A near optimal isosurface extraction algorithm using the span space

We present the ''Near Optimal IsoSurface Extraction'' (NOISE) algorithm for rapidly extracting isosurfaces from structured and unstructured grids. Using the span space, a new representation of the underlying domain, we develop an isosurface extraction algorithm with a worst case complexity of o(root n + k) for the search phase, where n is the size of the data set and k is the number of cells intersected by the isosurface. The memory requirement is kept at O(n) while the preprocessing step is O(n log n). We utilize the span space representation as a tool for comparing isosurface extraction methods on structured and unstructured grids. We also present a fast triangulation scheme for generating and displaying unstructured tetrahedral grids.