Shen Liyong  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 

  1. 2016.09~2017.10 Department of Physics and Mathematics, University of Alcalá

  2. 2016.05~2017.04 Department of Computer Science, Rice University

  3. 2015.11~2016.01 Department of Computer Science, Rice University

  4. 2015.09~2015.10 Graduate School of Science and Technology, Niigata University

  5. 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



International Journal

1.      Sonia Pérez-Díaz and Liyong ShenComputing the μ-basis of algebraic monoid curves and surfaces, Computers & Graphics, Volume 97, June 2021, Pages 78-87.

2.      Sonia Pérez-Díaz and Liyong ShenThe μ-basis of improper rational parametric surface and its application, Mathematics, 9(6), 640, 2021

3.      Chunming Yuan, Sonia Pérez-Díaz and Liyong ShenA Survey of the Representations of Rational Ruled SurfacesJournal of Systems Science and Complexity,, 2021.

4.      Sonia Pérez-Díaz and Liyong ShenInversion, Degree, Reparametrization and Implicitization of Improperly Parametrized Planar Curves Using µ-BasisComputer Aided Geometric Design, Vol.84, 101957, 2021.

5.      Chunming Yuan., Zhenpeng Mi, Xiaohong Jia, Fenming Lin, and Liyong Shen,   Tool Orientation Optimization and Path Planning for 5-Axis MachiningJournal of Systems Science and Complexity, Vol. 34, 83–106, 2021.

6.      Sonia Pérez-Díaz and Liyong Shen, Parametrization of rational translational surfaces. Theoretical Computer Sciences, Vol. 835, 156-167, 2020.

7.      Sonia Pérez-Díaz, Liyong ShenA Symbolic-Numeric Approach for Parametrizing Ruled SurfacesJournal of Systems Science and Complexity, Vol.33, 799–820, 2020.

8.      Shanshan Yao, Yifei Feng, Xiaohong Jia, Liyong Shen, A package to compute implicit equations for rational curves and surfaces, ACM Communications in Computer Algebra, Vol 53(2), 33-36, 2019 (Software Presentation in ISSAC’2019).

9.      Liyong Shen, Sonia Pérez-Díaz, Ron Goldman, Yifei Feng, Representing rational curve segments and surface patches using semi-algebraic sets, Computer Aided Geometric Design, Vol.74, 101770, 2019.

10.  Liyong Shen, Sonia Pérez-Díaz, Zhengfeng Yang, Numerical Proper Reparametrization of Space Curves and SurfacesComputer-Aided Design, Vol.106, 13-29, 2019.

11.  Liyong Shen, Sonia Pérez-Díaz, Numerical polynomial reparametrization of rational curvesComputer Aided Geometric Design, Vol. 71, 90-104, 2019. (GMP’2019)

12.  Fengming Lin, Liyong Shen, ChunMing Yuan, Zhenpeng Mi, Certified space curve fitting and trajectory planning for CNC machining with cubic B-splinesComputer-Aided Design. Vol. 106, 13-29,2019. (Invited paper presentation in SIAM/GD 2019)

13.  Liyong Shen, Ron Goldman, Combining complementary methods for implicitizing rational tensor product surfaces, Computer-Aided Design, 104, 100-112, 2018

14.  Liyong Shen, Ron Goldman, Implicitizing Rational Tensor Product Surfaces Using the Resultant of Three Moving Planes ACM Transactions on Graphics, Vol. 36, No. 5, Article 167, 2017. (Presented in Siggraph 2018)

15.  Liyong Shen, Ron Goldman, Strong µ-bases for rational tensor product surfaces and extraneous factors associated to bad base points and anomalies at infinitySIAM Journal on Applied Algebra and GeometryVol.1(1), 328–351, 2017.

16.  Liyong Shen, Ron Goldman, Algorithms for Computing Strong μ-Bases for Rational Tensor Product SurfacesComputer Aided Geometric Design, 52-53, 48 – 62. Geometric Modeling and Processing 2017 (Best Paper Award).

17.  Zhenpeng Mi, Chun-Ming Yuan, Xiaohui Ma, Liyong Shen, Tool orientation optimization for 5-axis machining with C-space method, The International Journal of Advanced Manufacturing Technology, Vol.88(5), 1243–1255, 2017.

18.  Liyong ShenComputing μ-bases from algebraic ruled surfacesComputer Aided Geometric Design, Vol. 46, 125-130, 2016.

19.  Ruyong Feng, Liyong ShenComputing the intersections of three conics according to their Jacobian curveJournal of Symbolic Computation, Vol. 73, 175-191,2016.

20.  Liyong Shen and Sonia Pérez-Díaz, Numerical proper reparametrization of parametric plane curvesJournal of Computational and Applied Mathematics. Vol. 277, 138–161, 2015.

21.  Zhengyuan Yang, Liyong Shen, ChunMing Yuan, XiaoShan Gao, Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splinesComputer-Aided Design. Vol. 66, 62-72,2015.

22.  Liyong Shen and Sonia Pérez-Díaz, Determination and (re)parametrization of rational developable surfacesJournal of Systems Science and Complexity, Vol. 28, 1426-1439, 2015.

23.  Bao Hai, Liyong ShenActive and Passive Factors of Oil PricesJournal of Donghua University (English Edition), Vol.2, 284-287, 2015.

24.  Liyong Shen and Sonia Pérez-Díaz, Characterization of rational ruled surfacesJournal of Symbolic Computation. Vol. 63, 21-45, 2014.

25.  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.

26.  Liyong shenSingularities of the Determinantal Curve of Three ConicsJournal of information and computational science, Vol. 9(3) : 575- 582, 2012.

27.  Bin Wu, Liyong Shen, Min Wu, Zhengfeng Yang, Zhenbing Zeng, Generating Preconditions for Termination of Loop ProgramsInternational Journal of Advancements in Computing Technology, Vol.4(7), 349-359, 2012.

28.  Liyong Shen, Jinsan Cheng, Xiaohong Jia, Homeomorphic approximation of the intersection curve of two rational surfacesComputer Aided Geometric Design, Vol. 29(8), 613-625, 2012.

29.  Liyong Shen, Chunming Yuan, Xiaoshan Gao, Certified Approximation of Parametric Space Curves with Cubic B-spline CurvesComputer Aided Geometric Design, Vol. 29(8), 648-663, 2012.

30.  Liyong Shen, Engwee Chionh, Xiao-Shan Gao and Jia Li, Proper reparametrization for inherently improper unirational varietiesJournal of System science and Complexity, Vol.24 (2): 367-380, 2011.

31.  Yin Chen, Liyong Shen and Chunming Yuan, Collision and intersection detection of two ruled surfaces using bracket methodComputer Aided Geometric Design, Vol.28, 114-126, 2011.

32.  Liyong Shen and Chunming Yuan, Implicitization using univariate resultantsJournal of System science and Complexity, Volume 23, Number 4, 804-814, 2010.

33.  Jia Li, Liyong Shen and Xiao-Shan Gao, Proper Reparametrization of Rational Ruled SurfaceJournal of Computer Science and technology, Vol. 23(2): 290-297, Mar. 2008.

34.  Falai Chen, Liyong Shen and Jiansong Deng, Implicitization and Parameterization of Quadratic and Cubic Surfaces by μ-BasesComputing, Springer, Vol.79, No.2-4, 131-142, 2007.4.

35.  Engwee Choinh, Xiao-Shan Gao and Liyong ShenInherently Improper Surface Parametric SupportsComputer Aided Geometric Design, 23, 629-639, 2006.

National Journal

36.  Shitao He, Liyong Shen, A Class of Parameterization Method of Accumulated Average Arc Length for Parametric Curves, Journal of Jilin University (Science Edition ), 59(2), 286-294, 2021, in Chinese.

37.  Yan Gao, Liyong Shen, Screen Defect Detection Based on Edge Detection, accepted by J. Sys. Sci. & Math. Scis., 2021, in Chinese.

38.  Shitao He, Liyong Shen, A Class of Parameterization Method of the Accumulated Average Arc Length for Parametric Curves, accepted by Journal of Jilin University, in Chinese 2021.

39.  Zhirong Jin, Liyong Shen, Time Optimal Trajectory Planning Based on Quadratic B-Spline, J. Sys. Sci. & Math. Scis., Vol.38(12), 1364-1375, 2018, in Chinese.

40.  Yuanyuan Wu, Liyong Shen, Imbalanced fuzzy multiclass support vector machine algorithm based on class-overlap degree undersampling, Journal of University of Chinese Academy of Sciences, Vol.35(4), 536-543, 2018, in Chinese.

41.  Xiaohui Ma, Fengming Lin, Liyong Shen, Optimal subdivision parameters of planar Bezier curvesJournal of University of Chinese Academy of Sciences, Vol.33(3), 311-316, 2016, in Chinese.

42.  Zhengyuan Yang, Liyong ShenB-spline curve fitting the gas explosion data curve fitting with multi-constraintsJournal of graphics, Vol.35(4), 595-602, 2014, in Chinese.

43.  Xiaohua Chen, Yufu Chen, Liyong ShenParametrization of a rational developable surface using the μ-basisJournal of the graduate school of Chinese Academy of Sciences, Vol.29(3), 289-293, 2012.

44.  Liyong ShenThe mu-basis and implicitization of space curvesJournal of computer aided design and computer graphics, 900-904, Vol.7, 2009, in Chinese.

45.  Liyong Shen, Chunming Yuan, Approximation proper reparametrization of rational curvesJournal of computer aided design and computer graphics,924-929, Vol.7,2009, in Chinese.

46.  Liyong Shen, zhangjin Huang, A class of curve subdivision schemes with several parametersJournal of computer aided design and computer graphics, Vol.4, 468-472, 2007, in Chinese.

47.  Yang Liu, Liyong ShenAn Algebraic Condition for Classifying the Positional Relationship of Two Planar EllipsesJournal of computer aided design and computer graphics, 555-560, 2003, in Chinese.

48.  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.


49.  Yuanyuan Wu, Liyong Shen, Sanguo Zhang, Fuzzy multiclass support vector machines for unbalanced data, Proc. of 29th Chinese Control and Decision Conference (CCDC’2017), 2227-2231, 2017

50.  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, ASCM’2014, 2014

51.  Sonia Pérez-Díaz and Li-Yong ShenParametrization of translational surfaces, Proc. 2014 Internat. Symp. on Symbolic-numeric Comput. (SNC 2014),128-129.

52.  Liyong ShenError Bounded Conic Spline Approximation for NC Code, Proc. of ICMV’2011, SPIE 8439.

53.  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 (ICCSA 2010), LNCS 6019, 482–496.

54.  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.

55.  Liyong Shen, Min Wu and Zhengfeng Yang, Simplification of numerical rational surfaces. Prof. of IEEE International Joint Conference on Computational Sciences and Optimization (CSO 2009), Vol.1, 617-621.

56.  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 (SNC 2009), 185-190.

57.  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.

58.  Jiansong Deng, Falai Chen, and Liyong ShenComputing the μ-bases of Rational Curves and Surfaces Using the Polynomial Matrix Factorization, Proceeding of ISSAC’2005, 132-139, ACM Press, 2005.


Li-Yong Shen, Haohao Wang, Jerzy Wojdylo, Linear Algebra, Mercury Learning & Information, Dulles, Virginia, Boston, Massachusetts, New Delhi, ISBN: 978-1-68392-376-3 Pub Date: January 2019.

Li-Yong Shen, Haohao Wang, Jerzy Wojdylo, Linear Algebra, Overseas Press India Private Limited, ISBN: 978-81-938368-7-3 Pub Date: 2018.

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).