Encoding Quadrilateral Meshes

An important problem in geometric compression is to find succinct representations (encoding schemes) for the conectivity of polygonal meshes. In this note, we show that the encoding scheme discussed in [1] for quadrilateral mesh connectivity can be improved from 3.5 bits per vertex to less than 3 bits per vertex. We also show that an easy equivalence between the labelling schemes of King et al [2] and of Kronrod-Gotsman [1], improves this further to 2.67 bits per vertex. The same upper bound has also been reported in [2], making an involved use of the CLRES labelling scheme.