文中首先介紹了自由曲面的描述方式，并提出了一種對點云數(shù)據(jù)進行NURBS 曲面
重建的改進算法。該算法通過對目標函數(shù)的修正及迭代處理，將測點數(shù)據(jù)的有理B 樣條曲線擬合問題轉(zhuǎn)化為一單變量的優(yōu)化問題。從而容易求得控制點三維坐標、權(quán)值、各測點所對應的參數(shù)值及最優(yōu)控制點的數(shù)目，進而有效地壓縮測量點云數(shù)據(jù)量。該方法克服了現(xiàn)有方法存在的需要求解多變量的非線性優(yōu)化問題，不能對最優(yōu)控制點數(shù)目進行求取等缺陷。實踐表明，文中提出的方法是行之有效的。
關鍵詞:逆向工程；數(shù)據(jù)處理；自由曲面重構(gòu)；非均勻有理B 樣條
Abstract：This paper has introduced the description way of the free-form surfaces
at first, and has put forward an improved algorithm of making the element data
reconstruct NURBS surfaces. This algorithm is to change the fitted problem of the
measurement data into an optimizing problem of one variable with modification and
iteration of the objective function. So we can apt to count up 3D of control points,
visual ， a parameter’ number of every measurement points and the number of
optimization of control points ,and compress the number of measurement points
effectively. This algorithm has overcomed the problems existing in the present
method, which like the necessary of solving the optimization question non-linear
of many variables and can’t figure out the number of optimization of control points.
The results of computer simulation and experiment verified the effectiveness of the
method.
Key words：reverse engineering；data processing；reconstruction of free-form
surfaces；NURBS