I would like to have an algorithm that interpolates the values attached to nodes in a concave mesh mesh.
To be me precise, assume we have a point cloud P (e.g. in 3 dimensions) and a list of edges E connecting it with form a concave mesh in the form $E=[[i_1,i_2],[j_,j_2],...]$, where $i,j$ are nodes. Further assume that each point in P is associated with a value V (e.g. Temperature).
The algorithm I am looking for takes these objects together with an arbitrary point x in space and returns an interpolated value iff the point lies within the concave mesh and something unique if it doesn't (e.g. NaN). Hence if has a signature like:
f(P,E,V,x) -> float
The algorithms I found mostly deal with convex point clouds exclusively. In that case the Delaunay triangulation is unique (except in some edge cases) and the interpolation can be done e.g. with a linear barycentric interpolation. However, I haven't found anything general about concave meshes. Yet I assume that this is something that has some general use as well and there must exist something already that I am not aware of.