快速判定几何约束奇异性的切面扰动法

针对冗余奇异和分支奇异的判定问题,提出一种新的切面扰动的判定方法.该方法将奇异的雅可比矩阵分为独立构型空间和奇异空间,变量沿独立构型空间的切面扰动,计算更新的雅克比矩阵的秩,依据秩亏的变化可以快速、稳定地判定约束奇异性.该算法克服了残量扰动法的数值迭代、计算量大和不稳定的缺点,并且在参数化特征造型系统InteSolid中得到验证.

A Perturbation on Tangent Plane Algorithm for Determining Geometric Constraint Singularity Efficiently

Singularity is an important factor that affects directly solving efficiency and ability of a geometric constraint solver.This paper presents a novel perturbation on tangent-plane algorithm to effectively differentiate between redundant and embranchment singular constraints.The presented algorithm obtains redundant constraint set by analyzing singular Jacobian matrix with Gaussian Elimination Method.Then,singular Jacobian matrix is separated into independent configuration space and singular space,and constraint system variables are divided into independent configuration space variables and singular space variables.Set a perturbing value for singular space variables,the increment of independent configuration space variables can be worked out by the relation of the two kinds of variables.Recalculating the rank of Jacobian matrix,embranchment singularity and redundant singularity can be differentiated in terms of the change of the rank deficit that the constraint is a redundant singular constraint if the rank deficit unchanged,otherwise an embranchment singular constraint.This method avoids numerical iteration solution and has the advantages over CRPM(Constraint Residue Perturbation Method) of less computational time and lower complexity.Some examples are given to illustrate the process of the approach.Its correctness and efficiency have been validated through its practical applications in parametric modeling system InteSolid.