Voxel-coding for tiling complex volumetric objects

This paper discusses voxel-coding for tiling complex volumetric objects with triangular meshes: first choosing cross-sections followed by extracting contours, and then triangulating them according to a given error threshold. The intervals between adjacent cross-sections and for sampling contour points for the tiling operation are determined by the difference in area between contour projections, enabling a relatively small number of triangles to reconstruct the object. Branching problems are solved by introducing a simplified skeleton extracted from the difference region and then finding matched segments of the skeleton for each contour i.e., converting multiple contour connections into a single pair connection. For all major problems involved in reconstruction, voxel-coding provides new and robust solutions. These problems include contour extraction, region filling with arbitrarily complex boundaries for difference region searches, simplified skeleton extraction, contour-skeleton matching, and mapping of curve pairs for contour tiling. The voxel-coding proposed can reconstruct surfaces from complex volumetric objects or contours themselves. The input data may have multiple branches or holes, and is processed in a fully automatic and systematic way. The algorithm is easy to implement, fast to compute and insensitive to abject complexity. This technique is of special importance for bridging discrete volumetric and continuous objects.