  A Triangulated Irregular Network (TIN) is a data structure that is usually
used for representing and storing monotone geographic surfaces, approximately.
In this representation, the surface is approximated by a set of triangular
faces whose projection on the XY-plane is a triangulation. The visibility graph
of a TIN is a graph whose vertices correspond to the vertices of the TIN and
there is an edge between two vertices if their corresponding vertices on TIN
see each other, i.e. the segment that connects these vertices completely lies
above the TIN. Computing the visibility graph of a TIN and its properties have
been considered thoroughly in the literature. In this paper, we consider this
problem in reverse: Given a graph G, is there a TIN with the same visibility
graph as G? We show that this problem is Complete for Existential Theory of The
Reals.
