Supercubes: A High-Level Primitive for Diamond Hierarchies

Abstract-- 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 clu...

• Type: Conference
• Year: 2009
• Where: VIS
• Authors: Kenneth Weiss, Leila De Floriani
• Keywords: Common Longest Edge, Edge Bisection Rule, Longest Edge Bisection, VIS 2009, Visualization