Shen Liyong   Asso. Professor
Address: School of Mathematical Sciences, University of the Chinese Academy of Sciences 19A Yuquanlu, Beijing,  P. R. China
Postcode: 100049

Research Areas

Computer aided geometric design, geometric modeling, collision detection, computer numerical control;
symoblic computation, implictization, proper reparametrization of rational curves and surfaces;
termination of program verification


2000~2005 PHD, Dept. of Mathmetics, University of Science and Technology of China
1996~2000 Bachelor, Dept. of Mathmetics, University of S
Science and Technology of China


Work Experience

2008.12~ School of mathematical Science, Graduate university of Chinese Academy of Sciences 

2016.05~Department of Computer Science, Rice University

2015.11~2016.01 Department of Computer Science, Rice University

2015.09~2015.10 Graduate School of Science and Technology, Niigata University

2010.02~2010.05 Department of Computer Science, Hongkong University

2007.07~2008.12 Shanghai Key Lab of Trustworthy Computing Software Engineering Institute, East normal university of China
2005.07~2007.07 Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Teaching Experience

2008.12~   Computer aided geometric design, Numerical analysis, Maple and its application
2007.07~2008.12  Matrix analysis, Mathematics Modeling



1. Liyong Shen,yang Liu, An Algebraic Condition for the Positional Relationship of an Ellipse and a Parabola(Hyperbola),Journal of system simulation,1208-1211, 2002, In chinese.
2. Yang Liu,Liyong Shen, An Algebraic Condition for Classifying the Positional Relationship of Two Planar Ellipses,Journal of computer aided design and computer graphics, 555-560, 2003. In chinese.
3. Liyong Shen, zhangjin Huang, A class of curve subdivision schemes with several parameters,Journal of computer aided design and computer graphics,Vol.4, 468-472, 2007.In chinese.
4. Liyong Shen, The mu-basis and implicitization of space curves, Journal of computer aided design and computer graphics,900-904, Vol.7,2009. In chinese.
5. Liyong Shen,Chunming Yuan, Approximation proper reparametrization of rational curves,Journal of computer aided design and computer graphics,924-929,Vol.7,2009. In chinese.
6. Jiansong Deng, Falai Chen, and Liyong Shen. Computing the μ-bases of Rational Curves and Surfaces Using the Polynomial Matrix Factorization, Proceeding of ISSAC’2005, 132-139, ACM Press, 2005.
7. Falai Chen, Liyong Shen and Jiansong Deng, Implicitization and Parameterization of Quadratic and Cubic Surfaces by μ-Bases, Computing, Springer, Vol.79, No.2-4, 131-142, 2007.4.
8. Liyong Shen, Falai Chen, Bert Juttler and Jiansong Deng, Approximate μ-Bases of Rational Curves and Surfaces, Proceedings of GMP ‘2006, M.S. Kim and K. Shimada eds., LNCS, 4077, 175-188, 2006.
9. Engwee Choinh, Xiao-Shan Gao and Liyong Shen,Inherently Improper Surface Parametric Supports, Computer Aided Geometry Design, 23, 629-639, 2006.
10. Liyong Shen, Engwee Chionh, Xiao-Shan Gao and Jia Li, Inherently Improper Parametric Supports for Unirational Varieties,Journal of System science and Complexity,24 (2): 367-380, 2011.
11. Jia Li, Liyong Shen and Xiao-Shan Gao, Proper Reparametrization of Rational Ruled Surface, Journal of Computer Science and technology 23(2): 290-297, Mar. 2008
12. Liyong Shen and Chunming Yuan, Implicitization using univariate resultants, Journal of Systems Science and Complexity Volume 23, Number 4, 804-814, 2010.
13. Bin Wu, Liyong Shen, Zongqin Bi and Zhenbin Zeng. Termination of a Class of the Program with Polynomial Guards. Proc. of IEEE International Conference on Information management and engineering (ICIME 2009), 274-277, 2009.
14. Liyong Shen, Min Wu and Zhengfeng Yang, Simplification of numerical rational surfaces. Proc. of IEEE International Joint Conference on Computational Sciences and Optimization (CSO 2009), Vol.1, 617-621.
15. Liyong Shen, Min Wu, Zhengfeng Yang and Zhenbin Zeng, Finding Positively Invariant Sets of a Class of Nonlinear Loops via Curve Fitting,ACM Symbolic and Numerical Computation (SNC2009), 185-190
16. Bin Wu, Liyong Shen, Zongqin Bi and Zhenbin Zeng. Termination of loop programs with polynomial guards, Proc. of International Conference on Computational Science and Applications 2010, LNCS 6019, 482–496.
17.Liyong Shen, Error Bounded Conic Spline Approximation for G01 Code, Proc. of International Conference on Machine Vision(ICMV,2011), SPIE 8359.
18. Yin Chen, Liyong Shen and Chunming Yuan, Collision and intersection detection of two ruled surfaces using bracket method, Computer Aided Geometry Design 2011 vol.28, 114-126, 2011.
19. Liyong shen, Singularities of the Determinantal Curve of Three Conics, journal of information and computational scince,Vol. 9 (3) : 575- 582, 2012.
20.Xiaohua Chen, Yufu Chen, Liyong Shen, Parametrization of a rational developable surface using the μ-basis, Journal of the graduate school of Chinese Academy of Sciences, Vol29(3), 289-293, 2012.
21. Bin Wu,Liyong Shen, Min Wu, Zhengfeng Yang, Zhenbing Zeng, Generating Preconditions for Termination of Loop Programs, International Journal of Advancements in Computing Technology, v 4, n 7, p 349-359, 2012.
22. Liyong Shen, Jinsan Cheng, Xiaohong Jia, Homeomorphic approximation of the intersection curve of two rational surfaces, Computer Aided Goemetric Design, Vol 29(8), 613-625, 2012.
23. Liyong Shen, Chunming Yuan, Xiaoshan Gao, Certified Approximation of Parametric Space Curves with Cubic B-spline Curves, Computer Aided Goemetric Design, Vol 29(8), 648-663, 2012.
24. Liyong Shen,Min Wu Zhenfeng Yang, Zhenbin Zeng, Generating Exact Nonlinear Ranking Functions by Symbolic-Numeric Hybrid Method,Journal of Systems Science and Complexity, Vol 26, 291-301, 2013.
25. Shen, Li-Yong and Perez-Diaz, Sonia, Characterization of rational ruled surfaces, J. Symbolic Comput. 63, 21--45,2014.
26. Pérez-Díaz and L.-Y. Shen, Determination and (re)parametrization of rational developable surfaces, Journal of Systems Science and Complexity. Accepted. (2014)
27.S. Pérez-Díaz and L.-Y. Shen, Parametrization of Translational Surfaces, Proceedings SNC2014, ACM, 128-129, 2014.
28.Liangyu Chen, Tuo Leng, Liyong Shen, Min Wu, Zhengfeng Yang and Zhenbing Zeng, Finding the Symbolic Solution of a Geometric Problem Through Numerical Computations, Proc. of Computer Mathematics, Springer-Verlag Berlin Heidelberg, 223-241, 2014.
29. Shen, Liyong and Perez-Diaz, Sonia, Numerical proper reparametrization of parametric plane curves, Journal of Computational and Applied Mathematics.Vol. 277, 138–161,2015
30. Zhengyuan Yang, Li-Yong Shen, Chun-Ming Yuan, Xiao-Shan Gao,Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splines,Computer-Aided Design. Vol 66, 62-72,2015.
Ruyong Feng, Li-Yong Shen, Computing the intersections of three conics according to their Jacobian curve, Journal of Symbolic Computation. Available online 2015 doi:10.1016/j.jsc.2015.06.004. 

32.Zhenpeng Mi, Chun-Ming Yuan, Xiaohui Ma, Li-Yong Shen, Tool orientation optimization for 5-axis machining with C-space method, Int J Adv Manuf Technol (2016). doi:10.1007/s00170-016-8849-0.

33. Li-Yong Shen, computing μ-basis from algebraic ruled surfaces​, Computer Aided Geometric DesignVolume 46, August 2016, Pages 125–130.

34. Li-Yong Shen, Ron Goldman, Strong µ-bases for rational tensor product surfaces and extraneous factors associated to bad base points and anomalies at infinity. to appear in SIAM Journal on Applied Algebra and Geometry, 2017. 

35. Li-Yong Shen, Ron Goldman, Algorithms for Computing Strong μ-Bases for Rational Tensor Product Surfaces, to Appear in Computer Aided Geometric DesignVolume, 2017.f

Research Interests

Approximation of the curves and surfaces, Intersection of the surfaces,
Proper reparametrization, Collision detection of geometric model.
Termination of the program


     1. The Fourteenth Annual Chinese-American Kavli Frontiers of Science Symposium, Shenzhen, China, Nov. 2011, (Organization Committee). 
2. The Fourth Computer Mathematics Conference of China, Guangzhou, China, Nov. 2011, (Program Committee).
3. International Conference on Software and Computing Technology Otc. 2010,. Kunming, China.
4. The Thirteenth Annual Chinese-American Kavli Frontiers of Science Symposium, Irvine, CA, USA, Sept. 2010.
5. The Third Computer Mathematics Conference of China, Shanghai, China, Oct. 2010.
6. International Conference on Algebraic Geometry and Geometric Modeling, July 21-26, 2009, Lijiang, China. Technical report.
7. International Conference on Mathematics Mechanization-In honor of Prof. Wen-Tsun Wu’s ninth birthday. Beijing, May 11-13, 2009.
8. IEEE International Joint Conference on Computational Sciences and Optimization (CSO 2009), Sectional Report. Sanya, China, April 23-27, 2009.
9. The 15th Computer aided design and computer graphics conferences (CAD/CG), Liaoning, Dalian, 2008, 07, conferences report.
10. International Seminar on Symbolic Real Algebra and Trustworthy Computing, ECNU, Shanghai, China, Mar., 2008, (Organization Committee).