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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 {xi}), “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 [12872]4, and can similarly be expected to show 2nd order convergence with the surface resolution.


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