A robust unfolding approach for 3-D domains

Unfolding is a spatial deformation technique used to flatten folded 3-D domains. It is a useful procedure to correctly model spatial data in some cases; however, it is sometimes difficult to apply. Most available algorithms are designed only for gently folded geometries or require sensitive inputs to work well, such as control lines and points. Here a robust geometric-based approach is provided aiming to simplify this transformation, even for complex cases. It is a three steps methodology. First, a reference surface for deformation is extracted via skeletonization. Second, the reference surface is flattened using multidimensional scaling. Third, the folded objects are mapped to the flattened space via optimization techniques. A mining case study is presented where the proposed approach is applied for several folded domains, with good results.