A three dimensional triangulation problem

Russell Miller (University of Manchester)

Frank Adams 2,

In this talk we consider the discrete geometric problem of finding an embedding of a three dimension finite element mesh in Euclidean space, given a subset of the dihedral angles defined on the tetrahedra. I will first present a review of results in the two dimensional case. Then I will derive the geometric constraints imposed on the dihedral angles of the tetrahedra and illustrate how these constraints define a locally unique embedding. This problem is important in the context of discrete EIT, since without knowledge of the underlying geometric constraints we cannot derive uniqueness results for discrete conductivity distributions on meshes with arbitrary interior vertex positions.

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