Abstract
A d-dimensional simplicial mesh is a Delaunay triangulation if the circumsphere of each of its simplices does not contain any vertices inside. A mesh is well-shaped if the maximum aspect ratio of all its simplices is bounded from above by a constant. It is a long-term open problem to generate well-shaped d-dimensional Delaunay meshes for a given polyhedral domain. In this paper, we present a re?nement-based method that generates well-shaped d-dimensional Delaunay meshes for any PLC domain with no small input angles. Furthermore, we show that the generated well-shaped mesh has O(n) d-simplices, where n is the smallest number of d-simplices of any almost-good meshes for the same domain. A mesh is almost-good if each of its simplices has a bounded circumradius to the shortest edge length ratio.
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© 2001 Springer-Verlag Berlin Heidelberg
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Li, XY. (2001). Generating Well-Shaped d-dimensional Delaunay Meshes. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_11
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DOI: https://doi.org/10.1007/3-540-44679-6_11
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