On the Optimality of Valence-based Connectivity Coding

We show that the average entropy of the distribution of valences in valence sequences for the class of manifold 3D triangle meshes and the class of manifold 3D polygon meshes is strictly less than the entropy of these classes themselves. This implies that, apart from a valence sequence, another essential piece of information is needed for valence-based connectivity coding of manifold 3D meshes. Since there is no upper bound on the size of this extra piece of information, the result implies that the question of optimality of valence-based connectivity coding is still open.