An algorithm for voxelised solids representation using chain codes

The paper introduces a new method to describe the surfaces of voxelised solids. It operates in three stages: a hierarchical linked list of chain code sequences is created first; the linked lists are pruned; and, finally, the content of the data structure is stored. The method uses chain codes from either a three- or nine-symbols alphabet. In the first case, two chain code symbols are needed to access the next face, while, in the second case, this is done by one symbol. The pair of chain codes from the three-symbols alphabet, or the individual symbol from the nine-symbols alphabet are considered as tokens. The sets of tokens are, in both cases, extended by two tokens, indicating the beginning and ending of the list. The method processes solids of any shape, including those containing holes, cavities, or multiple components existing in the same voxel space. Edge-connectivity is permitted. The method was compared against the method proposed by Lemus et al., which is designed for solids without holes. Although supporting a broader set of voxelised solids, the proposed method generates sequences of tokens that are, on average, up to 10% shorter. Since the information entropy of the sequences of tokens produced by the proposed method is also smaller, the obtained sequences are more compressible, as confirmed by applying gzip and bzip2 data compressors.