基于分层维的自由曲面反求建模技术研究

Layering Dimension-based Free Surface Modeling Technology in Reverse Engineering

针对CMM测量数据的特点,提出了基于分层维的自由曲面建模技术,以分层维量作为分层依据进行数据分层,利用首尾判断法进行层内数据的排序,建立了大规模数据的拓扑关系。以此为前提,研究并优化了NURBS求值快速算法,通过符号运算将B样条基函数描述为分段多项式的形式,通过分层维的设定来确定最小初始化数组,利用一个临时多项式存储中间计算结果,最终在大规模计算时进行的是多项式的求值,有效地加快了运算速度。经实例验证,本算法是准确可行的,满足工程实际需求。

With characteristics of CMM data, the free surface modeling technology based on layering dimension was put forward. According to the layering dimension quantity, the data sorting was realized. The method of beginning and end determination was used to rank the order of layer inner points, and then the topology relation was established. An optimal algorithm for B-spline evaluation was presented. The symbolic manipulation was used and a B-spline basis function was expressed as piecewise polynomials through coefficient calculation. The layering dimension was set to determine the minimum initial array. In such a way, the computing velocity was enhanced. The example shows that this algorithm is accurate and feasible. It meets the demand of engineering.