Summary: POINTERLESS IMPLEMENTATION OF HIERARCHICAL
SIMPLICIAL MESHES AND EFFICIENT NEIGHBOR
FINDING IN ARBITRARY DIMENSIONS
F. Betul Atalay David M. Mount
Department of Computer Science, University of Maryland, College Park, MD 20742.
We describe a pointerless representation of hierarchical regular simplicial meshes, based on a bisection approach proposed by
Maubach. We introduce a new labeling scheme, called an LPT code, that uniquely encodes each simplex of the hierarchy. We
present rules to compute the neighbors of a given simplex efficiently through the use of these codes. In addition, we show how to
traverse the associated tree and how to answer point location and interpolation queries. Our system works in arbitrary dimensions.
Keywords: Pointerless data structures, neighbor finding, hierarchical meshes, simplicial meshes, interpolation.
Hierarchical simplicial meshes have been widely used in var-
ious application areas such as finite element computations,
scientific visualization and geometric modeling. There has
been considerable amount of work in simplicial mesh re-
finement, particularly in 2- and 3-dimensions, and a num-
ber of different refinement techniques have been proposed
[1, 2, 3, 4, 5, 6, 7, 8]. Because of the need to handle data