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Submesh Splines over Hierarchical T-meshes  

Jin, Liangbing (Department of Mathematics, Zhejiang Normal University)
Deng, Jiansong (Department of Mathematics, University of Science and Technology of China)
Chen, Falai (Department of Mathematics, University of Science and Technology of China)
Publication Information
International Journal of CAD/CAM / v.9, no.1, 2010 , pp. 47-53 More about this Journal
Abstract
In this paper we propose a new type of splines-biquadratic submesh splines over hierarchical T-meshes. The biquadratic submesh splines are in rational form consisting of some biquadratic B-splines defined over tensor-product submeshes of a hierarchical T-mesh, where every submesh is around a cell in the crossing-vertex relationship graph of the T-mesh. We provide an effective algorithm to locate the valid tensor-product submeshes. A local refinement algorithm is presented and the application of submesh splines in surface fitting is provided.
Keywords
hierarchical T-mesh; submesh splines; local refinement; surface fittingy;
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1 L. Piegl and W. Tiller, The NURBS Book, 2nd ed. New York: Springer-Verlag, 1997.
2 Z. Huang, J. Deng, Y. Feng, and F. Chen, "New proof of dimension formula of spline spaces over T-meshes via smoothing cofactors", Journal of Computational Mathematics, 24(4), 2006, pp. 501-514.
3 D. R. Forsey and R. H. Bartels, "Hierarchical B-spline refinement", Computer Graphics, 22(4), 1988, pp. 205-212.   DOI
4 J. Deng, F. Chen, X. Li, C. Hu, W. Tong, Z. Yang, and Y. Feng, "Polynomial splines over hierarchical T-meshes", Graphical Models, 70, 2008, pp. 76-86.   DOI
5 G. Farin, Curves and Surfaces for CAGD-A Practical Guide, 5th ed. Morgan Kaufmann Publishers, 2002.
6 M. S. Floater and K. Hormann, "Surface parameterization: A tutorial and survey", in Advances in Multiresolution for Geometric Modelling, N. A. Dodgson, M. S. Floater , and M. A. Sabin, Eds. Springer-Verlag, 2004, pp. 157-186.
7 M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle, "Multiresolution analysis of arbitrary meshes", in SIGGRAPH 95 Proceedings, New York: ACM Press, 1995, pp. 173-182.
8 J. Deng, F. Chen, and L. Jin, "Dimensions of biquadratic spline spaces over T-meshes", Preprint, arXiv: math. NA/0804.2533, 29pages.
9 T. W. Sederberg, J. Zheng, A. Bakenov, and A. Nasri, "Tsplines and T-NURCCs", ACM Transactions on Graphics, 22(3), 2003, pp. 161-172.
10 J. Deng, F. Chen, and Y. Feng, "Dimensions of spline spaces over T-meshes", Journal of Computational and Applied Mathematics, 194, 2006, pp. 267-283.   DOI   ScienceOn
11 R. Kraft, "Adaptive and linearly independent multilevel Bsplines", in Surface Fitting and Multiresolution Methods, A. L. Mehaute, C. Rabut, and L. L. Schumaker, Eds. Nashville: Vanderbilt University Press, 1998, pp. 209-218.
12 T. W. Sederberg, D. L. Cardon, G. T. Finnigan, N. S. North, J. Zheng, and T. Lyche, "T-spline simplification and local refinement", ACM Transactions on Graphics, 23(3), 2004, pp. 276-283.   DOI   ScienceOn