【文章內(nèi)容簡介】 ually 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 rebuilt by ?tting data points with an unequal distribution, as shown in Fig. 2, the generated curve may differ from the real shape of the measured object. Figure 3 illustrates that a smoother and more accurate reconstruction may be obtained by ?tting an equally spaced set of data points. 5. The PreProcessing of Data Points To achieve the requirements for ?tting a set of data points into a Bspline curve as mentioned above, it is very important and necessary that the data points must be preprocessed before curve ?tting. In the following description, a useful and effective method for preprocessing the data points for curve ?tting is presented. The concept of this method is to regress a set of measuring data points into a nonparametric equation in implicit or explicit form, and this equation must also satisfy the continuity of the curvature. For a plane curve, the explicit nonparametric equation takes the general form: y = f(x). Figure 4 illustrates an overview of the procedure to preprocess the data points for reverse engineering. Data point ?ltering is the ?rst step in displacing the unwanted points and the noisy points. The original data points measured from a physical prototype or an existing sample by a CMM are in discrete format. When the measured points are plotted in a diagram, the noisy points which obviously deviate from the original curve can be selected and removed by a visual search by the designer for extensive processing. In addition,the distinct discontinuous points which apparently relate to a sharp change in shape may also be separated easily for further processing. Many approaches have been developed for generating a CAD model from measured points in reverse engineering. A plex model is usually constructed by subdividing the plete model into individual simple surfaces [8,9]. Each of the individual surfaces de?nes a single feature in a CAD system and a plete CAD model is obtained by further trimming, blending and ?lleting, or using other surfaceprocessing the designer is given a set of unanised data points measured from an existing object, data point segmentation is required to reconstruct a plete model by de?ning individual simple surfaces. Therefore, curvature analysis for the data points is used for subdividing the data points into individual groups. In order to extract the pro?le curves for CAD model reconstruction, in this step, data points are divided into different groups depending upon the result of curvature calculation and analysis of the data points. For each 2D curve, y = f(x), the curvature is de?ned as: If the data is expressed in discrete form, for any three consecutive points in the same plane(X1,Y1) (X2,Y2) (X3,Y3), the three points form a circle andthe centre (X0,Y0) can be calculated as (see Fig. 5): Figure 6 illustrates an example in which the curvatures of a plane curve consisting of a data point set are calculated using the previous method. The curvature of the curve determined by the data point set changes from 0 to , as shown in Fig. 7. This indicates that there is a ?llet feature with a radius 30 in the data points set. Thus, these points can be isolated from the original data points, and form a single feature. By curvature analysis, the total array of data points is divided into several groups. Each of these groups is a segmented form of the original data points which is devoid of any sharp change in shape. After segmentation, individual groups of data points are separately regressed into explicit nonparametric equations, and then the data points can be regenerated from the regression