Optimizing Surface Triangulation Via Near Isometry with Reference Meshes

Authors:
Xiangmin Jiao;Narasimha R. Bayyana;Hongyuan Zha
Affiliations:
College of Computing, Georgia Institute of Technology, Atlanta, GA 30332, USA;College of Computing, Georgia Institute of Technology, Atlanta, GA 30332, USA;College of Computing, Georgia Institute of Technology, Atlanta, GA 30332, USA
Venue:
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Year:
2007

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Abstract

Optimization of the mesh quality of surface triangulation is critical for advanced numerical simulations and is challenging under the constraints of error minimization and density control. We derive a new method for optimizing surface triangulation by minimizing its discrepancy from a virtual reference mesh. Our method is as easy to implement as Laplacian smoothing, and owing to its variational formulation it delivers results as competitive as the optimization-based methods. In addition, our method minimizes geometric errors when redistributing the vertices using a principle component analysis without requiring a CAD model or an explicit high-order reconstruction of the surface. Experimental results demonstrate the effectiveness of our method.