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Since then, various small improvements have been made.<ref>{{cite journal| doi=10.1142/S0218195905001592| first1=Gary | last1=Miller | first2=Steven | last2=Pav | first3=Noel | last3=Walkington | title=When and why Delaunay refinement algorithms work | journal=International Journal of Computational Geometry and Applications | year=2005 | volume=15 | issue=1 | pages=25–54}}</ref>
An extension of Ruppert's algorithm in two dimensions is implemented in the freely available
Ruppert's algorithm has been shown to terminate for any input PLS with no small angles. The algorithm can be extended to handle any input by slightly relaxing the quality requirement on the output (Miller et al., 2005).
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