Biharmonic fields and mesh completion

We discuss bi-harmonic fields which approximate signed distancefields. We conclude that the bi-harmonic field approximation can be apowerful tool for mesh completion in general and complex cases. Wepresent an adaptive, multigrid algorithm to extrapolate signeddistance fields. By defining a volume mask in a closed region boundingthe area that must be repaired, the algorithm computes a signeddistance field in well-defined regions and uses it as anover-determined boundary condition constraint for the biharmonic fieldcomputation in the remaining regions. We discuss this approximation in practical examples in the case of triangular meshes resulting from laser scan acquisitions which require massive hole repair. We conclude that the proposed algorithm is robust and general, being able to deal with complex topological cases. Suggested Reviewers: Paolo Cignoni [email protected] Daniel Cohen-Or [email protected] Tao Ju [email protected] Peter Liepa [email protected]