The concept of optimal Delaunay triangulation (ODT) and the
corresponding error-based quality metric are first introduced.
Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the
concept of ODT is examined. With regard to its problem of possible producing
illegal elements, this paper proposes a modified smoothing scheme with a constrained
optimization model for tetrahedral mesh quality improvement. The constrained optimization
model is converted to an unconstrained one and then solved by integrating chaos
search and BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm
efficiently. Quality improvement for tetrahedral mesh is finally achieved by
alternately applying the presented smoothing scheme and re-triangulation. Some
testing examples are given to demonstrate the effectiveness of the proposed
Cite this paper
S. Sun, H. Bao, M. Liu and Y. Yuan, "Quality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation," Intelligent Information Management
, Vol. 5 No. 6, 2013, pp. 191-195. doi: 10.4236/iim.2013.56021
 L. Chen and J. Xu, “Optimal Delaunay Triangulations,” Journal of Computational Mathematics, Vol. 22, No. 2, 2004, pp. 299-308.
 L. Chen, “Mesh Smoothing Schemes Based on Optimal Delaunay Triangulations,” Proceedings of 13th International Meshing Roundtable, Williamsburg 19-22 September 2004, pp. 109-120.
 P. Alliez, D. Cohen-Steiner, M. Yvinec and M. Desbrun, “Variational Tetrahedral Meshing,” ACM Transactions on Graphics, Vol. 24, No. 3, 2005, pp. 617-625.http://dx.doi.org/10.1145/1073204.1073238
 X. S. Li, “An Efficient Approach to a Class of Non-Smooth Optimization Problems,” Science in China Series A, Vol. 24, No. 4, 1994, pp. 371-377.
 S. L. Sun and J. F. Liu, “An Efficient Optimization Procedure for Tetrahedral Meshes by Chaos Search Algorithm,” Journal of Computer Science and Technology, Vol. 18, No. 6, 2003, pp. 796-803.http://dx.doi.org/10.1007/BF02945469
 J. F. Liu, S. L. Sun and D. C.Wang, “Optimal Tetrahedralization for Small Polyhedron: A New Local Transformation Strategy for 3-d Mesh Generation and Mesh Improvement,” CMES: Computer Modeling in Engineering & Sciences, Vol. 14, No. 1, 2006, pp. 31-43.