%0 Journal Article
%T 三次NURBS曲线的Obrechkoff参数化插值算法<br>A Third-order NURBS Interpolation Algorithm Based on Obrechkoff Parameterization
%A 董本志
%A 张小燕
%A 于鸣
%A 任洪娥
%J 机械科学与技术
%D 2016
%X 针对工程实践中对复杂曲线曲面零件高精度加工的要求，提出一种基于单步四阶Obrechkoff参数化法的三次非均匀有理B样条（NURBS）曲线的插值算法。该算法通过后向差分代替微分的方法，对Obrechkoff法求解微分方程的参数化插值算法进行了合理的简化，降低了计算复杂度，有效地保证了计算的精度和插值的实时性。考虑参数化算法对插值曲线的光顺性影响，在MATLAB上与累计弦长参数化法和阿当姆斯参数化法进行仿真比较。结果表明，该算法对应的插值曲线平均曲率最小，光顺性最好。<br>A third-order non-uniform rational B-spline (NURBS) interpolation algorithm based on Obrechkoff parameterization was proposed to satisfy the requirements of the high-precision machining of complex curve surface in the engineering practice. For furthermore ensuring the high-precision of calculation and real time control of interpolation, the parametric interpolation algorithm based on Obrechkoff was predigested by using rearward difference in place of differential to reduce the computational complexity of the algorithm. Considering the fairness effect of different parameterization, then compared the proposed algorithm with the accumulative chord length parameterization and the Adams parameterization in MATLAB, the computer simulation experiments indicate that the interpolation curve which simulated by the algorithm is more fairness because its average curvature is lowest
%K 参数化
%K NURBS
%K 计算复杂度
%K 实时性&lt
%K br&gt
%K parameterization
%K computational complexity
%K real time control
%K computer simulation
%U http://journals.nwpu.edu.cn/jxkxyjs/CN/abstract/abstract6552.shtml