Quality tetrahedral mesh smoothing via boundary-optimized Delaunay triangulation

Authors:
Zhanheng Gao;Zeyun Yu;Michael Holst
Affiliations:
Department of Computer Science, University of Wisconsin at Milwaukee, USA and College of Computer Science and Technology, Jilin University, China;Department of Computer Science, University of Wisconsin at Milwaukee, USA;Department of Mathematics, University of California, San Diego, USA
Venue:
Computer Aided Geometric Design
Year:
2012

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Abstract

Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing ''bad'' triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the L^1 error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method.