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, 459470.

S.C. Chou and X.S. Gao,
On the Parameterization of Algebraic Curves,
Journal of Applicable Algebra in Engineering,
Communication and Computing, 3, 2738 (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), 125136.

X.S. Gao and M. Li,
Rational Quadratic Approximation to Real Algebraic Curves,
Computer Aided Geometric Design, 21, 805828, 2004.

M. Li, X.S. Gao, and S.C. Chou,
Quadratic Approximation to Plane
Parametric Curves and Applications in Approximate Implicitization,
Visual Computers, 22, 906917, 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, 861874 2005.
 J.S. Cheng and X.S. Gao,
Constructing Blending Surface for Two Arbitrary Surfaces (in
Chinese), Journal of Engineering Graphics, 26(1), 3944, 2005.
Proper Reparametrization

E.W. Chionh, X.S. Gao and L.Y. Shen,
Inherently improper surface parametric supports,
Computer Aided Geometric Design, 23, 629639, 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, 331339, 2006.

J. Li, L. Shen, X.S. Gao,
Proper Reparametrization of Rational Ruled
Surface, Journal of Computer Science and Technology, 23(2), 290297, 2008.
Topology Determination
 J.S. Cheng, X.S. Gao, and M. Li,
Determine the Topology of Real Algebraic Surfaces,
Mathematics of Surfaces, 121146, LNCS, SpringerVerlag, 2005.

X.S. Gao and M. Li,
Rational Quadratic Approximation to Real Algebraic Curves,
Computer Aided Geometric Design, 21, 805828, 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, 8993, 2009.
 J.S. Cheng, X.S. Gao, J. Li,
Topology determination and isolation for implicit plane curves.
{\em Proc. ACM Symposium on Applied Computing}, 11401141, ACM Pres, 2009.