1、PDF外文：http:/ 3040 字 附 录 The Pre-Processing of Data Points for Curve Fitting in ReverseEngineering Reverse engineering has become an important tool for CAD model construction from the data points, measured by a coordi-nate measuring machine (CMM), of an existing part. A major probl
2、em in reverse engineering is that the measured points having an irregular format and unequal distribution are dif-cult to t into a B-spline curve or surface. The paper presents a method for pre-processing data points for curve tting in reverse engineering. The proposed method has been developed to p
3、rocess the measured data points before tting into a B-spline form. The format of the new data points regenerated by the proposed method is suitable for the requirements for tting into a smooth B-spline curve with a good shape. The entire procedure of this method involves ltering, curvature analysis,
4、 segmentation, regressing, and regenerating steps. The method is implemented and used for a practical application in reverse engineering. The result of the reconstruction proves the viability of the proposed method for integration with current commercial CAD systems. 1. Introduction With the progres
5、s in the development of computer hardware and software technology, the concept of computer-aided tech-nology for product development has become more widely accepted by industry. The gap between design and manufactur-ing is now being gradually narrowed through the development of new CAD technology. I
6、n a normal automated manufacturing environment, the operation sequence usually starts from product design via geometric models created in CAD systems, and ends with the generation of machining instructions required to convert raw material into a nished product, based on the geometric model. To reali
7、se the advantages of modern com-puter-aided technology in the product development and manu-facturing process, a geometric model of the part to be created in the CAD system is required. However, there are some situations in product development in which a physical modelor sample is produced before cre
8、ating the CAD model. 1） . Where a clay model, for example, in designing automobile body panels, is made by the designer or artist based on conceptual sketches of what the panel should look like. 2） . Where a sample exists without the original drawing or documentation denition. 3） . Where the CAD mod
9、el representing the part has to be revised owing to design change during manufacturing. In all of these situations, the physical model or sample must be reverse engineered to create or rene the CAD model. In contrast to this conventional manufacturing sequence,everse engineering typically starts wit
10、h measuring an existing physical object so that a CAD model can be deduced in order to exploit the advantages of CAD technologies. The process of reverse engineering can usually be subdivided into three stages, i.e. data capture, data segmentation and CAD modeling and/or updating. A physical mock-up
11、 or prototype is rst measured by a coordinate measuring machine or a laser scanner to acquire the geometric information in the form of 3D points.The measured results are then segmented into topological egions for further processing. Each region represents a single geometric feature that can be repre
12、sented mathematically by a simple surface in the case of model reconstruction. CAD modelling reconstructs the surface of a region and combines hese surfaces into a complete model representing the measured part or prototype . In practical measuring cases, however, there are many situ-ati
13、ons where the geometric information of a physical prototype or sample cannot be measured completely and accurately to reconstruct a good CAD model. Some data points of the measured surface may be irregular, have measurement errors,or cannot be acquired. As shown in Fig. 1, the main surface of measur
14、ed object may have features such as holes, islands,or roughness caused by manufacturing inaccuracy, consequently the CMM probe cannot capture the complete set of data points to reconstruct the entire surface. Fig. 1. The general problems in a practical measuring case. Measurement
15、 of an existing object surface in reverse engin-eering can be achieved by using either contact probing or non-contact sensing probing techniques. Whatever technique is applied, there are many practical problems with acquiring data points, for examples, noise, and incomplete data. Without extensive p
16、rocessing to adjust the data points, these problems will cause the CAD model to be reconstructed with an unde-sired shape. In order to rebuild the CAD model correctly and satisfactorily, this paper presents a useful and effective method to pre-process the data points for curve tting. Using the propo
17、sed method, the data points are regenerated in a specied format, which is suitable for tting into a curve represented in B-spline form without the problems previously mentioned.After tting all of the curves, the surface model can be completed by connecting the curves. 2. The Theory of B-spline Most
18、of the surface-based CAD systems express shape required for modelling by parametric equations, such as in Be zier or B-spline forms. The most used is the B-spline form B-splines are the standard for representing freeform curves and surfaces in current commercial CAD systems. B-spline curve and Be zi
19、er curves have many advantages in common Control points inuence the curve shape in a predictable natural way, making them good candidates for use in an interactive environment. Both types of curve are variation diminishing, axis independent, and multivalued, and both exhi bit the convex hull p
20、roperty. However, it is the local contro of curve shape which is possible with B-splines that gives the technique an advantage over the Be zier technique, as does the ability to add control points without increasing the degree othe curve. Considering the real-world applications requirement the B-spline technique is used to represent curves and surface in this research. A B-spline curve is a set of basis functions which combines the effects of n + 1 control points. A parametric B-spline curve is given by
