Abstract
Shewchuk’s Delaunay refinement algorithm is a simple scheme to efficiently tetrahedralize a 3D domain. The original analysis provided guarantees on termination and output edge lengths. However, the guarantees are weak and the time and space complexity are not fully covered. In this paper, we present a new analysis of this algorithm. The new analysis reduces the original 90o requirement for the minimum input dihedral angle to \(\arccos\frac{1}{3} \approx 70.53^o\). The bounds on output edge lengths and vertex degrees are improved. For a set of n input points with spread Δ (the ratio between the longest and shortest pairwise distance), we prove that the number of output points is O(n logΔ). In most cases, this bound is equivalent to O(n logn). This theoretically shows that the output number of tetrahedra is small.
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Si, H. (2009). An Analysis of Shewchuk’s Delaunay Refinement Algorithm. In: Clark, B.W. (eds) Proceedings of the 18th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04319-2_29
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DOI: https://doi.org/10.1007/978-3-642-04319-2_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04318-5
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