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- Jiansong Deng, Falai Chen, Li-Yong Shen
- ISSAC
- 2005

The μ-bases of rational curves/surfaces are newly developed tools which play an important role in connecting parametric forms and implicit forms of the rational curves/surfaces. They provide efficient algorithms to implicitize rational curves/surfaces as well as algorithms to compute singular points of rational curves and to reparametrize rational… (More)

- Eng-Wee Chionh, Xiao-Shan Gao, Li-Yong Shen
- Computer Aided Geometric Design
- 2006

We identify a class of monomial supports that are inherently improper because any surface rational parametrization defined on them is improper. A surface support is inherently improper if and only if the gcd of the normalized areas of the triangular sub-supports is non-unity. The constructive proof of this claim can be used to detect all and correct almost… (More)

- Li-Yong Shen, Chun-Ming Yuan
- J. Systems Science & Complexity
- 2010

Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univariate resultant computations. This method is more efficient than the other… (More)

- Li-Yong Shen, Chun-Ming Yuan, Xiao-Shan Gao
- Computer Aided Geometric Design
- 2012

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric… (More)

- Sonia Pérez-Díaz, Li-Yong Shen
- J. Symb. Comput.
- 2014

The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to determine and find the standard form. In this paper, we present algorithms to determine whether a given implicit surface is a… (More)

- Ying Chen, Li-Yong Shen, Chun-Ming Yuan
- Computer Aided Geometric Design
- 2011

- Li-Yong Shen, Min Wu, Zhengfeng Yang, Zhenbing Zeng
- SNC
- 2009

In this paper, we study positively invariant sets of a class of nonlinear loops and discuss the relation between these sets and the attractors of the loops. For the canonical Hénon map, a numerical method based on curve fitting is proposed to find a positively invariant set containing the strange attractor. This work can be generalized to find… (More)

- Jia Li, Li-Yong Shen, Xiao-Shan Gao
- 2007 10th IEEE International Conference on…
- 2007

Summary form only given. In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization… (More)

- Li-Yong Shen, Eng-Wee Chionh, Xiao-Shan Gao, Jia Li
- J. Systems Science & Complexity
- 2011

- Li-Yong Shen, Min Wu, Zhengfeng Yang, Zhenbing Zeng
- J. Systems Science & Complexity
- 2013