Quality Local Refinement of Tetrahedral Meshes Based on 8-Subtetrahedron Subdivision |
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Authors: | Anwei Liu Barry Joe |
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Institution: | Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2H1 ; Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2H1 |
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Abstract: | Let be a tetrahedral mesh. We present a 3-D local refinement algorithm for which is mainly based on an 8-subtetrahedron subdivision procedure, and discuss the quality of refined meshes generated by the algorithm. It is proved that any tetrahedron produces a finite number of classes of similar tetrahedra, independent of the number of refinement levels. Furthermore, , where , is a positive constant independent of and the number of refinement levels, is any refined tetrahedron of , and is a tetrahedron shape measure. It is also proved that local refinements on tetrahedra can be smoothly extended to their neighbors to maintain a conforming mesh. Experimental results show that the ratio of the number of tetrahedra actually refined to the number of tetrahedra chosen for refinement is bounded above by a small constant. |
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