While the original question https://mathoverflow.net/questions/353268/convex-triangulations/353274#353274 was aimed at the existence and calculation of convex triangulations of a given set of $n$ points in the Euclidean plane, I would like to ask the opposite  

>**Question:**  

>where do pointsets, that come close to the ideal of having a convex Delaunay triangulation, "naturally" occur?  

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It appears to me that the pointsets that are generated via [Weighted Voronoi Stippling](https://cs.nyu.edu/~ajsecord/stipples.html) algorithms diagrams or the nuclei of 2D biological cell structures are almost free of non-convex maximal unions of Delaunay triangles with a common inner points as a vertex.