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Linked References

1. H. Prautzsch and Q. Chen, “Analyzing midpoint subdivision,” Computer Aided Geometric Design, vol. 28, no. 7, pp. 407–419, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
2. D. Zorin, P. Schroder, and W. Sweldens, “Interpolating subdivision for meshes with arbitrary topology,” in Proceedings of the Computer Graphics Conference (ACM SIGGRAPH '96), pp. 189–192, August 1996. View at Scopus
3. X. Li and J. Zheng, “An alternative method for constructing interpolatory subdivision from approximating subdivision,” Computer Aided Geometric Design, vol. 29, no. 7, pp. 474–484, 2012. View at Publisher · View at Google Scholar
4. E. Catmull and J. Clark, “Recursively generated B-spline surfaces on arbitrary topological meshes,” Computer-Aided Design, vol. 10, no. 6, pp. 350–355, 1978. View at Scopus
5. D. Doo and M. Sabin, “Behaviour of recursive division surfaces near extraordinary points,” Computer-Aided Design, vol. 10, no. 6, pp. 356–360, 1978. View at Scopus
6. D. Levin, N. Dyn, and J. Gregory, “A butterfly subdivision scheme for surface interpolation with tension control,” ACM Transactions on Graphics, vol. 9, pp. 160–169, 1990.
7. L. Kobbelt, “$\sqrt{3}$-subdivision,” in Proceedings of the Computer Graphics Conference (ACM SIGGRAPH '00), pp. 103–112, July 2000. View at Scopus
8. C. Loop, Smooth subdivision surfaces based on triangles [M.S. thesis], Department of Mathematics, University of Utah, 1987.
9. U. Reif, “A unified approach to subdivision algorithms near extraordinary vertices,” Computer Aided Geometric Design, vol. 12, no. 2, pp. 153–174, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
10. J. Sadeghi and F. F. Samavati, “Smooth reverse Loop and Catmull-Clark subdivision,” Graphical Models, vol. 73, no. 5, pp. 202–217, 2011. View at Publisher · View at Google Scholar · View at Scopus
11. M. K. Jena, P. Shunmugaraj, and P. C. Das, “A non-stationary subdivision scheme for generalizing trigonometric spline surfaces to arbitrary meshes,” Computer Aided Geometric Design, vol. 20, no. 2, pp. 61–77, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
12. Y. J. Lee and J. Yoon, “Non-stationary subdivision schemes for surface interpolation based on exponential polynomials,” Applied Numerical Mathematics, vol. 60, no. 1-2, pp. 130–141, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. H. Zhang and J. G. Sun, “Weight-based direct manipulation of FFD,” Chinese Journal of Computers, vol. 25, no. 9, pp. 910–915, 2002 (Chinese). View at Scopus
14. A. A. Ball and D. J. T. Storry, “Conditions for tangent plane continuity over recursively generated b-spline surfaces,” ACM Transactions on Graphics, vol. 7, no. 2, pp. 83–102, 1988. View at Publisher · View at Google Scholar
15. D. Zorin and P. Schröder, “A unified framework for primal/dual quadrilateral subdivision schemes,” Computer Aided Geometric Design, vol. 18, no. 5, pp. 429–454, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. J. Peters and U. Reif, “Analysis of algorithms generalizing b-spline subdivision,” SIAM Journal on Numerical Analysis, vol. 35, no. 2, pp. 728–748, 1998. View at Publisher · View at Google Scholar
17. G. Umlauf, “Analyzing the characteristic map of triangular subdivision schemes,” Constructive Approximation, vol. 16, no. 1, pp. 145–155, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
18. D. Zorin, “A method for analysis of $C^1$-continuity of subdivision surfaces,” SIAM Journal on Numerical Analysis, vol. 37, no. 5, pp. 1677–1708, 2000. View at Publisher · View at Google Scholar
19. D. Zorin, “Subdivision for modeling and animation,” in Proceedings of the Computer Graphics Conference (ACM SIGGRAPH '96), ACM Press, New Orleans, La, USA, 2000.
20. J. Zhang, “C-curves: an extension of cubic curves,” Computer Aided Geometric Design, vol. 13, no. 3, pp. 199–217, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
21. Y. Lü, G. Wang, and X. Yang, “Uniform trigonometric polynomial B-spline curves,” Science in China. Series F, vol. 45, no. 5, pp. 335–343, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
22. X. J. Zhao, Research on mesh surface modeling [Doctor’s thesis], Zhejiang University, 2006.
23. C. de Boor, K. Höllig, and S. Riemenschneider, Box Splines, vol. 98 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993.
24. G. Li and W. Ma, “Composite $\sqrt{2}$ subdivision surfaces,” Computer Aided Geometric Design, vol. 24, no. 6, pp. 339–360, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
25. P. Oswald and P. Schröder, “Composite primal/dual $\sqrt{3}$-subdivision schemes,” Computer Aided Geometric Design, vol. 20, no. 3, pp. 135–164, 2003. View at Publisher · View at Google Scholar