【正文】 模型，一個明確的不含參數(shù)方程式的一般形式： 圖示說明 ， 一個總的逆向工程中預處理數(shù)據(jù)點的程序。因此，對于產(chǎn)生一個高質(zhì)量的 BSpline曲線，光滑有序的點云數(shù)據(jù)是必須的。 圖 2與不平等的分布曲線擬合的 數(shù)據(jù)點 它可以證明 ,該系數(shù)矩陣的完全是正面和聯(lián)合的帶寬小于 p,因此 ,線性系統(tǒng)可以解決無鏈安全地通過高斯消元。一條 Bspline 曲線設定了連接 n + 1 個 控點 。 2． Bspline曲線理論 通過含參數(shù)的方程 ，絕大多數(shù)外觀基礎上的 CAD 系統(tǒng)都表達了構造模型的要求， 如 Bezier 曲線或 Bspline 曲線形式，最長用的是 Bspline 形式，在目前商業(yè)系統(tǒng)中， Bspline 曲線是標準的代表自由曲線和外表的曲線。一些表面測量的數(shù)據(jù)可能是不規(guī)律的，還有一些測量誤差或者表面是不要求的。物理模型或樣本的建立是為了創(chuàng)建和建立 CAD 模型。在逆向工程中這種方法被實施和用于實踐應用。zier technique, as does the ability to add control points without increasing the degree othe curve. Considering the realworld applications requirement the Bspline technique is used to represent curves and surface in this research. A Bspline curve is a set of basis functions which bines the effects of n + 1 control points. A parametric Bspline curve is given by For Bspline curves, the degree of these polynomials is controlled by a parameter k and is usually independent of the number of control points, and the Bspline basis functions are de?ned by the following expression: Where k controls the degree (k?1) of the resulting polynomials in u and thus also controls the continuity of the Bspline surface is de?ned in a similar way to a tensor product in a Bspline curve. It is also possible to de?ne a Bspline surface having different degrees in the u and vdirections: 3. Curve Fitting Given a set of data points measured from existing object,curve ?tting is required to pass through the data points. The leastsquares ?tting technique is the most used algorithm which aims at approximating, based on an iterative method, a set of data points to form a Bspline .Given a set of data points Qk, k = 0,1,2,. . .,n, that lie on an unknown curve P for certain parameter values uk,k = 0,1,2,. . .,n。 it is necessary to determine an exact interpolation or best ?tting curve, P. To solve this problem, the parameter values (uk) for each of the data points must be assumed. The knot vector and the degree of the curve are also determined. The degree in practical applications is generally 3 (order = 4). The parameter values can be determined by the chord length method: Given the parameter values, a knot vector that re?ects the distribution of these parameters has the following form: It can be proved that the coef?cient matrix is totally positive and banded with a bandwidth of less than p, therefore, the linear system can be solved safely by Gaussian elimination without pivoting. 4. The Requirement for Fitting a Set ofData into a BSpline Curve In order to produce a Bspline curve with a “good shape”,some characteristics are required to ?t the data point set into a curve presented in Bspline form. First, the data points must be in a wellordered sequence. When applying the program to ?t a set of data points into a Bspline curve, the data points must be read one by one in a speci?ed order. If the data points are not in order, this will cause an undesired twist or an outofcontrol shape of the Bspline , an even dispersion of the data points is better for curve ?tting. In the measuring procedure, some factors, such as the vibration of the machine, the noise in the system, and the roughness of the surface of the measured object will in?uence the result of the measurement. All of these phenomena will cause local shakes in the curve which passes through the problem points. Therefore, a smooth gradation of the location of the data points is necessary for generating a “high quality” Bspline curve. Having the data points equally distributed is important for improving the result of parameterisation for ?tting a Bspline curve. As the mathematical presentation shows in Eq. (9), the control points matrix [P] is determined by the basis functions [N] and data points [Q], where the basis functions [N] are determined by the parameters ui which are correspond to the distribution of the data points. If the data points are distributed unequally, the control points will also be distributed unequally and will cause a lack of smoothness of the ?tting curve. As mentioned above, in practical measuring cases, the main surface of a physical sample often has some features such as holes,islands, and radius ?llets, which prevent the CMM probe from capturing data points with equal distribution. If a curve is rebu