RED-GREEN REFINEMENT OF SIMPLICIAL MESHES IN d DIMENSIONS

摘要

The local red-green mesh refinement of consistent, simplicial meshes in d dimensions is considered. We give a constructive solution to the green closure problem in arbitrary dimension d. Suppose that T is a simplicial mesh and that R is an arbitrary subset of its faces, which is refined with the Coxeter-Freudenthal-Kuhn (red) refinement rule. Green refinements of simplices S is an element of T are generated to restore the consistency of the mesh using a particular placing triangulation. No new vertices are created in this process. The green refinements are consistent with the red refinement on R, the unrefined mesh regions, and all other neighboring green refinements.