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You can have a near-180° obtuse triangle in a Delaunay triangulation, if all other vertices in the mesh are far from the long edge. However, after subdivision, the obtuse vertex may lie inside the circumcircle of the central subtriangle.


I hope I'm not overlooking something, but it seems obvious that the mesh so refined will not be Delaunay. EDIT: Turns out I misunderstood the procedure, and you are actually generating a fresh mesh through trimming curves/edge flips/equivalent. Essentially you are adding vertices to the midpoints of each edge of a triangle; these midpoints lie inside the ...


Accept-Reject (AR) sampling is probably the way to go here. AR sampling works in $n$ dimensional spaces just like it does in 1 dimensional space (e.g. sampling from a Gaussian via a Laplace/Double exponential) you define an envelope function and then sample uniformly under the envelope. Here the envelope function would need to be a function covering the ...

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