  We show how, given a sufficiently large point cloud sampled from an embedded
2-manifold in $\mathbb{R}^n$, we may obtain a global representation as a cell
complex with vertices given by a representative subset of the point cloud. The
vertex spacing is based on obtaining an approximation of the tangent plane
which insures that the vertex accurately summarizes the local data. Using
results from topological graph theory, we couple our cell complex
representation with the known Classification of Surfaces in order to classify
the manifold. The algorithm developed gives a meaningful description of the
embedding as a piecewise linear structure, which is obtained from combinatorial
data by projecting points in the point cloud into estimates of tangent planes.

Numerical Analysis