Compact array-based mesh data structures

In this paper, we present simple and efficient array-based mesh data structures, including a compact representation of the half-edge data structure for surface meshes, and its generalization - a half-face data structure - for volume meshes. These array-based structures provide comprehensive and efficient support for querying incidence, adjacency, and boundary classification, but require substantially less memory than pointer-based mesh representations. In addition, they are easy to implement in traditional programming languages (such as in C or Fortran 90) and convenient to exchange across different software packages or different storage media. In a parallel setting, they also support partitioned meshes and hence are particularly appealing for large-scale scientific and engineering applications. We demonstrate the construction and usage of these data structures for various operations, and compare their space and time complexities with alternative structures.