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The production of high-quality 3D mesh models has seen important technological advancements in recent years and is increasingly becoming a crucial asset for several application domains. However, the intrinsic nature of the problem (acquisition constraints and real objects complexity) makes hole filling and mesh completion still critical tasks for the effectual finalization of the models. In this work, we propose a new solution for filling holes and gaps and for reconstructing missing parts of mesh models that is capable to guarantee the full preservation of the input mesh. On the implicit function obtained from a Poisson Reconstruction computed on a set of oriented points derived from the input mesh, we develop an interpolation method which allows a fast and continuous surface-oracle computation which is exploited to efficiently guide a restricted Delaunay triangulation. This can be used to confine the tessellation inside the holed zones, while protecting the input mesh and the boundary curves so that simple tailoring routines can merge the obtained surface-reconstruction driven patches with the input mesh without stitching artifacts. The proposed technique is versatile and evidences its effectiveness in dealing with multiple complex holes, gaps and surface blending, and it compares favorably with respect to different, and usually more specialized, hole filling and global mesh repair techniques. As a parallel benefit, we also show how the same proposed solution can be exploited as an effective and high-quality meshing or remeshing tool.

Quality surface meshes for molecular models are desirable in the studies of protein shapes and functionalities. However, there is still no robust software that is capable to generate such meshes with good quality. In this paper, we present a Delaunay-based surface triangulation algorithm generating quality surface meshes for the molecular skin model. We expand the restricted union of balls along the surface and generate an /spl epsiv/-sampling of the skin surface incrementally. At the same time, a quality surface mesh is extracted from the Delaunay triangulation of the sample points. The algorithm supports robust and efficient implementation and guarantees the mesh quality and topology as well. Our results facilitate molecular visualization and have made a contribution towards generating quality volumetric tetrahedral meshes for the macromolecules.

It is a well-known fact that, under mild sampling conditions, the restricted Delaunay triangulation provides good topological approximations of 1- and 2-manifolds. We show that this is not the case for higher-dimensional manifolds, even under stronger sampling conditions. Specifically, it is not true that, for any compact closed submanifold M of R^n, and any sufficiently dense uniform sampling L of M, the Delaunay triangulation of L restricted to M is homeomorphic to M, or even homotopy equivalent to it. Besides, it is not true either that, for any sufficiently dense set W of witnesses, the witness complex of L relative to M contains or is contained in the restricted Delaunay triangulation of L.