Boundary recovery after 3D Delaunay tetrahedralization without adding extra nodes

In this paper, we investigate boundary recovery, the problem that has troubled researchers ever since Delaunay‐based methods were applied to generate mesh. There are a number of algorithms for boundary recovery already and most of them depend heavily on adding extra nodes. In this paper, we make an effort to seek a method to recover boundaries without using extra nodes. It was noted that some previous algorithms imposed artificial boundary constraints on a meshing problem at the recovering stage; we first try to discard these artificial constraints and thus make things easier. Then a new method is proposed by which the boundaries can be recovered by means of two operations: (1) creating a segment in the mesh and (2) removing a segment from the mesh. Both operations are special cases of a general local transformation called small polyhedron reconnection operation. The method works well when coupled with the sphere‐packing method proposed by the first author. If the mesh sizing function is suitable, a good configuration of nodes will be created accordingly by the sphere‐packing method and the boundary can be recovered by the local transformation presented here without inserting extra nodes. Copyright © 2007 John Wiley & Sons, Ltd.