Singularity Analysis of Geometric Constraint Systems

Singularity analysis is an importantsubject of the geometric constraint satisfaction problem. In this paper,three kinds of singularities are described and correspondingidentification methods are presented for both under-constrained systemsand over-constrained systems. Another special but common singularity forunder-constrained geometric systems, pseudo-singularity, is analyzed.Pseudo-singularity is caused by a variety of constraint matching ofunder-constrained systems and can be removed by improving constraintdistribution. To avoid pseudo-singularity and decide redundantconstraints adaptively, a differentiation algorithm is proposed in thepaper. Its correctness and efficiency have been validated through itspractical applications in a 2D/3D geometric constraint solver CBA.