Data Structures for Multiresolution Representation of Unstructured Meshes

A major impediment to the implementation of visualization algorithms on very-large unstructured scientific data sets is the suitable internal representation of the data. Not only must we represent the data elements themselves, but we must also represent the connectivity or topological relationships between the data. We present three data structures for unstructured meshes that are designed to fully represent the topological connectivity in the mesh, but also minimize the data storage requirements in representing the mesh. The key idea is to represent the topology of the mesh by the use of a single data item – the lath – which can be used to encapsulate the topological relationships within the mesh. We present and analyze algorithms that query the spatial relations and properties of these data structures, and analyze the data structures of the dual mesh induced by each.