The problem of maintaining a valid mesh (triangulation) within a certain domain that deforms over time arises in many applications. During a period for which the underlying mesh topology remains unchanged, the deformation moves vertices of the mesh and thus potentially turns a mesh invalid, or as we call it,  tangled . We introduce the notion of  locally removable regions , which are certain tangled regions in the mesh that allow for local removal and re-meshing. We present an algorithm that is able to quickly compute, through local explorations, a minimum locally removable region containing a "seed" tangled region in an invalid mesh. By re-meshing within this area, the "seed" tangled region can then be removed from the mesh without introducing any new tangled region. The algorithm is output-sensitive in the sense that it never explores outside the output region.
['Pankaj K. Agarwal', 'Bardia Sadri', 'Hai Yu']
Untangling triangulations through local explorations