# Triangle mesh (set of points 2D) with minmal total area: ' Convave Hull' [duplicate]

modified question

In the following example

pr = RandomReal[{0, 1}, {100, 2}];
p = Select[pr , #[] #[] < .2 &];
Show[{ DelaunayMesh[p], ListPlot[p, PlotStyle -> Black], Plot[.2/x, {x, 0, 1}, PlotRange -> {{0, 1}, {0, 1}}]}] meshing (same with ConvexHullMesh) shows several elements above the hyperbolean which I would like to remove.

How to solve this problem for an arbitrary point set with Mathematica?

Thanks!

• But one can still cut out some triangles from your last plot to reduce the area even more. And maybe make it = 0. What is the exact mathematical definition of the hull you are looking for? Notice that fig. 2 does not represents a convex hull. – yarchik Feb 21 at 15:55
• You're right, the example is to simple. In my underlying problem I need to discretize a region (something like a triangle with a concave side) for further interpolation. Convexhull of this region expands the region unacceptable. Thanks for your interest! – Ulrich Neumann Feb 21 at 17:34
• @yarchik I'll modify my question... – Ulrich Neumann Feb 21 at 17:44
• Relevant keywords are "concave hull" and "α-concave hull". – yarchik Feb 22 at 18:35
• @yarchik Appears to be promising, I'll test it. – Ulrich Neumann Feb 23 at 10:46