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Displaying 1-20 out of 20 total
Complete Solution Classification for the Perspective-Three-Point Problem
Found in: IEEE Transactions on Pattern Analysis and Machine Intelligence
By Xiao-Shan Gao, Xiao-Rong Hou, Jianliang Tang, Hang-Fei Cheng
Issue Date:August 2003
pp. 930-943
<p><b>Abstract</b>—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 decomposition algorithm to giv...
 
AI in China: A Survey
Found in: IEEE Intelligent Systems
By Xiao-shan Gao, Dan-tong Ouyang, Ji-gui Sun, San-jiang Li, Tian-shun Yao, Ru-zhan Lu, Chun-yi Shi, Zhan-gang Han, Jue Wang, Cun-gen Cao, Ruqian Lu
Issue Date:November 2008
pp. 26-32
This article consists of nine short essays discussing research pursued by AI researchers in China and their perspectives on research in several AI subareas. The article first introduces the mechanization of mathematics, an area in which Chinese scientists ...
 
Rational Quadratic Approximation to Real Plane Algebraic Curves
Found in: Geometric Modeling and Processing
By Xiao-Shan Gao, Ming Li
Issue Date:April 2004
pp. 93
An algorithm is proposed to give a global approximation to an implicit real plane algebraic curve with rational quadratic B-splines. The algorithm consists of three steps: curve segmentation, segment approximation and curve tracing. The curve is first divi...
 
Classification and Solving of Merge Patterns in Geometric Constraint Solving
Found in: Shape Modeling and Applications, International Conference on
By Xiao-Shan Gao, Gui-Fang Zhang
Issue Date:May 2003
pp. 89
A basic idea of geometric constraint solving is to divide a large geometric constraint problem into several subproblems according to certain patterns and then to merge these subproblems to obtain a solution to the original problem. In this paper, we give a...
 
Construct Piecewise Hermite Interpolation Surface with Blending Methods
Found in: Geometric Modeling and Processing
By Xiao-Shan Gao, Ming Li
Issue Date:July 2002
pp. 53
Three methods are proposed to construct a piecewise Hermite interpolation surface (PHIS), which is a piecewise algebraic surface interpolating a set of given points with associated normal directions. The surface is obtained by blending together some low-de...
 
Sparse difference resultant
Found in: Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation (ISSAC '13)
By Chun-Ming Yuan, Wei Li, Xiao-Shan Gao
Issue Date:June 2013
pp. 275-282
In this paper, the concept of sparse difference resultant for a Laurent transformally essential system of Laurent difference polynomials is introduced and its properties are proved. In particular, order and degree bounds for the sparse difference resultant...
     
Sparse differential resultant
Found in: Proceedings of the 36th international symposium on Symbolic and algebraic computation (ISSAC '11)
By Cum-Ming Yuan, Wei Li, Xiao-Shan Gao
Issue Date:June 2011
pp. 225-232
In this paper, the concept of sparse differential resultant for a differentially essential system of differential polynomials is introduced and its properties are proved. In particular, a degree bound for the sparse differential resultant is given. Based o...
     
Root isolation for bivariate polynomial systems with local generic position method
Found in: Proceedings of the 2009 international symposium on Symbolic and algebraic computation (ISSAC '09)
By Jia Li, Jin-San Cheng, Xiao-Shan Gao
Issue Date:July 2009
pp. 5-6
A local generic position method is proposed to isolate the real roots of a bivariate polynomial system ∑={f(x,y),g(x,y)}. In this method, the roots of the system are represented as linear combinations of the roots of two univariate polynomial equatio...
     
Topology determination and isolation for implicit plane curves
Found in: Proceedings of the 2009 ACM symposium on Applied Computing (SAC '09)
By Jia Li, Jin-San Cheng, Xiao-Shan Gao
Issue Date:March 2009
pp. 1-5
A method is proposed to generate an isolation for a plane curve, which is a set of boxes covering the curve, having the same topology as the curve, and approximating the curve to any given precision. The method uses symbolic computation to guarantee correc...
     
Complete numerical isolation of real zeros in zero-dimensional triangular systems
Found in: Proceedings of the 2007 international symposium on Symbolic and algebraic computation (ISSAC '07)
By Chee-Keng Yap, Jin-San Cheng, Xiao-Shan Gao
Issue Date:July 2007
pp. 92-99
We present a complete numerical algorithm of isolating all the real zeros of a zero-dimensional triangular polynomial system Fn Z[x1…,xn]. Our system Fn is general, with no further assumptions. In particular, our algorithm successfully treat multiple...
     
Resolvent systems of difference polynomial ideals
Found in: Proceedings of the 2006 international symposium on Symbolic and algebraic computation (ISSAC '06)
By Chun-Ming Yuan, Xiao-Shan Gao
Issue Date:July 2006
pp. 101-108
In this paper, a new theory of resolvent systems is developed for prime difference ideals and difference ideals defined by coherent and proper irreducible ascending chains. Algorithms to compute such resolvent systems are also given. As a consequence, we p...
     
Spatial geometric constraint solving based on k-connected graph decomposition
Found in: Proceedings of the 2006 ACM symposium on Applied computing (SAC '06)
By Gui-Fang Zhang, Xiao-Shan Gao
Issue Date:April 2006
pp. 979-983
We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a well-constrained problem into some smaller ones if possible. We also show how to merge two rigid bodies if they share two or t...
     
Editorial message: technical track on geometric computing and reasoning
Found in: Proceedings of the 2006 ACM symposium on Applied computing (SAC '06)
By Dominique Michelucci, Pascal Schreck, Xiao-Shan Gao
Issue Date:April 2006
pp. 962-962
Geometric Computing and Reasoning (GCR) is a new track of SAC and it is dedicated to the recent trends in the domain of geometric constraint solving and automated, or computer aided, deduction in geometry.
     
Decomposition of differential polynomials with constant coefficients
Found in: Proceedings of the 2004 international symposium on Symbolic and algebraic computation (ISSAC '04)
By Mingbo Zhang, Xiao-Shan Gao
Issue Date:July 2004
pp. 175-182
In this paper, we present an algorithm to decompose differential polynomials in one variable and with rational number as coefficients. Besides arithmetic operations, the algorithm needs only factorization of multi-variable polynomials and solution of linea...
     
Rational general solutions of algebraic ordinary differential equations
Found in: Proceedings of the 2004 international symposium on Symbolic and algebraic computation (ISSAC '04)
By Ruyong Feng, Xiao-shan Gao
Issue Date:July 2004
pp. 155-162
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 solution if it exists. The algorithm is based on the relation ...
     
Geometric constraint solving via C-tree decomposition
Found in: Proceedings of the eighth ACM symposium on Solid modeling and applications (SM '03)
By Gui-Fang Zhang, Xiao-Shan Gao
Issue Date:June 2003
pp. 45-55
This paper has two parts. First, we propose a method which can be used to decompose a geometric constraint graph into a c-tree. With this decomposition, solving for a well-constrained problem is reduced to the solving for smaller rigid bodies if possible. ...
     
Solving spatial basic geometric constraint configurations with locus intersection
Found in: Proceedings of the seventh ACM symposium on Solid modeling and applications (SMA '02)
By Christoph M. Hoffmann, Wei-Qiang Yang, Xiao-Shan Gao
Issue Date:June 2002
pp. 95-104
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 involving points, lines, and planes containing up to six g...
     
Automated geometry theorem proving by vector calculation
Found in: Proceedings of the 1993 international symposium on Symbolic and algebraic computation (ISSAC '93)
By Jing-Zhong Zhang, Shang-Ching Chou, Xiao-Shan Gao
Issue Date:July 1993
pp. 284-291
We discuss in this paper the problems arised in the implementation in Macsyma of a direct algorithm for computing the formal solutions of differential systems in the neighborhood of regular singular point.The differential system to be considered is of the ...
     
Solving parametric algebraic systems
Found in: Papers from the international symposium on Symbolic and algebraic computation (ISSAC '92)
By Shang-Ching Chou, Xiao-Shan Gao
Issue Date:July 1992
pp. 335-341
We discuss in this paper the problems arised in the implementation in Macsyma of a direct algorithm for computing the formal solutions of differential systems in the neighborhood of regular singular point.The differential system to be considered is of the ...
     
Computations with parametric equations
Found in: Proceedings of the 1991 international symposium on Symbolic and algebraic computation (ISSAC '91)
By Shang-Ching Chou, Xiao-Shan Gao
Issue Date:July 1991
pp. 122-127
We discuss in this paper the problems arised in the implementation in Macsyma of a direct algorithm for computing the formal solutions of differential systems in the neighborhood of regular singular point.The differential system to be considered is of the ...
     
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