Hierarchyless Simplification, Stripification and Compression of Triangulated Two Manifolds

In this paper we explore the algorithmic space in which stripification, simplification and geometric compression of triangulated 2-manifolds overlap. Edge-collase/uncollapse based geometric simplification algorithms develop a hierarchy of collapses such that during uncollapse the reverse order has to be maintained. We show that restricting the simplification and refinement operations only to, what we call, the collapsible edges creates hierarchyless simplification in which the operations on one edge can be performed independent of those on another. Although only a restricted set of edges is used for simplification operations, we prove topological results to show that, with minor retriangulation, any triangulated 2-manifold can be reduced to either a single vertex or a single edge using the hierarchyless simplification, resulting in extreme simplification. The set of collapsible edges helps us analyze and relate the similarities between simplification, stripification and geometric comp...

• Type: Journal
• Year: 2005
• Where: CGF
• Authors: Pablo Diaz-Gutierrez, Meenakshisundaram Gopi, Renato Pajarola
• Keywords: CGF 2005, Collapsible Edges, Hierarchyless Simplification, Simplification