A New Mesh Deformation Techinique for Simplicial and Non-Simplicial Meshes

We present a mesh deformation scheme based on a pseudo-structure defined by a network of linear springs. Departing from the classical edge spring method, our springs are specifically constructed in such a way as to oppose element collapsing. Both for simplicial and non simplicial structured and unstructured meshes, an invalid element is formed when a mesh vertex leaves its ball, i.e. the polyhedral cavity formed by all triangular faces (in three dimensions) or edges (in two dimensions) that are edge-connected to the vertex. Therefore, our procedures are based on the idea of connecting by a linear spring each vertex in the grid with its normal projection on the ball boundaries. This way mesh entanglement is avoided by construction of the pseudo-structure, which in turn allows for large grid deformations with minimum need for remeshing. The new method is here compared with the classical edge spring and torsional spring techniques highlighting the performance improvements achieved by the new procedure.