三维几何约束闭环的动态识别与满足

Dynamic Recognition and Solution of 3D Geometric Constraint Loops

针对三维几何约束闭环的满足问题 ,提出了“充分推理 +最小数值”的约束求解策略及其具体的实施方法 .自由度传播法可在动态求解约束的过程中识别出约束闭环 ;几何归约法将约束闭环子图归约简化为层次分明的归约树 ,并进一步明确了闭环的组成和结构 ;矢量闭环法建立了约束闭环的矢量模型 ,据此模型可以建立最小规模的方程组来求解约束闭环 ,方程组的变量具有明确的几何意义 ,便于初值的确定和多解的处理 ,并能求解欠约束的闭环 .

The strategy of “maximal reasoning+least variables” to solve 3D geometric constraint loop satisfaction problem is presented. The approach of DOF propagation can recognize the geometric constraint loops in the dynamic process of solving constraints. The method of geometric reduction simplifies the loop to a reducibility tree and clarifies the structure of the loop. The vector loop model with the least variables contained in the constraint equations is created. The variables have unambiguous geometric meaning, so it is easy to assign the initial value to the variables to cope with multi solution and under constrained problems.