Computational techniques for automatically tiling and skinning branched objects

Reconstructing the surfaces of objects from planar contours can be done by either tiling (connecting contours with polygonal facets) or skinning (connecting contours with parametric spline surfaces). In this paper, we break down the surface reconstruction problem into three steps for tiling (grouping, transition, tiling) and four steps for skinning (grouping, transition, parameter correspondence, skinning). Many techniques for completing the grouping, tiling and skinning steps exist. However, the transition step, while treated in the literature, does not have an adequate solution for the most general contours. In this paper, we present a computational technique for completing the transition step, as well as offer new solutions to the grouping and parameter correspondence steps. Our techniques are implemented in a computer environment for a variety of multi-branched objects whose contours vary significantly in shape. In addition it requires no user interaction. Illustrative examples are included.