A Mesh Warping Algorithm Based on Weighted Laplacian Smoothing

We present a new mesh warping algorithm for tetrahedral meshes based upon weighted laplacian smoothing. We start with a 3D domain which is bounded by a triangulated surface mesh and has a tetrahedral volume mesh as its interior. We then suppose that a movement of the surface mesh is prescribed and use our mesh warping algorithm to update the nodes of the volume mesh. Our method determines a set of local weights for each interior node which describe the relative distances of the node to its neighbors. After a boundary transformation is applied, the method solves a system of linear equations based upon the weights to determine the final position of the interior nodes. We study mesh invertibility and prove a theorem which gives sufficient conditions for a mesh to resist inversion by a transformation. We prove that our algorithm yields exact results for affine mappings and state a conjecture for more general mappings. In addition, we prove that our algorithm converges to the same point a...

• Type: Conference
• Year: 2003
• Where: IMR
• Authors: Suzanne M. Shontz, Stephen A. Vavasis
• Keywords: Computational Geometry, IMR 2003, Mesh Warping Algorithm, Surface Mesh, Weighted Laplacian Smoothing