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- Xiao-Shan Gao, Xiaorong Hou, Jianliang Tang, Hang-Fei Cheng
- IEEE Trans. Pattern Anal. Mach. Intell.
- 2003

In this paper, we use two approaches to solve the Perspective-Three-Point (P3P) problem: the algebraic approach and the geometric approach. In the algebraic approach, we use Wu-Ritt’s zero… (More)

- Xiao-Shan Gao, Shang-Ching Chou
- ISSAC
- 1992

For a parametric polynomial system: p1 = 0, · · · , pr = 0, d1 6= 0, · · · , ds 6= 0 where pi and di are in K[u1, · · · , um, x1, · · · , xn] and the u are parameters, we present a method for… (More)

- Xiao-Shan Gao, Christoph M. Hoffmann, Wei-Qiang Yang
- Symposium on Solid Modeling and Applications
- 2002

A basic idea of geometric constraint solving is to decompose the constraint problem into smaller ones according to some basic configurations. In this paper, we find all spatial basic configurations… (More)

- Ruyong Feng, Xiao-Shan Gao
- ISSAC
- 2004

We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For an autonomous first order ODE, we give an algorithm to compute a rational general… (More)

- Xiao-Shan Gao, Shang-Ching Chou
- Computer-Aided Design
- 1998

This paper reports a geometric constraint solving approach based on symbolic computation. With this approach, we can compute robust numerical solutions for a set of equations. We give complete… (More)

- Xiao-Shan Gao, Qiang Lin
- Automated Deduction in Geometry
- 2002

We introduce a software package, MMP/Geometer, developed by us to automate some of the basic geometric activities including geometric theorem proving, geometric theorem discovering, and geometric… (More)

- Ruyong Feng, Xiao-Shan Gao
- J. Symb. Comput.
- 2006

We improve the algorithm given in [3]. Through analysing the structural properties of a first order autonomous ODE with a rational solution, we give a polynomial time algorithm to find a rational… (More)

- Shang-Ching Chou, Xiao-Shan Gao, Jing-Zhong Zhang
- Journal of Automated Reasoning
- 1996

We present a set of rules based on full-angles as the basis of automated geometry theorem proving. We extend the idea of eliminating variables and points to the idea of eliminating lines. We also… (More)

- Xiao-Shan Gao
- J. Symb. Comput.
- 2003

- Shang-Ching Chou, Xiao-Shan Gao, Jing-Zhong Zhang
- LICS
- 1993

We present a method which can produce traditional proofs for a class of geometry statements whose hypotheses can be described constructively and whose conclusions can be represented by polynomial… (More)