外文翻譯---在逆向工程中對擬合曲線的數(shù)據(jù)點云的預(yù)處理-文庫吧資料
2024-11-14 10:35本頁面
【正文】 e 5thorder of the regression equation is used, the coef?cient of the 5thorder item bees zero. . the . error of the 4thorder equation is equal to the 5thorder equation. This means that the designer only has to regress the data points into a 4thorder equation. In practice, a 4thorder equation has already satis?ed the demand for curvature continuity in CAD model construction for industrial applications. 6. Conclusion Geometric modelling is a technology that is already used extensively in industrial applications for developing new products. Reverse engineering has bee an important tool for CAD model construction for an existing part from the measuring data. A major dif?culty in reverse engineering techniques is to ?t the irregular data points of an unequal distribution into a Bspline curve. The procedure of the preprocessing of data points for curve ?tting in reverse engineering is described in this paper. The method proposed has been developed to process the data points measured from an existing object before curve ?tting, and then new data points are regenerated which are suitable for the requirement for ?tting into a smooth Bspline curve with a good shape. The entire procedure of this method involves ?ltering, curvature analysis, segmentation,regressing, and regenerating steps. The proposed method is implemented for practical applications in reverse engineering, and is an effective tool for integrating with current mercial CAD systems for reconstructing the geometric models of physical parts. A broader interpretation of the term “reverse engineering”might perhaps involve deducing the intent of the original designer to some degree. An ideal system of reverse engineering would be able to not only construct a plete geometric model of the source object but also catch the initial design intent. By applying the method proposed above, designers may regroup the data points in order to produce the individual feature curves for reconstructing a plete CAD model of the source object to achieve the original design intent. 在逆向工程中對擬合 曲線的數(shù)據(jù)點云的預(yù)處理 逆向工程已經(jīng)成為一種從現(xiàn)存物體通過 CMM測量的數(shù)據(jù)點重建 CAD模型的重要工具 .在逆向工程中首要的問題是 :測量到的點具有不規(guī)律形式和不對等分布很難用 Bspline 曲線擬合。 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 dis
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