逆向模型重建技术的研究
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摘要
逆向工程技术是随着计算机技术的发展和成熟以及数据测量技术的进步而迅速发展起来的一门新兴学科与技术,它的出现,改变了原来CAD系统中从图纸到实物的设计模式,为产品的迅速开发以及快速原型化设计提供了一条新的途径。曲线重建、曲面重建是逆向工程中重要的问题,从已知的采样数据点出发,构造出物体的几何模型,是对物体进行分析、计算和绘制的根据,是研究曲面性质的重要工具。散乱数据点的三角网格剖分是逆向工程中的一个重要环节,是进行后续曲面重建的前提和基础,随着激光和三维坐标测量机等三维数据采样技术和硬件设备的日益完善,人们采用先进的测量设备可以获得物理模型的数据信息。这些数据往往是散乱数据点,而且数据量非常大。对这样的数据直接进行NURBS曲面重构存在很大困难,为此,人们开始研究多项式网格曲面。网格曲面可以表达任意复杂的形体,尤其是三角网格曲面具有计算简单、数值稳定性好以及显示效率高等优点,但是随着数据量的明显增多,扫描获取的几何体的细节以及外形的日渐丰富,对有效生成、处理超大规模几何模型的新方法的需求也日渐增长,单纯采用传统的基于三角面片的绘制方法难以满足真实性、实时性和交互性的要求,三角形网格生成以及进一步简化成为又一个研究热点。
本文介绍了文章的选题背景、意义以及目前逆向工程中逆向模型重建的主要技术。本文主要工作如下:
1.以Bézier曲线为例,对重新参数化和参数最优化进行了研究,并将参数最优化方法应用到散乱点的曲线重建。
2.在判断多边形顶点凹凸性的基础上,提出一种基于多边形的三角剖分方法。
3.提出基于边删除和改进二次误差测度的带有属性的三角网格简化方法,在现有的三角网格简化方法的基础上加入了属性的处理。
最后对全文进行总结,并指出了今后进一步的研究方向。
Reverse engineering is a new subject and technology coming up with the development of computer science and data digitization.Its help to change the design mode from draft to models in conventional CAD systems.It's a new approach for rapid prototype manufacture.Curve and surface reconstruction are two basilica questions in reverse engineering.With the data acquired from one existent object,the geometrical models can be reconstructed which is a useful tools to study the existent object such as analysis,computing and rendering.Triangulation of scattered data is the first important step and the base of later step of reconstructing curved Surface in Reverse Engineering.Meanwhile,with the recent development of 3D data collection technologies and hardware facilities,people can get the data information of the physical model by using the advanced measurement tools.
The data often is scattered,and the volume of the data is very large.It is very difficult to directly reconstruct NURBS surface from such data,so people divert attention to the Polynomial meshes.Meshes can descript complex shape objects,especially triangular mesh is with the advantages of simple calculation,great numerical stability and high showing efficiency, but with the volume of the data significantly increasing,the geometry details got by scanning and the shape is becoming rich gradually,the need to new method which can effectively produce and process ultra-large-scale geometric model is growing day by day.It is very difficult for meeting the requirements of authenticity real-time performance and interactive performance only to use the traditional rendering method based on triangular mesh,it is another new field to produce triangular mesh and to simplify the triangular mesh.
This paper introduces the background of article topic,significance and the main technology in reverse engineering.
1.Considering the Bezier curve as an example,it is to research on the re-parametric and optimal parameterization and use the optimal parameterization method into the curve reconstruction.
2.Judging the polygon as concave or convex,a triangulation method of polygon is proposed.
3.Considering Edge collapse and improved Quadric-error metric as a basis,a simple and speedy mesh simplification algorithm with additional properties such as color,texture etc is proposed.
At last.some conclusions are made for the whole article and tb.e future work to do in related research fields is suggested.
本文介绍了文章的选题背景、意义以及目前逆向工程中逆向模型重建的主要技术。本文主要工作如下:
1.以Bézier曲线为例,对重新参数化和参数最优化进行了研究,并将参数最优化方法应用到散乱点的曲线重建。
2.在判断多边形顶点凹凸性的基础上,提出一种基于多边形的三角剖分方法。
3.提出基于边删除和改进二次误差测度的带有属性的三角网格简化方法,在现有的三角网格简化方法的基础上加入了属性的处理。
最后对全文进行总结,并指出了今后进一步的研究方向。
Reverse engineering is a new subject and technology coming up with the development of computer science and data digitization.Its help to change the design mode from draft to models in conventional CAD systems.It's a new approach for rapid prototype manufacture.Curve and surface reconstruction are two basilica questions in reverse engineering.With the data acquired from one existent object,the geometrical models can be reconstructed which is a useful tools to study the existent object such as analysis,computing and rendering.Triangulation of scattered data is the first important step and the base of later step of reconstructing curved Surface in Reverse Engineering.Meanwhile,with the recent development of 3D data collection technologies and hardware facilities,people can get the data information of the physical model by using the advanced measurement tools.
The data often is scattered,and the volume of the data is very large.It is very difficult to directly reconstruct NURBS surface from such data,so people divert attention to the Polynomial meshes.Meshes can descript complex shape objects,especially triangular mesh is with the advantages of simple calculation,great numerical stability and high showing efficiency, but with the volume of the data significantly increasing,the geometry details got by scanning and the shape is becoming rich gradually,the need to new method which can effectively produce and process ultra-large-scale geometric model is growing day by day.It is very difficult for meeting the requirements of authenticity real-time performance and interactive performance only to use the traditional rendering method based on triangular mesh,it is another new field to produce triangular mesh and to simplify the triangular mesh.
This paper introduces the background of article topic,significance and the main technology in reverse engineering.
1.Considering the Bezier curve as an example,it is to research on the re-parametric and optimal parameterization and use the optimal parameterization method into the curve reconstruction.
2.Judging the polygon as concave or convex,a triangulation method of polygon is proposed.
3.Considering Edge collapse and improved Quadric-error metric as a basis,a simple and speedy mesh simplification algorithm with additional properties such as color,texture etc is proposed.
At last.some conclusions are made for the whole article and tb.e future work to do in related research fields is suggested.
引文
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[2] Zhu, H. and Menq, C.H. B-Rep model simplification by automatic fillet/round suppressing for efficient automatic feature recognition, Computer-Aided Design, 2002, 34(2): 109-123
[3] Sapidis, N.S. and Besl, P.J. Direct construction of polynomial surfaces from dense range images through region growing, ACM Transactions on Graphics, 1995, 14(2): 171-200
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[5] McAllister, D.F. and Roulier, J.A. An algorithm for computing a shape preserving oscillatory quadratic spline. ACM Transactions on Mathematical Software, 1991, 7: 331-347
[6] Fritsch, F.N. and Carlson, R.E. Monotone piecewise cubic interpolation, SIAM Journal of Numerical Analysis, 1980, 17, 238-246
[7] Fritsch, F.N. and Butland, J.A method for constructing local monotone piecewise cubic interpolates. SIAM Journal of Scientific and Statistical Computing, 1984, 5,303-304
[8] Passow, E. and Roulier, J.A. Monotone and convex spline interpolation, SIAM Journal of Numerical Analysis, 1977, 904-909.
[9] Gregory, J.A. Shape preserving spline interpolation. Computer-Aided Design, 1986, 18(1): 53-57
[10] Sarfraz, M. Preserving monotone shape of the data using piecewise rational cubic functions. Computers & Graphics, 1997, 21(1):5-14
[11] Sarfraz, M. A rational cubic spline for the visualization of monotonic data, Computers & Graphics, 2000, 24:509-516
[12] Lavery, J.E. Shape-preserving, multi-scale fitting of univariate data by cubic L~1 smoothing splines, Computer Aided Geometric Design, 2000, 17:715-727
[13] Yang ,X. and Wang, G. Planar point set fair and fitting by arc splines, Computer-Aided Design, 2001, 33:35-43
[14] Korsters, M. Curvature-dependent parameterization of curves and surfaces. Computer Aided Design 1991, 23(8), 569-578
[15] McLain, D. Drawing contours form arbitrary data pints, The Computer Journal, 1974, 17:318-324
[16] McLain, D. Two dimensional interpolation from random data, The Computer Journal, 1976, 19:178-181
[17] Lancaster, P. Moving weighted least-squares methods, Polynomial and Spline Approximation, Reidel, 103-120
[18] Lee, I. K. Curve reconstruction from unorganized points, Computer Aided Geometric Design, 2000, 17:161-177
[19] Fang, L. and Gossard, D.C. Multidimensional curve fitting to unorganized data points by nonlinear minimization, Computer-Aided Design, 1995, 27(1):48-58
[20] Taubin, G. and Ronfard, R. Implicit simplicial models for adaptive curve reconstruction, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1996,18(3):321-325
[21] Blum, H. A transformation for extracting new descriptors shape, In: Models for the Perception of Speech and Visual Form, Wathen-Dunn ed. MIT Press, Cambridge, MA, 1967, 362-380
[22] Arcelli, C. Pattern thinning by contour tracing, Computer Graphics and Image Processing, 1981, 17:130-144
[23] Arcelli, C. and di Baja, G. S. A width-independent fast thinning algorithm, IEEE Transactions on Pattern Anal. Mach. Intel., 1985, 7:463-473
[24] Yun, X. Skeletonization via the realization of the fire front's propagation and extinction in digital binary shapes, IEEE Transactions on Pattern Anal. Mach. Intell, 1989, 11:1076-1086
[25] Eckhardt, U. and Maderlechner, G. Invariant Thinning, International Journal of Pattern Recognition and Artificial Intelligence, 1993, 7(5): 1115-1144
[26] Pottmann, H. and Randrup, T. Rotational and helical surface approximation for reverse engineering, Computing, 1998, 60, 307-322
[27] Goshtasby, A. A Grouping and parameterizing irregularly spaced points for curve fitting, ACM Transactions on Graphics, 2000, 19(3): 185-203
[28] Boehm, W. Farin, G. and Kahmann, J. A survey of curve and surface methods in CAGD, Computer Aided Geometric Design, 1984, 1(1): 1-60
[29] Bajaj, C.L. Bernardini, F. and Xu, G. Automatic reconstruction of surfaces and scalar fields form 3D scans, SIGGRAPH '95,109-118
[30] Eck, M. and Hoppe, H. Automatic reconstruction of B-spline surfaces of arbitrary topological type, SIGGRAPH, 1996, 335-342
[31] Guo, B. Surface reconstruction: from points to splines, Computer-Aided Design, 1997, 29(4):269-277
[32] Yang, M. and Lee, E. Segmentation of measured point data using a parametric quadric surface approximation, Computer-Aided Design, 1999, 31:499-457
[33] Floater, M.S. Meshless parameterization and B-spline surface approximation, The Mathematics of Surfaces, 1-18
[34] Muraki. S. Volumetric shape description of range data using "blobby model", SIGGRPAH, 1991,227-235
[35] Sapidis, N.S. and Besl, P.J. Direct construction of polynomial surfaces from dense range images through region growing, ACM Transactions on Graphics, 1995, 14(2): 171-200
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