摘要
针对两个刚体之间的三维几何约束求解问题,依据几何约束的参数结构分析了角度约束和距离约束的解耦性,给出了角度约束和距离约束可解耦求解的条件;然后对两个刚体之间的几何约束进行组合分析,总结出约束度不小于2的几何约束构成的组合只有几十种,且均可采用几何推理方法进行求解;最后阐述了附加方向约束、冗余约束和矛盾约束对数值求解的不利影响,提出了三维几何约束组合的分类求解策略,并用实例验证了该求解策略的有效性。
It is a key problem to solve the geometric constraint system between two rigid bodies(GCSBTRD) efficiently and stably when 3D geometric constraint system has been decomposed into a series of GCSBTRDs using equivalent constraint substitution method. In this paper, the decoupling conditions to separately solve angle constraints and distance constraints of GCSBTRDs are presented after analyzing the parametric structure of angle constraints and distance constraints. Then, with the geometric analysis of GCSBTRDs, it is found that the GCSBTRDs consisting of the geometric constraints with more than one constraint degrees can be divided into dozens of patterns, which can all be solved analytically by geometric reasoning method. Subsequently, the adverse impact on numerical solution of GCSBTRDs from additional direction constraint, redundant constraint and contradictory constraint is addressed to demonstrate the advantage of geometric reasoning method. Finally, a hybrid solving strategy based on the classification of constraint combinations is proposed to solve GCSBTRDs, whose effectiveness has been validated by a practical example.
出处
《图学学报》
CSCD
北大核心
2014年第2期236-242,共7页
Journal of Graphics
基金
国家自然科学基金资助项目(51375185)
中国工程物理研究院总体工程研究所创新与发展基金资助项目(13cxj19)
关键词
几何约束
解耦性分析
冗余约束
几何推理
geometric constraint
decoupling analysis
redundant constraint
geometric reasoning
