Abstract
We present a novel approach named T-Base for smoothing planar and surface quadrilateral meshes. Our motivation is that the best shape of quadrilateral element—square—can be virtually divided into a pair of equilateral right triangles by any of its diagonals. When move a node to smooth a quadrilateral, it is optimal to make a pair of triangles divided by a diagonal be equilateral right triangles separately. The finally smoothed position is obtained by weighting all individual optimal positions. Three variants are produced according to the determination of weights. Tests by the T-Base are given and compared with Laplacian smoothing: The Vari.1 of T-Base is effectively identical to Laplacian smoothing for planar quad meshes, while Vari.2 is the best. For the quad mesh on underlying parametric surface and interpolation surface, Vari.2 and Vari.1 are best, respectively.
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Acknowledgments
This research was supported by the Natural Science Foundation of China (Grant Numbers 40602037 and 40872183) and the Fundamental Research Funds for the Central Universities of China.
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Mei, G., Tipper, J.C., Xu, N. (2013). T-Base: A Triangle-Based Iterative Algorithm for Smoothing Quadrilateral Meshes. In: Lu, W., Cai, G., Liu, W., Xing, W. (eds) Proceedings of the 2012 International Conference on Information Technology and Software Engineering. Lecture Notes in Electrical Engineering, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34531-9_32
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DOI: https://doi.org/10.1007/978-3-642-34531-9_32
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