On optimal interpolation triangle incidences
SIAM Journal on Scientific and Statistical Computing
Optimality of the Delaunay triangulation in Rd
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Automatic mesh generator with specified boundary
Computer Methods in Applied Mechanics and Engineering
Approximating constrained tetrahedrizations
Computer Aided Geometric Design
On the shape of tetrahedra from bisection
Mathematics of Computation
Bubble mesh: automated triangular meshing of non-manifold geometry by sphere packing
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Improvements on Delaunay-based three-dimensional automatic mesh generator
Finite Elements in Analysis and Design - Special issue: adaptive meshing part 2
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Smoothing and cleaning up slivers
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Mesh generation for domains with small angles
Proceedings of the sixteenth annual symposium on Computational geometry
Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations
Proceedings of the sixteenth annual symposium on Computational geometry
A point-placement strategy for conforming Delaunay tetrahedralization
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Conforming delaunay triangulations in 3D
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Alternative Breast Imaging: Four Model-based Approaches (Kluwer International Series in Engineering and Computer Science)
Discrete & Computational Geometry
Three-dimensional constrained boundary recovery with an enhanced Steiner point suppression procedure
Computers and Structures
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Numerous high-quality, volume mesh-generation systems exist. However, no strategy can address all geometry situations without some element qualities being compromised. Many 3D mesh generation algorithms are based on Delaunay tetrahedralization which frequently fails to preserve the input boundary surface topology. For biomedical applications, this surface preservation can be critical as they usually contain multiple material regions of interest coherently connected. In this paper we present an algorithm as a post-processing method that optimizes local regions of compromised element quality and recovers the original boundary surface facets (triangles) regardless of the original mesh generation strategy. The algorithm carves out a small sub-volume in the vicinity of the missing boundary facet or compromised element, creating a cavity. If the task is to recover a surface boundary facet, a natural exit hole in the cavity will be present. This hole is patched with the missing boundary surface face first followed by other patches to seal the cavity. If the task was to improve a compromised region, then the cavity is already sealed. Every triangular facet of the cavity shell is classified as an active face and can be connected to another shell node creating a tetrahedron. In the process the base of the tetrahedron is removed from the active face list and potentially three new active faces are created. This methodology is the underpinnings of our LAST RESORT method. Each active face can be viewed as the trunk of a tree. An exhaustive breath and depth search will identify all possible tetrahedral combinations to uniquely fill the cavity. We have streamlined this recursive process reducing the time complexity by orders of magnitude. The original surfaces boundaries (internal and external) are fully restored and the quality of compromised regions improved.