Publications

Journal articles

Jin-San Cheng, Bingwei Zhang, Yikun Xiao, Ming Li: Topology-driven approximation to rational surface-surface intersection via interval algebraic topology analysis, accepted by SIGGRAPH2023 (to appear on ACM Transaction on Graphics).
Jin-San Cheng, Junyi Wen, Bingwei Zhang: Certified numerical real root isolation for bivariate nonlinear systems. Journal of Symbolic Computation, 114: 149-171, 2023
Xiaohong Jia, Kai Li, Jin-San Cheng: Computing the Intersection of Two Rational Surfaces Using Matrix Representations. Computer Aided Design, 150: 103303, 2022 .
Kai Jin, Jin-San Cheng: On the Complexity of Computing the Topology of Real Algebraic Space Curves. Journal of Systems Science and Complexity, 34(2): 809--826 (2021)
Kai Jin, Jin-San Cheng: On the Topology and Isotopic Meshing of Plane Algebraic Curves. Journal of Systems Science and Complexity, 33(1): 230--260 (2020)
Kai Jin, Jin-San Cheng: Isotopic Meshing of a Real Algebraic Space Curve.Journal of Systems Science and Complexity, 33(4): 1275--1296 (2020)
Jin-San Cheng, Xiaojie Dou, Junyi Wen: A new deflation method for verifying the isolated singular zeros of polynomial systems. Journal of Computational and Applied Mathematics. 376: 112825, 2020.
Xiaojie Dou, Jin-San Cheng. A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems. Mathematics 2018, 6, 166.
Jin-San Cheng, Kai Jin, A Generic Position Based Method for Real Root Isolation of Zero-Dimensional Polynomial Systems, Journal of Symbolic Computation, 68:204-224, 2015.
Cheng, J.-S., Jin, K., Lazard, D. Certified Rational Parametric Approximation of Real Algebraic Space Curves with Local Generic Position Method. Journal of Symbolic Computation, 58: 18--40, 2013.
Cheng, J.-S., Gao, X.-S.: Multiplicity Preserving Triangular Set Decomposition of Two Polynomials. Journal of Systems Science and Complexity, 27(6): 1320-1344, 2014.
Shen, L., Cheng, J.-S., Jia,X.: Homeomorphic approximation of the intersection curve of two rational surfaces. Computer Aided Geometric Design 29(8): 613-625 (2012).
Cheng, J.-S., Gao, X.-S., Guo, L. Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation. Journal of Symbolic Computation,47(7): 843-858 (2012).
Cheng, J.-S., Lazard, S., Penaranda, L., Pouget, M., Rouillier, F., and Tsigaridas, E. On the topology of planar algebraic curves, Mathematics in Computer Science, 2010(4):113-137.
Cheng, J.-S., Gao, X.-S., and Yap, C.K. Complete Numerical Isolation of Real Zeros in Zero-dimensional Triangular Systems, Journal of Symbolic Computation, 44(7): 768-785 (2009).
Cheng, J.-S., and Gao, X.-S. Constructing Blending Surface for Two Arbitrary Surfaces (in Chinese). Journal of Engineering Graphics, 26(1),2005, pp. 39-44.
Li, M., Gao, X.-S., and Cheng, J.-S. Generating Symbolic Interpolants for Scattered Data with Normal Vectors, Journal of Computer Science and Technology, Nov. 2005, Vol. 20, No.6, 861-874.
Wu, T., Lei, N., and Cheng, J.-S. Wu WenTsun Formulae for the blending of pipe surfaces. Northeast Math. J., 17(4), 2001, pp. 383-386.

Conference articles

Jin-San Cheng, Bingwei Zhang, Yikun Xiao, Ming Li: Topology-driven approximation to rational surface-surface intersection via interval algebraic topology analysis, to appear on ACM Transaction on Graphics (accepted by SIGGRAPH2023).
Qing Li, Yu-Shen Liu, Jin-San Cheng, Cheng Wang, Yi Fang, Zhizhong Han, HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces, Accepted by the 36th Conference on Neural Information Processing Systems (NeurIPS 2022).
Jin-San Cheng, Junyi Wen: Certified Numerical Real Root Isolation for Bivariate Polynomial Systems. ISSAC 2019: 90-97.
Jin-San Cheng, Junyi Wen, Wenjian Zhang: Plotting Planar Implicit Curves and Its Applications. ICMS 2018: 113--122.
Jin-San Cheng, Xiaojie Dou: Certifying Simple Zeros of Over-Determined Polynomial Systems. CASC 2017: 66--76.
Cheng, J.-S.: A New Criterion for the Existence of Real Zeros of Polynomial Systems (Extended abstract), ACA2013.
Li, J., Cheng, J.-S., Tsigaridas, E.P.: Local Generic Position for Root Isolation of Zero-Dimensional Triangular Polynomial Systems. CASC 2012: 186-197.
Cheng, J.-S., Gao, X.-S., and Guo, L., Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation, In proceeding of ASCM/MACIS2009, Kobe, Dec.2009.
Cheng, J.-S., Lazard, S., Penaranda, L., Pouget, M., Rouillier, F., and Tsigaridas, E. On the topology of planar algebraic curves, In Proc. SoCG 2009 (Full paper).
Cheng, J.-S., Gao, X.-S., and Li, J. Topology determination and isolation for implicit plane curves. SAC 2009: 1140-1141
Cheng, J.-S., Gao, X.-S., and Li, J. Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities. CASC 2009: 89-93
Cheng, J.-S., Gao, X.-S., and Li, J. Root Isolation for Bivariate Polynomial Systems with Local Generic Position Method, Proc. ISSAC'09, ACM Press, Souel, 2009.
Cheng, J.-S., Lazard, S., Penaranda, L., Pouget, M., Rouillier, F., and Tsigaridas, E. On the topology of planar algebraic curves, In Proc. of the 24th European Workshop on Computational Geometry, March 2008 (abstract).
Cheng, J.-S., Gao, X.-S., and Yap, C.K. Complete Numerical Isolation of Real Zeros in General Triangular Systems , Proc. ISSAC'07, 92-99, ACM Press, New York, 2007.
Cheng, J.-S., Gao, X.-S., and Li, M. Determining the Topology of Real Algebraic Surfaces, Mathematics of Surfaces XI, R. Martin, H. Bez, M. Sabin (editors), LNCS 3604, Springer-Verlag, 2005, pp. 121-146.
Cheng, J.-S. Blending Quadric Surfaces via Base Curve Method , Proceeding of ASCM2003, Ziming Li and William Sit (editors), World Scientific, 2003, pp. 77-85.

Posters

Cheng, J.-S., Gao, X.-S., and Li, M., The Intrinsic Topology Determination of Real Algebraic Surfaces. Poster at ISSAC2005, Jul. 2005, Beijing, China.

Thesis

Topology determination and approximation of real algebraic curves and surfaces (in Chinese).
Ph.D. thesis in sciences, Key Lab of Mathematics Mechanization, AMSS, CAS, advised by Professor Xiao-Shan Gao Beijing, 2006.