Generalized surface and volume decimation for unstructured tessellated domains

A general algorithm for decimating unstructured discretized data sets is presented. The discretized space may be a planar triangulation, a general 3D surface triangulation, or a 3D tetrahedrization. The decimation algorithm enforces Dirichlet boundary conditions, uses only existing vertices, and assumes manifold geometry. Local dynamic vertex removal is performed without history information, while preserving the initial topology and boundary geometry. The research focuses on how to remove a vertex from an existing unstructured n-dimensional tessellation, not on the formulation of decimation criteria. Criteria for removing a candidate vertex may be based on geometric properties or any scalar governing function specific to the application.