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“Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation”
Zhonggui Chen, Wenping Wang, Bruno Lévy, Ligang Liu and Feng Sun
SIAM Journal Scientific Computing, 2014

Abstract: This paper proposes a new algorithm to generate a graded three-dimensional tetrahe- dral mesh. It revisits the class of methods based on optimal Delaunay triangulation (ODT) and pro- poses a proper way of injecting a background density function into the objective function minimized by ODT. This continuous/analytic point of view leads to an objective function that is continuous and Delaunay consistent, in contrast with the discrete/geometrical point of view developed in previous work. To optimize the objective function, this paper proposes a hybrid algorithm that combines a local search (quasi-Newton) with a global optimization (simulated annealing). The benefits of the method are both improved performances and an improved quality of the result in terms of dihedral angles. This results from the combination of two effects. First, the local search has a faster speed of convergence than previous work due to the better behavior of the objective function, and second, the algorithm avoids getting stuck in a poor local minimum. Experimental results are evaluated and compared using standard metrics.

BibTex reference

   TITLE      = "Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generati
   AUTHOR     = "Zhonggui Chen and Wenping Wang and Bruno Lévy and Ligang Liu a
                   nd Feng Sun",
   JOURNAL    = "SIAM Journal Scientific Computing",
   YEAR       = "2014",