形成它们的四面体的最长边唯一地特征化，并通过将钻石的最长边与超立方体中的独特边相关联来聚类到超立方体中。因此，超立方体是一种紧凑且高效的方法，可以将信息与通过最长边二分法生成的网格的顶点、边和四面体子集相关联。我们展示了在规则网格的子集上构建的多分辨率钻石层次结构的编码中，超立方体表示的有效性。我们还展示了如何使用超立方体从钻石层次结构中高效提取网格，并减少此类可变分辨率网格的存储要求。
