附 录The Pre-Processing of Data Points for Curve Fitting in Reverse EngineeringReverse 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 problem in reverse engineering is that the measured points having an irregular format and unequal distribution are diffi-cult to fit into a B-spline curve or surface. The paper presents a method for pre-processing data points for curve fitting in reverse engineering. The proposed method has been developed to process the measured data points before fitting into a B-spline form. The format of the new data points regenerated by the proposed method is suitable for the requirements for fitting into a smooth B-spline curve with a good shape. The entire procedure of this method involves filtering, curvature analysis, 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. IntroductionWith the progress 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. In 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 finished product, based on the geometric model. To realise 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 creating 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 definition.3）. Where the CAD model 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 refine the CAD model. In contrast to this conventional manufacturing sequence,everse engineering typically starts with 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 or prototype is first 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 represented 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-ations 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 measured object may have features such as holes, islands,or roughness caused by manufacturing inaccuracy, consequentlythe 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 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 processing 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 fitting. Using the proposed method, the data points are regenerated in a specified format, which is suitable for fitting into a curve represented in B-spline form without the problems previously mentioned.After fitting all of the curves, the surface model can be completed by connecting