### 2.3 Finite-element parameterizations

Another way to parameterize a 2-surface is via finite elements where the surface is modelled as a
triangulated mesh, i.e. as a set of interlinked “vertices” (points in the slice, represented by their spatial
coordinates ), “edges” (represented by ordered pairs of vertices), and faces. Typically only triangular
faces are used (represented as oriented triples of vertices).
A key benefit of this representation is that it allows an arbitrary topology for the surface. However,
determining the actual surface topology (e.g. testing for whether or not the surface self-intersects) is
somewhat complicated.

This representation is similar to that of Regge
calculus [128, 72],
and can similarly be expected to show 2nd order convergence with the surface resolution.