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.

展开是一种空间变形技术，用于展平折叠的 3-D 域。在某些情况下，这是对空间数据进行正确建模的有用过程；然而，有时很难申请。大多数可用的算法仅设计用于轻轻折叠的几何图形或需要敏感输入才能正常工作，例如控制线和点。这里提供了一种稳健的基于几何的方法，旨在简化这种转换，即使对于复杂的情况也是如此。这是一个三步法。首先，通过骨架化提取变形的参考表面。其次，使用多维缩放来展平参考表面。第三，折叠对象通过优化技术映射到扁平空间。提出了一个挖掘案例研究，其中将所提出的方法应用于多个折叠域，并取得了良好的结果。