参数化CAD中参数有效范围的算法研究

Research on an algorithm for solving valid range of parameters in parametric CAD

为了解决在参数化CAD系统中由于参数赋值不合理而导致的几何实体重建失败的问题,提出了确定一类二维参数化CAD模型中参数有效范围的代数算法。该算法可以实时求解所有简单多边形中距离约束参数的有效取值范围,并利用几何变换简化求解规模,提高求解效率。研究结果表明,该算法提供的有效取值范围内的任一赋值,均可保证重建后几何实体的拓扑形状不发生改变,在一定程度上提高了参数化CAD软件的设计效率和人机交互的智能化水平。同时对算法复杂度进行了分析,该算法的复杂度为O(n^2)。

To resolve the problem that in parametric CAD systems, unreasonable parameter values in a parametric model often result in an improper shape of a geometric object, the paper proposes an algebraic algorithm for determining the valid range of parameter values in certain 2-dimensional parametric CAD models. This algorithm can solve the valid value range of distance constraint parameters in all simple polygons in real time, and make use of the geometric transformation to sim- plify the solving scale and improve the solving efficiency. The result of the study shows that all values within the valid range provided by this algorithm can ensure that the topological shape of a geometric object does not change after recon- struction, and to some extent, this algorithm can improve the efficiency of parametric CAD software design and the intel- lectual level of human-computer interaction. The analysis shows the complexity of this algorithm is O（n2）.