C/C++ function to return minimum set of points required to represent a geometric shap

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I am looking for a method from Grass, GEOS, or similar that will delete those points in a geometry which do not affect its shape.

Example 1

+----+----+p0 p1 p2p1 can be deleted without affecting the shape of the line

Example 2

p0 p1 +----+ | \p4 + \ | \p3 +--------+ p2 p4 can be deleted without affecting the shape of the polygon

I am sure this has been asked/answered and there is probably a name for the output point set (akin to convex hull) but I am not sure what to search for.

It would be relatively straightforward (no pun intended) to write my own function but obviously silly if there is something out there already.



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