12th International Meshing Roundtable
September 1417, 2003
Santa Fe, New Mexico, U.S.A.
Center for Applied Mathematics
Cornell University, Ithaca, NY 14853
shontz@cam.cornell.edu
Department of Computer Science
Cornell University, Ithaca, NY 14853
vavasis@cs.cornell.edu
Abstract
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 suficient conditions for a mesh to resist inversion by a
transformation. We prove that our algorithm yields exact results for a?ne mappings and state a conjecture for more
general mappings. In addition, we prove that our algorithm converges to the same point as both the local weighted
laplacian smoothing algorithm and the GaussSeidel algorithm for linear systems. We test our algorithmís robustness
and present some numerical results. Finally, we use our algorithm to study the movement of the canine heart.
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