中文摘要：

为提高二维对称几何模型重构的整体品质，反映其初始的设计意图，提出二维对称几何模型的约束重构理论及方法。首先构建参数化点，反射对称以对称轴为中心将对称部分的点集作镜像变换映射到基本点集的一边，旋转对称以旋转中心点为中心将对称部分的点集作旋转变换映射到基本点集的一边，形成参数化的点集。其次识别并处理二维曲线间的约束以及对称模型的边界约束。最后将参数化的点集与基本点集一起作为曲线拟合的目标点集，建立带约束的目标拟合函数，将其转化成无约束优化问题，采用L-M方法迭代求解。实例表明反求结果在满足初始几何约束的同时，能够保证几何模型严格的对称。

英文摘要：

In order to improve the whole quality of reconstruction model and reflect the original design intention, theory and method are proposed to solve the constraint reconstruction problem of 2D symmetry geometry model. Firstly, the parametric points are constructed： the reflectional symmetry points are mirrored through the symmetry axis, and the rotational symmetry points are rotated about the rotational center. Secondly, the constraints between curves and the boundary constraints of the symmetry model are identified and handled. Finally, the objective fitting function with constraints is constructed based on objective points which include the parametric and the basic points. The optimization problem is recursively solved using L-M method. The examples show that the results of reconstruction not only satisfy the original constraints but keep rigid symmetric.