Any simplex of constant nonzero curvature (with finite/suitable circumradius) admits a Freudenthal-style subdivision whose simplices have fatness bounded below by a positive constant depending only on the original fatness and circumradius.
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A dimension-dependent approximate Carathéodory theorem yields explicit contraction rates for Delaunay mesh refinement that exceed those of standard subdivision.
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Simplicial subdivision of simplices of arbitrary dimension in spaces of constant curvature with bounded quality
Any simplex of constant nonzero curvature (with finite/suitable circumradius) admits a Freudenthal-style subdivision whose simplices have fatness bounded below by a positive constant depending only on the original fatness and circumradius.
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Sharp approximate Carath\'eodory theorem and application to iterated Delaunay refinement
A dimension-dependent approximate Carathéodory theorem yields explicit contraction rates for Delaunay mesh refinement that exceed those of standard subdivision.