**Distance Ranked Connectivity
Compression of Triangle Meshes **

We present a new, single-rate
method for compressing the connectivity information of a connected 2-manifold triangle
mesh with or without boundary. Traditional compression schemes interleave
geometry and connectivity coding, and are thus typically unable to utilise
information from vertices (mesh regions) they have not yet processed. With the
advent of competitive point cloud compression schemes, it has become feasible
to develop separate connectivity encoding schemes which can exploit complete,
global vertex position information to improve performance.

Our scheme demonstrates the
utility of this separation of vertex and connectivity coding. By traversing the
mesh edges in a consistent fashion, and using global vertex information, we can
predict the position of the vertex which completes the unprocessed triangle
attached to a given edge. We then rank the vertices in the neighbourhood of this predicted position by their
Euclidean distance. The distance rank of the correct closing vertex is stored. Typically,
these rank values are small, and the set of rank values thus possesses low
entropy and compresses very well. The sequence of rank values is all that is
required to represent the mesh connectivity — no special split or merge codes
are necessary.

Results indicate improvements
over traditional valence-based schemes for more regular triangulations. Highly irregular
triangulations or those containing a large number of slivers are not well
modelled by our current set of predictors and mayyieldpoorerconnectivitycompressionratesthanthoseprovidedbythebestvalence-basedschemes.