Since transmitting various files around Internet is one of common activities in everyday life, the compression is important technical issue in these days. Shape models are also frequently transmitted and therefore its compression has also been studied. Considering the large portion of shape model can be normal vectors, a new scheme was recently presented to compress normal vectors using clustering and mixed indexing scheme. Presented in this paper is a mathematical investigation of the scheme to analyze the probability distribution of normal index distances in Normal Index array which is critical for the compression. The probability distribution is formulated so that the values can be easily calculated once the relative probabilities of C, R, E, S, and L op-codes in Edgebreaker are known. It can be shown that the distribution of index distances can be easily transformed into a few measures for the compression performance of the proposed algorithm.

As the transmission of 3D shape models through Internet becomes more important, the compression issue of shape models gets more critical. The issues for normal vectors have not yet been explored as much as it deserves, even though the size of the data for normal vectors can be significantly larger than its counterparts of topology and geometry. Presented in this paper is an approach to compress the normal vectors of a shape model represented in a mesh using the concept of clustering. It turns out that the proposed approach has a significant compression ratio without a serious sacrifice of the visual quality of the model.