Boundary recovery for 3D Delaunay triangulation

Abstract

New ideas are presented in this paper for the boundary recovery of 3D Delaunay triangulation. Fully constrained Delaunay triangulations in terms of geometrical and topological integrities on all boundary edges and facets are required in many applications, such as meshing by components, fluid–structure interactions, parallel mesh generation, local remeshing and interface problems. The geometry of boundary edges and facets can be recovered by the introduction of Steiner points. However, for a fully constrained Delaunay triangulation, these Steiner points have to be removed or repositioned towards the interior of the domain to restore the topological integrity of the boundary edges and the facets. It is found that Steiner points on edges could be removed more systematically following a specific sequence in an alternative manner rather than a random selection commonly adopted in practice; whereas for Steiner points on a facet, a weight on the Steiner point adjacency would lead to an optimal order to facilitate their removal. A linear programming technique is also employed to determine the feasible region for the relocation of Steiner points in the interior of the domain. Work examples and industrial applications with details in the boundary recovery are presented to illustrate how the algorithm works on objects with difficult boundary conditions.