在現今產品的外形愈趨複雜，精度要求日漸提昇的情形下，量測檢驗的問題也因而更加地受到重視，為了快速精確地完成量測工作，除了硬體量測設備的精進之外，軟體的整合亦是極為重要，本論文的主要目的即在於發展一以軟體工程為架構之虛擬三次元量測系統，所謂的虛擬三次元量測系統，意指利用軟體工程及電腦快速運算的功能，用以分析由硬體量測獲得之外形資料，進行一般之幾何分析、工差分析，即以軟體技術達到三次元量測分析的各項功能。
要發展虛擬之三次元量測系統，首先需要以量測得來之點資料，利用逆向工程之理論方法建立一虛擬元件以供檢測，本論文以三角網格架構，利用非接觸式掃瞄儀之掃描資料建立多面體架構的之樣品模型，首先需要對樣品做不同方向的掃瞄，以取得完整的量測資料，然後再透過資料座標定位、資料結合、平滑化、資料縫補等技術來建構模型。之後即可用所開發之虛擬三次元量測系統對此點資料做一般之幾何分析或工差分析，並可與原始設計之CAD模型進行比對，使用此一方法不但能減少產品之檢測時間，並可增加產品可靠度，進而提高產品之競爭力。

In these days, the hardware of measurement has gotten lots of improvement. Therefore, it is not difficult to get large and accurate measuring data. To make the measurement quick and accurate, it is also important to care about the software development for handling the measuring data. So, it is a challenge to find a way to convert these data to useful information effectively today. The Virtual-CMM (Virtual Coordinate Measuring Machine) system provides a good solution for it. The Virtual-CMM that we made is a software to get the measuring information by analyzing the virtual part. The virtual part is based on the data points that scanned by any type of DME (dimensional measuring equipment ), such as laser scanner or CMM. It is polygen-based model established by the reverse engineering technique like surface meshing, data registration, data merging and smoothing.
The main object of this paper is to develop a virtual measuring system. It provides general analysis function such as models alignment, tolerance analysis and model difference analysis.

【1】 K. S. Arun, T. S. Huang, and S. D. Blostein, “Least-Squares Fitting of Two 3-D Point Sets,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 9, No. 5, pp. 698-700, 1987.

【2】 P. J. Besl and D. McKay, “A Method for Registration of 3-D Shapes,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 2, pp. 239-256, 1992.

【3】 Y. Chen and G. Medioni, “Object Modelling by Registration of Multiple Range Images,” Image Vision Computer, Vol. 10, pp.145-155, 1992.

【4】 G. Blais and M. D. Levine, “Registering Multiview Range data to Create 3D Computer Objects,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, pp.820-824, 1995.

【5】 F. Lu and E. E. Milios, “Robot Pose Estimation in Unknown Environments by Matching 2D Range Scans,” Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, pp.935-938, 1994.

【6】 J. Feldmar, G. Malandain, J. Declerck, and N. Ayache, “Extension of the ICP algorithm to Non-rigid Intensity-based Registration of 3D Volumes,” Proceedings of the Workshop on Mathematical Method in Biomedical Image Analysis, San Fransico, pp.84-93, 1996.

【7】 G. Turk and M. Levoy, “Zippered Polygon Meshes from Range Images,” Proceedings of SIGGRAPH94, Orland, pp. 311-318, 1994.

【8】 David W. Eggert, Andrew W. Fitzgbbon, and Robert B. Fisher,
“Simultaneous Registration of Multiple Range Views for Use in Reverse Engineering of CAD Models,” Computer Vision and Image Understanding, Vol. 69, No. 3, March, pp.253-272, 1998.

【9】 A. E. Johnson and M. Hebert, “Surface Registration by Matching Oriented Points,” Proceedings of International Conference on Recent Advances in 3-D Digital Imaging and Modeling, pp.121-128, 1997.

【10】T. Masuda, K. Sakaue, N. Yokoya, “Registration and Integration of Multiple Range Images for 3-D Model Construction,” Proceedings of the 13th International Conference on Pattern Recognition, Vol. 1, pp. 879 -883, 1996.

【11】 T. Masuda, “A Unified Approach to Volumetric Registration and Integration of Multiple Range Images,” Proceedings of International Conference on Pattern Recognition, Vol. 2, pp.977-981, 1998.

【12】C. S. Chua and R. Jarvis, “3D Free-Form Surface Registration and Object Recognition,” International Journal of Computer Vision, Vol.17, pp.77-99, 1996.

【13】Daniel J. Filip and Thomas W. Ball, “Procedurally Representing Lofted Surfaces,” IEEE Computer Graphics and Applications , Vol. 9, Issue 6 ,1989, pp. 27-33.

【14】C. S. Chen, Y. P. Hung, J. B. Cheng, and M. Ouhyoung, “Registration and Integration of Multi-view Range Images,” 電腦視覺、圖學暨影像處理研討會論文集，pp. 376-383, 1997.

【15】T. Masuda and N. Yokoya, “A Robust Method for Registration and Segmentation of Multiple Range Images,” Computer Vision Image Understanding, Vol. 61, pp.295-307, 1995.

【16】C.S Chen, Y.P. Hung, “A Fast Automatic Method for Registration of Partially-Overlapping Range Images”, Proceeding of International Conference on Computer Vision, pp. 242-248, 1998.

【17】N. L. Lee and C. H. Menq, “Segmentation of Scanned Data Points for Reverse Engineering,” Proceeding of ASME International Computers in Engineering Conference, pp. 1-12, 1995.

【18】D. J. Filip and T. W. Ball, “Procedurally Representing Lofted
Surfaces,” IEEE Computer Graphics and Applications , Vol. 9, Issue 6, pp. 27-33, 1989.

【19】G. Turk and M. Levoy, “Zippered Polygon Meshes from Range Images,” Proceeding of Annual Conference Series on Computer Graphics, pp. 311-318, 1994.

【20】S. A. Nene and S. K. Nayar, “A Simple Algorithm for Nearest Neighbor Search in High Dimensions,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 9, pp. 989-1003, 1997.

【21】S. A. Nene and S. K. Nayar, “Closet Point Search in High Dimensions,” Proceeding of Computer Vision and Pattern Recognition 96, pp. 859-865, 1996.

【22】B.K. Choi, H.Y. Shin, Yoon, Y.I. and J.W. Lee , “Triangulation of Scattered Data in 3D Space” , Computer-Aided Design, Vol. 20, pp. 239-261, 1988.

【23】T. P. Fang and L. A. Piegl, “Delaunay Triangulation in Three Dimensions,” IEEE Computer Graphics and Applications, pp.62-69, 1995.

【24】M. DoCarmo, “Differential Geometry of Curves and Surfaces,” Prentice Hall, 1976.

【25】J. A. Thorpe, “Elementary Topics in Differential Geometry,” Springer-Verlag, 1979.

【26】G. Taubin, “Curve and Surface Smoothing without Shrinkage,” Proceeding of International Conference on Computer Vision, pp. 852-857, 1995.

【27】G. Taubin, “Estimating the Tensor of Curvature of a Surface From a Polyhedral Approximation,” Proceeding of International Conference on Computer Vision, pp. 902-907, 1995.

【28】H. Edelsbrunner and E. P. Mucke, “Three-Dimensional Alpha Shapes,” ACM Trans. Graph, Volume 13, Issue 1, pp. 43-72, 1994.

【29】H. L. Cheng, T. K. Dey, H. Edelsbrunner and J. Sullivan, “Dynamic skin triangulation,” Discrete Comput. Geom., to appear, 2000.

【30】D.F. Watson, “Computing the N-dimensional Delaunay Tessellation with Application to Voronoi Polytypes” , Computer Journal, Vol. 24, pp. 167-172, 1981.

【31】N.A. Golias, and R.W. Dutton, “Delaunay Triangulation and 3D Adaptive Mesh Generation” , Finite Elements in Analysis and Design, Vol. 25, pp. 331-341, 1997.

【32】H. Park, and K. Kim, “An Adaptive Method for Smooth Surface Approximation to Scattered 3D Points” , Computer-Aided Design, Vol. 27, No. 12, pp. 929-939, 1995.

【33】A. Okabe, B. Boots and K. Sugihara, “Spatial Tessellations Concepts and Applications of Voronoi Diagrams,” JOHN WILEY & SONS, 2000.

【34】I.F. Isselhard, G. Brunnett, and T. Schreiber, “Polyhedral Approximation and First Order Segmentation of Unstructured Point Sets,” Proceeding of International Conference on Computer Graphics, pp. 433-441, 1998.

【35】Chin Seng Chua, Ray Jarvis, “3D Free-Form Surface Registration and Object Recognition,” International Journal of Computer Vision, Vol.17, pp. 77-99, 1996.

【36】Jacques Feldmar, Nicholas Ayache, “Rigid,Affine and Locally Affine Registration of Free-Form Surfaces,” International Journal of Computer Vision, Vol.18(2), pp. 99-119, 1996.

【37】I.F. Isselhard, G. Brunnett, and T. Schreiber, “Polyhedral Approximation and First Order Segmentation of Unstructured Point Sets,” Proceeding of International Conference on Computer Graphics, pp. 433-441, 1998.

【38】呂建豪, “智慧型虛擬三次元量測系統之發展”, 碩士論文, 中正大學機械工程研究所, 2000.

【39】蔡明倫, “三度空間腦部結構較準”, 碩士論文, 交通大學資訊科學系, 2000.

【40】林淑君, 蔡裕祥, “精密量測及檢驗”, 2000.