TY - CONF T1 - Constant-time navigation in four-dimensional nested simplicial meshes T2 - Shape Modeling Applications, 2004. Proceedings Y1 - 2004 A1 - Lee,M. A1 - De Floriani, Leila A1 - Samet, Hanan KW - 4-dimensional KW - adaptive KW - algorithm; KW - approximations; KW - bit KW - codes; KW - computational KW - constant-time KW - continuous KW - decomposition; KW - face-adjacent KW - faces; KW - fields; KW - finding KW - following; KW - four-dimensional KW - generation; KW - geometry; KW - hierarchy; KW - hypercube; KW - location KW - manipulation KW - mesh KW - meshes; KW - multiresolution KW - navigation; KW - neighbor KW - nested KW - operations; KW - pentatopes; KW - pointer KW - recursive KW - representation; KW - scalar KW - simplexes; KW - simplicial KW - tetrahedral AB - We consider a recursive decomposition of a four-dimensional hypercube into a hierarchy of nested 4-dimensional simplexes, that we call pentatopes. The paper presents an algorithm for finding the neighbors of a pentatope along its five tetrahedral faces in constant time. To this aim, we develop a labeling technique for nested pentatopes that enables their identification by using location codes. The constant-time behavior is achieved through bit manipulation operations, thus avoiding traversing the simplicial hierarchy via pointer following. We discuss an application of this representation to multi-resolution representations of four-dimensional scalar fields. Extracting adaptive continuous approximations of the scalar field from such a model requires generating conforming meshes, i.e., meshes in which the pentatopes match along their tetrahedral faces. Our neighbor finding algorithm enables computing face-adjacent pentatopes efficiently. JA - Shape Modeling Applications, 2004. Proceedings M3 - 10.1109/SMI.2004.1314509 ER -