Constant-Time Navigation in Four-Dimensional Nested Simplicial Meshes

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SMI '04 Proceedings of the Shape Modeling International 2004
Year:
2004

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Abstract

We consider a recursive decomposition of a four-dimensionalhypercube into a hierarchy of nested 4-dimensional simplexes,that we call pentatopes. The paper presents an algorithm for findingthe neighbors of a pentatope along its five tetrahedral facesin constant time. To this aim, we develop a labeling techniquefor nested pentatopes that enables their identification by usinglocation codes. The constant-time behavior is achieved throughbit manipulation operations, thus avoiding traversing the simplicialhierarchy via pointer following. We discuss an applicationof this representation to multi-resolution representations of four-dimensionalscalar fields. Extracting adaptive continuous approximationsof the scalar field from such a model requires generatingconforming meshes, i.e., meshes in which the pentatopes matchalong their tetrahedral faces. Our neighbor finding algorithm enablescomputing face-adjacent pentatopes efficiently.