曲率自适应条件下特征点选取的非均匀B样条曲线插值方法

Non-Uniform B-Spline Curve Interpolation Method for Feature Points Selection under Curvature Adaptive Condition

针对计算机数控编程阶段生成的海量离散刀位数据,在满足预设插值精度的条件下,提出一种基于曲率自适应选取特征点的非均匀B样条曲线插值方法.首先,采用相邻3点形成近似圆弧的方法计算各个离散刀位数据点的曲率,将曲率分段点、曲率极大值点等特征数据点作为初始插值数据点,构造生成初始非均匀B样条插值曲线;其次,建立插值误差计算模型,并用于计算所有未参与插值的数据点与非均匀B样条插值曲线间的插值误差,在超出预设插值误差的曲率段内增加新的特征点,生成新的非均匀B样条插值曲线;重复上述过程,直至所有不在非均匀B样条插值曲线上的数据点都满足插值精度条件为止.对实际加工离散刀位数据的仿真计算结果表明,该方法即便去除了大量原始离散刀位数据,也能更好地保留原始刀位数据曲线在外形和精度方面的特征,且具有迭代计算次数少、数据点去除量大等特点,在海量离散刀位数据的样条化数控编程方面具有较高的应用价值.

Aiming at the massive discrete tool position data generated in the computer numerically controlled programming stage,a non-uniform B-spline curve interpolation method based on curvature adaptive select-ing feature point is proposed under the condition of satisfying the preset interpolation accuracy.Firstly,the curvature of each discrete data point is calculated by the method of forming an approximate arc from three adjacent points,and the feature data points such as the segment point of the curvature segment and the maximum point of curvature are used as the initial interpolation data points to construct and generate the initial non-uniform B-spline interpolation curve.Secondly,the interpolation error calculation model is es-tablished and used to calculate the interpolation errors between all the data points not participating in the interpolation and the non-uniform B-spline interpolation curve,and the new feature points that are beyond the preset interpolation error in the curve segments are added to generate a new non-uniform B-spline inter-polation curve.Repeat the above processes until all data points that are not on the non-uniform B-spline int-erpolation curve can meet the interpolation accuracy condition. The simulation calculation results of the ac- tual tool position data show that the method can better retain the characteristics of the original data curve in terms of shape and accuracy even when a large amount of the original tool position data is removed, and it has advantages of fewer iteration calculations and larger removing the data points. The method will have high application value to the spline computer numerically controlled programming of massive discrete tool position data.