Singularity Analysis of Geometric Constraint Systems

Singularity analysis is an important subject of the geometric constraint satisfaction problem. In this paper, three kinds of singularities are described and corresponding identification methods are presented for both under-constrained systems and over-constrained systems. Another special but common singularity for under-constrained geometric systems, pseudo-singularity, is analyzed. Pseudo-singularity is caused by a variety of constraint matching of under-constrained systems and can be removed by improving constraint distribution. To avoid pseudo-singularity and decide redundant constraints adaptively, a diferentiation algorithm is proposed in the paper. Its correctness and efficiency have been validated through its practical applications in a 2D/3D geometric constraint solver CBA. This research is partly supported by the National ‘863’ High-Tech Programme of China under grant No.9842-003. PENG Xiaobo received his B.S. and M.S. degrees from Huazhong University of Science and Technology, Wuhan, in 1995 and 1998 respectively. Now he is a Ph.D. candidate in the National CAD Support Software Engineering Research Center, Huazhong University of Science & Technology. He specializes in geometric constraint solving, solid modeling and design automation. His current research activities focus on the research of key technologies of 3D variable geometry, whose primary goal is to provide an effective geometric constraint solver for 2D/3D CAD system applications. CHEN Liping received his Ph.D. degree from Huazhong University of Science and Technology, Wuhan, in 1995. He is currently a professor in the National CAD Support Software Engineering Research Center, Huazhong University of Science & Technology. His research interests are in the areas of geometric constraint solving, kinematics and dynamics, feature-based and dimension-driven solid modeling and CAD/CAM integration. ZHOU Fanli is a Ph.D. candidate in the National CAD Support Software Engineering Research Center, Huazhong University of Science & Technology, Wuhan. His research interests include kinematics, dynamics and stimulation. ZHOU Ji received his Ph.D. degree from the State University of New York at Buffalo in 1984. He is a member of Chinese Academy of Engineering and a professor at Huazhong University of Science & Technology, Wuhan. His research interests focus on CAD/CAM systems, geometric modeling, optimization and intelligent design.