Isosurfacing in higher dimensions

Visualization algorithms have seen substantial improvements inthe past several years. However, very few algorithms have beendeveloped for directly studying data in dimensions higher thanthree. Most algorithms require a sampling in three-dimensionsbefore applying any visualization algorithms. This samplingtypically ignores vital features that may be present whenexamined in oblique cross-sections, and places an undo burden onsystem resources when animation through additional dimensionsis desired. For time-varying data of large data sets, smoothanimation is desired at interactive rates. This paper provides afast Marching Cubes like algorithm for hypercubes of anydimension. To support this, we have developed a new algorithm toautomatically generate the isosurface and triangulation tables forany dimension. This allows the efficient calculation of 4Disosurfaces, which can be interactively sliced to provide smoothanimation or slicing through oblique hyperplanes. The formerallows for smooth animation in a very compressed format. Thelatter provide better tools to study time-evolving features as theymove downstream. We also provide examples in using thistechnique to show interval volumes or the sensitivity of aparticular isovalue threshold.