Despite of quite high time complexity of the optimal searching algorithm, the presented approach can be significantly speeded up by some deliberate strategies. As a new local transformation scheme and a potential substitute for the existing ones, the presented method seeks for the optimal tetrahedralization of a polyhedron with a certain number of vertexes and faces (typically composed of 20 to 40 tetrahedral elements) rather than simply making a selection from several possible configurations within a small region that consists of several tetrahedra, and therefore will give better results than existing ones.
In this paper, the concept of optimal tetrahedralization for small polyhedron and corresponding small polyhedron re-connection (or SPR for abbreviating) approach are presented. Although these local transformations are easy to implement and effective in removing poorly-shaped tetrahedra, it is still possible to improve the quality of mesh further by expanding the space of transformation region. node-element connectivity relationship) within a relatively small region composed of several tetrahedra, such as 2-3 flip, 3-2 flip, 2-2 flip, 4-4 flip, etc.
The commonly used local transformations for tetrahedral mesh involve changing in mesh topology (i.e. Local transformation, or topological re-connection, is one of effective procedures of mesh improvement method, especially in three-dimensional situation.
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