Pointerless Implementation of Hierarchical Simplicial Meshes and Efficient Neighbor Finding in Arbitrary Dimensions

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, which uniquely encodes the geometry of each simplex of the hierarchy, and 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.