基于度量映射机制的NURBS曲面网格自适应生成研究及应用
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摘要
网格生成技术是计算机图形学研究的重要内容之一，在计算与工程科学中有着重要的应用，曲面网格生成技术在网格生成技术中占据特殊地位。本文基于服装CAD系统DressingSim EX系统的功能设计要求，对参数化NURBS曲面网格自适应生成进行了一定的研究，为进一步的服装曲面造型，曲面裁片2D展平等功能提供了几何模型基础。
应用于EX系统的NURBS曲面模型是本文的主要研究对象，EX系统从外部CAD／CAM系统获取曲面模型参数信息，通过IGES文件传递，将参数化曲面模型转化为系统可操作的几何模型。本文第二章从介绍数据交换文件IGES文件开始，在分析IGES文件结构的基础上，实现了基于IGES文件五段结构分段提取信息的NURBS曲面实体信息获取后处理器，并给出了参数化NURBS曲面程序表示。
从外部系统获取的NURBS曲面只有参数数据，需要对其进行网格剖分才能转化为可显示、可操作的几何模型。本文的研究目的是要获取符合EX系统要求的NURBS曲面三角网格模型。第三章阐述NURBS曲面三角网格剖分度量映射机制建立过程。先给出建立度量映射机制的数据结构基础，包括基于Z序编码线性四叉树数据结构的建立过程、满树邻域查找计算公式推导过程。并在此基础上提出把单元结点满树八邻域查找推广到任意的非满树情况。最后介绍如何利用Z序编码线性四叉树建立度量映射机制。
映射法曲面网格生成技术要解决的一个关键技术问题就是映射扭曲变形问题，第四章首先给出了一个NURBS曲面基于自适应离散边界的简单映射法网格剖分方法，然后阐述如何利用基于Z序编码线性四叉树结构的度量映射机制与AFM网格生成技术相结合，对NURBS曲面进行基于曲率大小的自适应网格剖分。给出在度量映射机制下AFM方法三角网格生成过程以及曲面剖分网格后续处理过程。
基于上述研究内容，第五章简要介绍服装CAD系统EX的系统框架和流程，并通过例子展示本文研究内容在该系统中的应用。
最后，第六章对本文的研究内容进行了总结，并对后续的研究工作提出了一些建议和发展方向。
Mesh generation is one of important research contents on computer graphics. There has been a great deal of applications of mesh generation on computing and engineering science. Surface mesh generation plays a special role in engineering analysis. The thesis implements adaptive mesh generation of parametric NURBS surface using metric map. The surface mesh is used in a GCAD system DressingSim EX.
Our research aims at NURBS surface models. The models are transferred from exterior CAD/CAM system to EX system by IGES files. Chapter 2 starts from the introduction of IGES data exchange file formats. The details of IGES file structures are presented. A back processor of IGES file is designed to extract NURBS surface parametric data.
The NURBS surface models from exterior CAD/CAM system only have parametric data. They must be transformed to geometrical model presented by triangular mesh for EX system. In chapter 3, a metric map for NURBS surface triangular mesh generation is described. The detail of data structure for metric map is presented, including a Z-ordering linear quadtree data structure、 neighbors navigation equations. Last, a procedure of how to build the metric map using Z-ordering linear quadtree is introduced.
A key problem of surface mesh generation by mapping technology is mapping distortion. In chapter 4, based on adaptive discretization boundary of surface, a simple mapping mesh generation method is presented firstly. Then the thesis will describe how to use the metric map in AFM meshing procedure. The details of NURBS surface adaptive mesh generation based on surface curvature using AFM technology with the metric map are presented in this chapter. An algorithm for search remained holes on surface also is introduced.
Based on the above research, EX system frame is introduced in chapter 5. Brief introduction on development environment of EX system is described. Detailed description on application of this thesis in EX system is provided as well.
Finally, a summary of the thesis research is included in chapter 6. The advices and prospects for the perspectives of technology and application of this project are also included.
应用于EX系统的NURBS曲面模型是本文的主要研究对象，EX系统从外部CAD／CAM系统获取曲面模型参数信息，通过IGES文件传递，将参数化曲面模型转化为系统可操作的几何模型。本文第二章从介绍数据交换文件IGES文件开始，在分析IGES文件结构的基础上，实现了基于IGES文件五段结构分段提取信息的NURBS曲面实体信息获取后处理器，并给出了参数化NURBS曲面程序表示。
从外部系统获取的NURBS曲面只有参数数据，需要对其进行网格剖分才能转化为可显示、可操作的几何模型。本文的研究目的是要获取符合EX系统要求的NURBS曲面三角网格模型。第三章阐述NURBS曲面三角网格剖分度量映射机制建立过程。先给出建立度量映射机制的数据结构基础，包括基于Z序编码线性四叉树数据结构的建立过程、满树邻域查找计算公式推导过程。并在此基础上提出把单元结点满树八邻域查找推广到任意的非满树情况。最后介绍如何利用Z序编码线性四叉树建立度量映射机制。
映射法曲面网格生成技术要解决的一个关键技术问题就是映射扭曲变形问题，第四章首先给出了一个NURBS曲面基于自适应离散边界的简单映射法网格剖分方法，然后阐述如何利用基于Z序编码线性四叉树结构的度量映射机制与AFM网格生成技术相结合，对NURBS曲面进行基于曲率大小的自适应网格剖分。给出在度量映射机制下AFM方法三角网格生成过程以及曲面剖分网格后续处理过程。
基于上述研究内容，第五章简要介绍服装CAD系统EX的系统框架和流程，并通过例子展示本文研究内容在该系统中的应用。
最后，第六章对本文的研究内容进行了总结，并对后续的研究工作提出了一些建议和发展方向。
Mesh generation is one of important research contents on computer graphics. There has been a great deal of applications of mesh generation on computing and engineering science. Surface mesh generation plays a special role in engineering analysis. The thesis implements adaptive mesh generation of parametric NURBS surface using metric map. The surface mesh is used in a GCAD system DressingSim EX.
Our research aims at NURBS surface models. The models are transferred from exterior CAD/CAM system to EX system by IGES files. Chapter 2 starts from the introduction of IGES data exchange file formats. The details of IGES file structures are presented. A back processor of IGES file is designed to extract NURBS surface parametric data.
The NURBS surface models from exterior CAD/CAM system only have parametric data. They must be transformed to geometrical model presented by triangular mesh for EX system. In chapter 3, a metric map for NURBS surface triangular mesh generation is described. The detail of data structure for metric map is presented, including a Z-ordering linear quadtree data structure、 neighbors navigation equations. Last, a procedure of how to build the metric map using Z-ordering linear quadtree is introduced.
A key problem of surface mesh generation by mapping technology is mapping distortion. In chapter 4, based on adaptive discretization boundary of surface, a simple mapping mesh generation method is presented firstly. Then the thesis will describe how to use the metric map in AFM meshing procedure. The details of NURBS surface adaptive mesh generation based on surface curvature using AFM technology with the metric map are presented in this chapter. An algorithm for search remained holes on surface also is introduced.
Based on the above research, EX system frame is introduced in chapter 5. Brief introduction on development environment of EX system is described. Detailed description on application of this thesis in EX system is provided as well.
Finally, a summary of the thesis research is included in chapter 6. The advices and prospects for the perspectives of technology and application of this project are also included.
引文
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[2] Thompson J F, Warsi F C, Martin C W. Automatic Numerical Generation of Body-fitted Curvilinear Coordinates System for Field Containing any Number of Arbitrary Two-dimensional Bodies[J]. Journal of Computational Physics, 1974, 150: 299～319
[3] Thompson J F, Warsi Z U A, Mastin C W. Boundary-fitted Coordinate System for Numerical Solution of Partial Differential Equations—A review[J]. Journal of Computational Physics, 1982, 470: 1～108
[4] Thompson J F, Warsi Z U A, Mastin C W. Numerical Grid Generation: Foundations and Applications[M]. New York: Elsevier, 1985
[5] Thompson J F. A Composite Grid Generation Code for General 3D Regions—The EAGLE Code[J]. AIAA Journal, 1988, 26(3): 271～272
[6] Hsu K, Lee S L. A Numerical Technique for Two-dimensional Grid Generation with Grid Control at all of the Boundaries[J]. Journal of Computational Physics, 1991, 96(2): 451～469
[7] Spekreijse S P. Elliptic Grid Generation Based on Laplace Equations and Algebraic Transformations[J]. Journal of Computational Physics, 1995, 118(1): 38～61
[8] Brown P R. A Non-interactive Method for the Automatic Generation of Finite Element Meshes Using the Schwarz-Christoffel Transformation[J]. Computer methods in applied mechanics and engineering, 1981, 25(1): 101～126
[9] Baldwin K H, Schreyer H L. Automatic Generation of Quadrilateral Elements by a Conformal Mapping[J]. Engineering with Computers, 1985, 2 (2): 187～194
[10] 杨国伟，鄂秦，李凤蔚．保角变换在复杂外形网格生成中的应用[J]．空气动力学学报，1997，15(3)：378-385
[11] Gordon W J, Hall C A. Construction of Curvilinear Coordinate Systems and Applications to Mesh Generation[J]. International Journal for Numerical Methods in Engineering, 1973, 70: 461～477
[12] Eriksson L E. Generation of Boundary Conforming Grids Around Wing-body Configurations Using Transfinite Interpolation[J]. AIAA Journal, 1982, 20(10): 1313～1320
[13] 杨伟军，包忠诩，扶明福等．映射法在三维六面体有限元网格生成中的应 用[J]. 南昌大学学报, 1999, 21(4): 39-43
[14] Kadivar M H, Sharifi H. Double Mapping of Isoparametric Mesh Generation[J]. Computer & Structure, 1996. 59(3): 471-477
[15] Tam T K H, Armstrong C G 2D Finite Element Mesh Generation by Medial Axis Subdivision[J]. Advances in Engineering Software, 1991, 13(5/6): 313-324
[16] Price M A, Armstrong C G Hexahedral Mesh Generation by Medial Surface Subdivision: Part I[J]. International Journal for Numerical Methods in Engineering, 1995, 38(19): 3335-3359
[17] Price M A, Armstrong C G Hexahedral Mesh Generation by Medial Surface Subdivision: Part II[J]. International Journal for Numerical Methods in Engineering, 1997,40(1): 111-136
[18] Lu Y, Gadh R, Tautges T J. Feature Based Hex Meshing Methodology: Feature Recognition and Volume Decomposition[J]. Computer-Aided Design, 2001,33(3): 221-232
[19] Sheffer A, Etzion M, Rappoport A, et al. Hexahedral Mesh Generation Using the Embedded Voronoi Graph[A]. In: Proceedings of the 7~(th) International Meshing Roundtable, Dearborn, 1998, 347-364
[20] Li T S, McKeag R M, Armstrong C G Hexahedral Meshing Using Midpoint Subdivision and Integer Programming[J]. Computer Methods in Applied Methanics and Engineering, 1995,124(): 171-193
[21] Yerry M A, Shephard M S. A Modified Quadtree Approach to Finite Element Mesh Generation[J]. IEEE Computer Graphics & Applications, 1983, 3(1): 39-46
[22] Schroeder W J, Shephard M S. A Combined Octree/Delaunay Method for Fully Automatic 3-D Mesh Generation[J]. International Journal for Numerical Methods in Engineering, 1990,29(1): 37-55
[23] McMorris H, Kallinderis Y. Octree-Advancing Front Method for Generation of Unstructured Surface and Volume Meshes[J]. AIAA Journal, 1997, 35(6): 976-984
[24] Saxena M, Perucchio R. Parallel FEM Algorithm Based on Recursive Spatial Decomposition—I: Automatic Mesh Generation[J]. Computers & Structures, 1992,45(5/6): 817-831
[25] Lohner R, Juan R C. Parallel Advancing Front Grid Generation[A]. In: Proceedings of the 8~(th) International Meshing Roundtable, South Lake Tahoe, CA, 1999, 67-74
[26] Boris, N.Delaunay. Sur la Sphere. Vide.Izvestia Akademia Nauk SSSR, VII Seria, Otdelenie Matematicheskii i Estestvennyka Nauk, 1934, Vol7pp.793-800
[27] Sibon R. Locally Equiangular Triangulation[J]. Comp J, 1978,21 (3): 243-245
[28] C.L.Lawson. Software for C~1 Surface Interpolation[J]. Mathematical Software Ⅲ, 1977, pp.161～194
[29] David F. Watson. Computing the Delaunay Tesselation with Application to Voronoi Polytopes[J]. The Computer Journal, 1981, 24(2): 167～172
[30] Timothy J. Baker. Automatic Mesh Generation for Complex Three-Dimensional Regions Using a Constrained Delaunay Triangulation. Engineering with Computers, 1989, 5: 161～175
[31] Bowyer A. Computing Dirichlet tessellations[J]. The Computer Journal, 1981, 24(2): 162～166
[32] George P L, Hecht F, Saltel E. Automatic Mesh Generator with Specified Boundary[J]. Computer Methods in Applied Mechanics and Engineering, 1991, 92(3): 269～288
[33] George P L, Borouchaki H. Delaunay Triangulation and Meshing: Application to Finite Elements[M]. Paris: Editions HERMES, 1998
[34] N. P. Weatherill and O. Hassan. Efficient Three-dimensional Delaunay Triangulation with Automatic Point Creation and Imposed Boundary Constraints[J]. International Journal for Numerical Methods in Engineering. 1994, 37: 2005～2039
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