Local Topological Modification of Hexahedral Meshes Part I: a Set of Dual-based Operations

For hexahedral meshes, it is difficult to make topological modifications which preserve conformal property and which are local to the modified elements. This is most easily understood in how changes affect the dual surfaces (“sheets”) and lines (“chords”), which have non­local extent in hexahedral meshes. A set of three operations is proposed which represent distinct local changes to the hex mesh and its dual. These operations are shown to compose the larger set of “flipping” operations described by Bern et. al. The relation between these dual­based operations and the insertion of a Boy surface in the dual, described by Bern, is also discussed.