Early-split coding of triangle mesh connectivity

The two main schemes for coding triangle mesh connectivity traverse a mesh with similar region-growing operations. Rossignac's Edgebreaker uses triangle labels to encode the traversal whereas the coder of Touma and Gotsman uses vertex degrees. Although both schemes are guided by the same spiraling spanning tree, they process triangles in a different order, making it difficult to understand their similarities and to explain their varying compression success.We describe a coding scheme that can operate like a label-based coder similar to Edgebreaker or like a degree-based coder similar to the TG coder. In either mode our coder processes vertices and triangles in the same order by performing the so-called "split operations" earlier than previous schemes. The main insights offered by this unified view are (a) that compression rates depend mainly on the choice of decoding strategy and less on whether labels or degrees are used and (b) how to do degree coding without storing "split" offsets. Furthermore we describe a new heuristic that allows the TG coder's bit-rates to drop below the vertex degree entropy.