Constructive Methods for Algebraic Curves and Surfaces

Implicitization and Parametrization

• S.C. Chou and X.S. Gao, Implicitization of Rational Parametric Equations, Journal of Symbolic Computation, 1992, 14, 459--470.
• S.C. Chou and X.S. Gao, On the Parameterization of Algebraic Curves, Journal of Applicable Algebra in Engineering, Communication and Computing, 3, 27--38 (1992).
• X.S. Gao and S.C. Chou, On the Normal Parameterization of Curves and Surfaces, The International Journal of Computational Geometry & Applications, Vol. 1, No. 2 (1991), 125--136.
• X.S. Gao and M. Li, Rational Quadratic Approximation to Real Algebraic Curves, Computer Aided Geometric Design, 21, 805-828, 2004.
• M. Li, X.S. Gao, and S.C. Chou, Quadratic Approximation to Plane Parametric Curves and Applications in Approximate Implicitization, Visual Computers, 22, 906-917, 2006.
• M. Li, X.S. Gao, and J.S. Cheng, Generating Symbolic Interpolants for Scattered Satat with Normal Vectors, Journal of Computer Science and Technology, 20, 861-874 2005.
• J.S. Cheng and X.S. Gao, Constructing Blending Surface for Two Arbitrary Surfaces (in Chinese), Journal of Engineering Graphics, 26(1), 39-44, 2005.

Proper Reparametrization

• E.W. Chionh, X.S. Gao and L.Y. Shen, Inherently improper surface parametric supports, Computer Aided Geometric Design, 23, 629-639, 2006.
• J. Li and X.S. Gao, The Proper Parametrization of a Special Class of Rational Parametric Equations, J. of Sys. Sci. and Complexity, 19, 331-339, 2006.
• J. Li, L. Shen, X.S. Gao, Proper Reparametrization of Rational Ruled Surface, Journal of Computer Science and Technology, 23(2), 290-297, 2008.

Topology Determination

• J.S. Cheng, X.S. Gao, and M. Li, Determine the Topology of Real Algebraic Surfaces, Mathematics of Surfaces, 121-146, LNCS, Springer-Verlag, 2005.
• X.S. Gao and M. Li, Rational Quadratic Approximation to Real Algebraic Curves, Computer Aided Geometric Design, 21, 805-828, 2004.
• J.S. Cheng, X.S. Gao, J. Li, Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities, In {\em Computer Algebra in Scientific Computing}, LNCS 5743, 89-93, 2009.
• J.S. Cheng, X.S. Gao, J. Li, Topology determination and isolation for implicit plane curves. {\em Proc. ACM Symposium on Applied Computing}, 1140-1141, ACM Pres, 2009.