Dihedral deformation and rigidity.

We consider defining the embedding of a triangle mesh into R3, up to translation, rotation, and scale, by its vector of dihedral angles. On the theoretical side, we show that locally the map from realizable vectors of dihedrals to mesh embeddings is one-to-one almost everywhere. On the implementation side, we are interested in using the dihedral parameterization in shape analysis. This demands a way to visualize statistical results, for instance an average shape. To this end, we give a heuristic method for mapping interpolations in dihedral space to interpolations between input mesh embeddings, and we visualize statistical analyses of several families of organic shapes.