Topology preserving simplification of meshes with embedded structures.

Dilip Mathew Thomas

Abstract

Several visualization applications require simplification of high resolution meshes for faster processing. Many of these meshes contain interesting substructures, called embedded structures, within the mesh. There are applications that require the topology of the embedded structure as well as the mesh to be preserved during the simplification process. Such a simplification technique that uses edge contractions has been recently developed and shown to work on different datasets. This technique constructs what is known as an extended complex and contracts edges that satisfy link conditions on the extended complex. In this project, we prove mathematically that such edge contractions preserve the topology of the mesh and the embedded structures. We allow embedded structures to be on the boundary of the mesh and propose modifications to the existing algorithm to handle such cases. We also show that evaluation of link conditions are almost always necessary in ensuring that topology is preserved.

[PDF]