Beta-connection: an approach to generate families of models from planar sections

A new three-dimensional reconstruction technique is presented that uses an integer control parameter, denoted β, to produce a family of models from a given set of planar cross-sections. Parameter β supports multiple choices for solving the correspondence problem, i.e., the problem of deciding which regions from two consecutive cross-sections must be connected into a single component. Thus, unlike current reconstruction methods, the beta-connection algorithm enables the consideration of multiple alternatives when establishing region correspondence. In addition to this flexibility, which is useful in creating models with complex topologies, the algorithm produces PL-manifolds and respects the re-sampling condition, thus providing an interesting reconstruction solution for many practical visualization and numerical simulation applications.