Speeding Up Isosurface

The interval tree is an optimally eecient search structure proposed by Edelsbrunner 5] to retrieve intervals of the real line that contain a given query value. We propose the application of such a data structure to the fast location of cells intersected by an isosurface in a volume dataset. The resulting search method can be applied to both structured and unstructured volume datasets, and it can be applied incrementally to exploit coherence between isosurfaces. We also address issues about storage requirements, and operations other than the location of cells, whose impact is relevant in the whole isosurface extraction task. In the case of unstructured grids, the overhead due to the search structure is compatible with the storage cost of the dataset, and local coherence in the computation of isosurface patches is exploited through a hash table. In the case of a structured dataset, a new conceptual organization is adopted, called the chessboard approach, wich exploits the regular structure of the dataset to reduce memory usage and to exploit local coherence. In both cases, eeciency in the computation of surface normals on the isosurface is obtained by a pre-computation of the gradients at the vertices of the mesh. Experiments on diierent kinds of input show that the practical performance of the method reeects its theoretical optimality.