面向实时可视化与数值模拟3DSIS数据模型研究
|
摘要
岩土信息发育分布规律及岩土介质稳定性是岩土工程最关心的两个问题，三维地质可视化与数值模拟是解决这两个问题有效途径。但是，目前三维地质模型主要基于三维可视化或数据库技术而构建的，难以进行力学分析；而数值模拟存在着建模困难，甚至无法进行的致命弱点。鉴于此，本文针对3DSIS数据模型难以实现实时可视化与力学分析等不足，提出了一种面向实时可视化和数值模拟三维地质模型——NMTINF-BR模型，并实现了一些初步功能，主要工作概括如下：
1．综合分析研究地质信息特点、三维地质模型、可视化技术及网格剖分技术等表明，采用非流形边界表达不仅能有效表达岩土工程复杂的地质现象，而且可以为岩土工程稳定性分析提供地质力学模型。
2．在数据模型表达上，采用以二维流形(或二维带边流形)不规则三角网为边界面片，通过宏观和微观两个拓扑层次来表示各拓扑实体间拓扑关系的非流形B-Rep来表达复杂的地质现象，建立了一种面向实时可视化和数值模拟三维地质模型——NMTINF-BR模型。
3．在微观拓扑层次(不规则三角网拓扑结构)上，NMTINF-BR模型将非流形信息引入四方边缘结构，既保留了四方边缘结构对流形形体优雅的拓扑操作，同时又将流形形体与非流形形体的表达有机地结合起来。
4．在宏观拓扑层次上，以PES数据结构为基础，对其加以改进使之将不规则三角形网、区域内的单点、线框边等不同维实体之间的拓扑关系表达出来。
5．用面向对象的编程方法实现了上述数据结构C++类的定义，并初步实现了NMTINF-BR模型一些相关的基本拓扑操作。
6．详细探讨了基于钻孔信息NMTINF-BR地层模型建模算法，采用基于数据预处理后，自下而上逐层交叉判断算法能简洁、有效地建立NMTINF-BR地层模型，模型建立关键技术是不规则三角形网格动态更新算法以及求交算法。
7．NMTINF-BR模型能直接被网格剖分器剖分，因而可以有效地为数值模拟提供地质力学模型，本文初步实现了为二维和三维数值模拟提供地质力学模型的功能。
The most concerned problems in geotechnical engineering are the analysis and tectonic interpretation of geological structures and the stability analysis of rock and (or) soil medium. The available methods to solve the two problems are 3D visualization of geological structures and numerical simulations. However, the most of geological models based on visualization technique or database technique are difficult to mechanical analysis, while the current numerical simulations are difficult in geological modeling, or rather can't realize. Aiming at the situation, especially the lacks of 3DSIS data model which can't realize real-time visualization and is difficult to mechanical analysis, this paper present a geological model went by the name of NMTINF_BR for real-time visualization and numerical simulation. The main jobs of this paper are as follows:
1. The systematical study on geological features, 3D geological model, visualization technique and automatic mesh generation technique indicates that the non-manifold B-Rep can not only represent the complex geological structures, but also provide the geomechanical model for numerical simulations.
2. The data model (NMTINF_BR) in addressing the representation of non-manifold complex geological structures consists of decomposing them into simpler manifold (or manifold with boundary) triangular irregular network and (or) single-vertex and (or) wire edge, and using a two-level representation to stitch them together.
3. The lower level data structure represents topological structure of triangular irregular network. NMTINF_BR introduces the non-manifold information into quad-edge data structure. In this way, the elegant topological operations of quad-edge data structure are preserved, while the representation of manifold and non-manifold objects is skillfully integrated.
4. The higher level data structure stitches the triangular irregular networks and (or) single-vertexes and (or) wire edges together. It represents topological relationships of the lower level components.
5. The implementation of NMTINF_BR data structure is object-oriented design in C++, and
1．综合分析研究地质信息特点、三维地质模型、可视化技术及网格剖分技术等表明，采用非流形边界表达不仅能有效表达岩土工程复杂的地质现象，而且可以为岩土工程稳定性分析提供地质力学模型。
2．在数据模型表达上，采用以二维流形(或二维带边流形)不规则三角网为边界面片，通过宏观和微观两个拓扑层次来表示各拓扑实体间拓扑关系的非流形B-Rep来表达复杂的地质现象，建立了一种面向实时可视化和数值模拟三维地质模型——NMTINF-BR模型。
3．在微观拓扑层次(不规则三角网拓扑结构)上，NMTINF-BR模型将非流形信息引入四方边缘结构，既保留了四方边缘结构对流形形体优雅的拓扑操作，同时又将流形形体与非流形形体的表达有机地结合起来。
4．在宏观拓扑层次上，以PES数据结构为基础，对其加以改进使之将不规则三角形网、区域内的单点、线框边等不同维实体之间的拓扑关系表达出来。
5．用面向对象的编程方法实现了上述数据结构C++类的定义，并初步实现了NMTINF-BR模型一些相关的基本拓扑操作。
6．详细探讨了基于钻孔信息NMTINF-BR地层模型建模算法，采用基于数据预处理后，自下而上逐层交叉判断算法能简洁、有效地建立NMTINF-BR地层模型，模型建立关键技术是不规则三角形网格动态更新算法以及求交算法。
7．NMTINF-BR模型能直接被网格剖分器剖分，因而可以有效地为数值模拟提供地质力学模型，本文初步实现了为二维和三维数值模拟提供地质力学模型的功能。
The most concerned problems in geotechnical engineering are the analysis and tectonic interpretation of geological structures and the stability analysis of rock and (or) soil medium. The available methods to solve the two problems are 3D visualization of geological structures and numerical simulations. However, the most of geological models based on visualization technique or database technique are difficult to mechanical analysis, while the current numerical simulations are difficult in geological modeling, or rather can't realize. Aiming at the situation, especially the lacks of 3DSIS data model which can't realize real-time visualization and is difficult to mechanical analysis, this paper present a geological model went by the name of NMTINF_BR for real-time visualization and numerical simulation. The main jobs of this paper are as follows:
1. The systematical study on geological features, 3D geological model, visualization technique and automatic mesh generation technique indicates that the non-manifold B-Rep can not only represent the complex geological structures, but also provide the geomechanical model for numerical simulations.
2. The data model (NMTINF_BR) in addressing the representation of non-manifold complex geological structures consists of decomposing them into simpler manifold (or manifold with boundary) triangular irregular network and (or) single-vertex and (or) wire edge, and using a two-level representation to stitch them together.
3. The lower level data structure represents topological structure of triangular irregular network. NMTINF_BR introduces the non-manifold information into quad-edge data structure. In this way, the elegant topological operations of quad-edge data structure are preserved, while the representation of manifold and non-manifold objects is skillfully integrated.
4. The higher level data structure stitches the triangular irregular networks and (or) single-vertexes and (or) wire edges together. It represents topological relationships of the lower level components.
5. The implementation of NMTINF_BR data structure is object-oriented design in C++, and
引文
1．李忠武，张红军，吴新林．GIS在地质学中的应用研究现状综述[J]．青海地质科技情报，1998(2)：1～3
2．沈芳，黄润秋，苗放．地理信息系统与地质环境评价[J]．地质灾害与环境保护，2000，11(1)：6～10
3. Jean Benoit, Pedro A de Alba, Stephen M Sawyer. National geotechnical experimentation sites center data repository [A]. David Frost J, Jean2Lou A Chameau. Proceedings of Geographic Information Systems and Their Application in Geotechnical Earthquake Engineering [C]. Atlanta: American Society of Civil Engineers, 1993. 17～21.
4．方海东，施斌，王宝军．GIS在环境岩十工程中应用的回顾与展望[J]．桂林工学院学报．2001，21(4)：371～375
5. Gupta R P and Joshi B C. Landslide Hazard Zoning Using the GIS Approach. Engineering Geology, 1990(2): 119～133
6. Van Dijke J J and Van Westen C J, Rockfall hazard: A geomorphological application of neighbourhood analysis with ILWIS. ITC Journal, 1990(1): 40～44
7. Emmi Jose Macari, James R Martin, Thomas L. Brandon (ASCE A. M.). Liquefaction potential of puertorico [A]. David Frost J, Jean2Lou A Chameau. Proceedings of Geographic Information Systems and Their Application in Geotechnical Earthquake Engineering [C]. Atlanta: American Society y of Civil Engineers, 1993, 72～77
8. James R Martin. Development of geographical information system (GIS) for seismic hazard study of Charleston. SC[A]. David Frost J, Jean2Lou A Chameau. Proceedings of Geographic Information Systems and Their Application in Geotechnical Earthquake Engineering [C]. Atlanta: American Society of Civil Engineers, 1993, 77～82
9．梅希亚—纳瓦罗M著，石宏仁编译．用GIS进行的地质灾害、易损性与风险评价：科罗拉多州伍德斯普林斯市的模式．地质科技动态，1997(6)：15～21
10. Fell R. Landslide risk assessment and acceptable risk. Canadian Geotechnical Journal. 1994(2): 261～272
11. Carlson E. Three Dimensional Conceptual Modeling of Subsurface Structures. ASPRS ACSM, Annual Convention, 1987(4): 188～200
12. Carl Youngmann. Spatial Data Structures for Modeling Subsurface Features. Three Dimensional Applications in GIS, 1989
13. Molenaar Martien. A Formal Data Structure for Three Dimensional Vector Maps. In:Proceedings of 4th Int. Sympo-siumon Spatial Data Handing, Zurich, 1990:830-843
14. Raper J F. Key 3D modeling concepts for geoscientific analysis. In: Turner A K(ed), Three-Dimensional Modeling with Geoscientific Information Systems. NATO ASI 354, Dordrecht, Kluwer Academic Publishers, 1992:215～232
15. Turner A.K. Three-dimensional modeling with geoscientific information systems. NATO ASI 354, Dordrecht: Kluwer Academic Publishers, 1992
16. Thomas R.Fisher. Use of 3D Geographic Information Systems in Hazardous Waste Site Investigations. Oxford University Press. Environmental Modeling with GIS, 1993
17. Rongxing Li. Data structures and application issues in 3D geographic information systems. GEOMATICA, 1994, 48(3): 209～224
18. Pack R T, Tarboton D G, Goodwin C N. The SINMAP approach to terrain stability mapping. In: Moore D, Hungr O, eds. Proceedings of 8th Congress of the International Association of Engineering Geology, RotterDam, Netherlands: AA Balkema Publisher, 1998, 1157～1165
19．李咸亨，谢浩明，郭祺华．应用分散式系统架构于台湾省大地工程资料库之建立．土木水利(台)．1991(4)：37～51
20．陈雷．地理信息系统(GIS)在工程勘察中的应用．工程勘察．1998(2)：10～12
21．孙国庆，郑先昌．城市工程勘察信息系统建设的思路和方法．城市勘测1999(2)：42～48
22．雷明堂，蒋小珍．地理信息系统在岩溶塌陷评价中的运用．中国岩溶．1994，13(4)：351～356
23．江东，王建华，陈佩佩．RS、GIS技术在煤矿地质灾害预测中的应用[J]．遥感信息，1999，(2)：19～21
24．张凌，施斌，王宝军．GIS环境中砂土液化评价方法[J]．水文地质工程地质，2000，27(5)：15～16．
25．张菊明．三维地质模型得设计和显示．中国数学地质进展，1995(7)：189～195
26．柴贺军，黄地龙，黄润秋等．岩体结构三维可视化及其工程应用研究．岩土工程学报，2001(2)：217～220
27．齐安文，吴立新，李冰等．一种新的三维地学空间构模方法——类三棱柱法．煤炭学报，2002(2)：158～163
28．何满潮，刘斌，徐能雄．工程岩体三维可视化构模系统的开发．中国矿业大学学报，2003(1)：38～43
29．李冬田．岩坡摄影地质测量与岩坡空间信息系统．河海大学学报，1999(1)：25～28
30．王笑海．基于三维拓扑格网结构的GIS地层模型研究．中国科学院武汉岩土力学研究所博士学位论文，1999
31．陈健．三维地层信息系统的建模与分析研究．中国科学院武汉岩土力学研究所博士学位论文，2001
32．李先华，林珲，陈晓清等．GIS支持下降雨滑坡的启动机制研究与数字仿真．工程地质学报，2001(1)：133～140
33．李先华，管群，杨武年等．数字地形图上滑坡动态方向稳定性系数的确定与滑坡滑动方向的确定，岩石力学与工程学报．1999(3)：308～311
34．李先华，陈晓清，胡凯衡等．GIS支持下的滑坡运动过程数字仿真．岩石力学与工程学报，2001(2)：175～179
35．王旭春，何满潮，蒋宁静等．在GIS中实现基于力学原理的滑坡稳定性计算．岩石力学与工程学报，2003(6)：977～980
36．谢谟文，江崎哲郎，周国云等．基于GIS空间数据库的三维边坡稳定性分析．岩石力学与工程学报，2002(10)：1494～1499
37．李冬田，余运华．岩坡稳定的层分析方法与抗滑系数图谱．岩土工程学报，200l(1)：18～22
38．陈昌彦，张菊明，杜永廉等．边坡工程地质信息的三维可视化及其在三峡船闸边坡工程中的应用．岩土工程学报，1998(4)：1～6
39．赵晓东，宋振骐．开采沉陷预测的GIS面元栅格数字化模型及其应用．煤炭学报，2000(5)：472～477
40．赵晓东，蒋宇静，宋振骐等．基于GIS平台开采沉陷预测模型的构建与应用．岩石力学与工程学报，2003(6)：981～984
41．王纯祥，白世伟，贺怀建．三维地层可视化中地质建模研究．岩石力学与工程学报，2003(11)：1722～1726
42. Kelk B. 3-D modelling with geoscientific infromation systems: the problem[A]. In: Turner A. K. (ed), Three-Dimensional Modeling with Geoscientific Information Systems[C], NATO ASI 354, 1992, 29-37, Kluwer Academic Publishers, Dordrecht
43. Turner A. K.. Three-Dimensional Modeling with Geoscientific Information Systems [M], 1992, NATO ASI 354, Kluwer Academic Publishers, Dordrecht
44．吴立新，史文中．地理信息系统原理与算法．科学出版社，2003．
45. Ho-Le K. Finite Element Mesh Generation Methods: a Review and Classification. CAD, 20,1988,27-38
46．肖乐斌，钟耳顺，刘纪远，宋关福．三维GIS的基本问题探讨中国图象图形学报．2001，09
47．方海东，施斌，王宝军．GIS在环境岩土工程中应用的回顾与展望[J]．桂林工学院学报，2001，21(4)：371-375．
48．吴立新，史文中．论三维地学空间构模．地理与地理信息科学，2005，第21卷，第1期
49．王纯祥．三维地层信息系统及其力学分析功能研究．中国科学院武汉岩土力学研究所博士学位论文，2003
50．王明华．工程岩体三维地质建模与可视化研究．中国科学院武汉岩土力学研究所博士学位论文，2004．6
51. G.L. Dirichlet, Uber die reductoin der positiven quadratischen formen mit drei underestimm-ten ganzen zahlen. Z. Reine Angew. Math. 40 209-227, 1850.
52. G. Voronoi. Nouvelles applications des patametre continus a la theorie des formes quadratiques. Recherches sur les parallelloedres primitifs, J. Reinie angew. Math. 134, 1908
53 F.P.普雷帕拉塔，M.I.沙莫斯著．计算几何导论．科学出版社，1990．
54. Lee,D.T. and Schachter, B.J. Two Algorithms for Constructing a Delaunay Triangulation. Int'J.of Comp. And Info. Sci.vol.9,no.3,1980,219-242.
55. Shamos M I. and Hoey D. Closest Point Problems. In: Proceedings of the 16th Annual Symposium on the Foundations of Computer Science, 1975. 151～162
56. Lewis B A. and Robinson J S. Triangulation of Planar Regions with Applications. The Computer Journal, 1978, 21 (4): 324～332
57. Sibson R. Locally Equiangular Triangulations. Computer Journal, 1978, 21 (3): 243～245
58. Dawy'er R A. A fast divide and conquer algorithm for constructing Delaunay triangulations[J]. Algorithmica, 1987, (2): 137～151
59. Lawson C L Generation of a triangular grid with application to contour plotting[A]. In: Technical Memorandum [c], Institute of Technology, Jet Pollution Laboratory, California, 1972: 299.
60. Charles L. Lawson. Software for Surface Interpolation. Mathematical Software III (John R. Rice, editor), pages 161-194. Academic Press, New York, 1977.
61. Adrian Bowyer. Computing Dirichlet Tessellations. Computer Journal 24(2): 162-166, 1981.
62. David F. Watson. Computing the n-dimensional Delaunay Tessellation with Application to Voronoi Polytopes. Computer Journal 24(2): 167-172, 1981.
63. Green P J. and Sibson R. Computing Dirichlet Tesselat ions in the Plane. The Computer Journal, 1978, 21 (2): 168— 173
64. Brassel K E. and Reif D. Procedure to Generate Thiessen Polygons. Geophysical Analysis, 1979(11) : 289— 303
65. McCaullaghM T. and Ross C G. Delaunay Triangulat ion of a Random Data Set For Iirarithmic Mapping. The Cartographic Journal, 1980 (17): 93— 99
66. Maus A. Delaunay Triangulation and the Convex Hull of n Points in Expected Linear Time. B IT, 1984 (24): 151— 163
67. 凌海滨,吴兵. 改进的自连接 Delaunay 三角网生成算法[J]. 计算机应用, 1999, 19(12)
68. Blacker Ted D. Paving : a New Approach to Automated Quadrilateral Mesh Generation [ J ] . International Journal for Numerical Methods in Engineering ,1991 ,32 :811 - 8471.
69. Bih - Yaw Shih ,Hiroshi Sakurai. Automated Hexahedral Mesh Generation by Swept Volume Decomposition and Recomposition [ A ] . 5th International Meshing Roundtable [ C ] . Sandia National Laboratories , 1996. 273 - 2801.
70. Schneiders R ,Weiler F. Octree - based Generation of Hexahedral Element Mesher [A ] 15th International Meshing Roundtable[C] . Sandia National Laboratories ,1996. 205 - 2161
71. L. Paul Chew. Constrained Delaunay Triangulations. Algorithmica 4(1):97—108, 1989.
72 Hazlewood C.Approximating Constrained Tetrahedrizations. Computer Aided Geometric Design, 1993, (10): 67-87
73 Weatherill N P, Hassan O. Efficient Three-dimensional Delaunay Triangulation with Automatic Point Creation and Imposed Boundary Constraints. International Journal of Numerical Methods in Engineering, 1994,.37: 2005-2039
74. Lin, M. C., Manocha, D., And Gottschalk, S. Collision detection between geometric models: a survey. In IMA Conference on Mathematics of Surfaces. 1998, vol. 1,602～608.
75. Held, M., Klosowski, J. T., And Mitchell, J. Evaluation of collision detection methods for virtual reality fly-throughs. In Proc. Seventh Canadian Conf. Computer Geometry, 1995, vol. 3,205～210.
76. Jimenez, P., And Torras, C. Collision detection: a geometric approach. In modeling and planning for sensor based intelligent robot systems. World Scientific Pub. Co. 1995, 68～85
77. Gottschalk S, Lin M C, Manoeha D. OBBTree: A Hierarchical structure for rapid interference detection. Computer Graphics, 1996, 30(8): 171～180
78. Moller, Tomas. A fast triangle-triangle intersection test. Journal of Graphics Tools, 1997, 2(2):25-30.
79. Moller, Tomas, and EricHaines. Real-Time Rendering. A.K. Peters, Ltd., Natick, MA. 1999.
80. Lam NSN Spatial interpolation methods: a review[J], the American Cartographer, 1983, 10(2): 129～149
81．李培军，层状地质体的三维模拟与可视化，地学前缘，2002，7，271～277
82. Houlding SW. 3D geoscience modeling computer techniques for geological characterization [M]. Berlin Heidelberg: Springer Verlag, 1994
83．龚健雅 当代GIS的若干理论与技术[M]武汉：武汉测绘科技大学出版社，19991
84．熊伟，毛善君，马蔼乃，沈大勇．面向地质应用的三维数据模型研究．煤田地质与勘探，2002年06期
85．王继周，李成名，林宗坚．三维GIS的基本问题与研究进展．计算机工程与应用，2003年24期
86．李青元，朱小弟，曹代勇．三维地质模型的数据模型研究．中国煤田地质，2000年，第12卷，第3期
87 Shephard MS, Georges MK. Reliability of automatic 3D mesh generation. Computer Methods in Applied Mechanics and Engineering 1992; 101 (1-3):443～462
88. Jonathan Richard Shewchuk, Delaunay refinement algorithms for triangular mesh generation. Computational Geometry 22 (2002) 21-74
89. J. R. Shewchuk, Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery. Eleventh International Meshing Roundtable (Ithaca, New York), pages 193-204. Sandia National Laboratories, September 2002.
90. Gary L. Miller, Dafna Talmor, Shang-Hua Teng, Noel Walkington, and Han Wang. Control Volume Meshes using Sphere Packing: Generation, Refinement and Coarsening. Fifth International Meshing Roundtable (Pittsburgh, Pennsylvania), pages 47-61, October 1996.
91. Delaunay Boris N., Sur la Sph'ere Vide. Izvestia Akademia Nauk SSSR, Ⅶ Seria, Otdelenie Matematicheskii i Estestvennyka Nauk 7:793-800, 1934.
92. Lemon A M, Jones N L. Building solid models from boreholes and user-defined cross-section[J]. Computers and Geosciences, 2003, 29(3): 547—555
93. Shephard M. S. and Georges M. K., Three-dimensional Mesh Generation by Finite Octree Technique. J. Numer. Methods in Engineer. 32: 709-749, 1991.
94. Shewchuk J. R., A Condition Guaranteeing the Existence of Higher-Dimensional Constrained Delaunay Triangulations. Proceedings of the Fourteenth Annual Symposium on Computational Geometry (Minneapolis, Minnesota), pages 76-85, 1998
95．颜七笙．郑盛贵与距离成反比加权法的数据插值方法及程序实现．东华理工学院学报，第28卷，第1期，2005年3月
96．周小文，付晖，吴昌瑜．地层特性随机场插值方法应用研究．岩土力学，第26卷，第2期．2005年2月
97．朱求安，张万昌，余钧辉．基于GIS的空间插值方法研究．江西师范大学学报(自然科学版)，第28卷，第2期，2004年3月
98．吴春发，李星．地质模拟中数据插值方法的应用．地球信息科学，第6卷，第2期，2004年6月
99．王明强，朱永梅，刘文欣．有限元网格划分方法应用研究．机械设计与制造，Feb．2004．No 1
100．黄志超，包忠诩，周天瑞，陈泽中．有限元网格划分技术研究．南昌大学学报(工科版)，第23卷，第4期，2001年12月
101．杜平安．有限元网格划分的基本原则．机械设计与制造，Feb．2000，No 1
102．王华侨．结构有限元分析中的网格划分技术及其应用实例．CAD／CAM与制造业信息化．2005，01
103．郑贵洲，申永利．地质特征三维分析及三维地质模拟现状研究．地球科学进展，第19卷，第2期，2004年4月
104. L. De Floriani, M.M. Mesmoudi, E. Puppo, and F. Morando. Non-manifold decomposition in arbitrary dimensions. In A. Vialard A. Braquelaire, J.O. Lachaud, editor, Discrete Geometry for Computer Imagery, volume 2301 of Lecture Notes in Computer Science, pages 69-80. Springer-Verlag, 2002. Extended version to appear in Graphical Models
105. L. De Floriani, Franco Morando, and Enrico Puppo. A Representation for Abstract Simplicial Complexes: An Analysis and a Comparison. Discrete Geometry for Computer Imagery, volume 2886 of Lecture Notes in Computer Science, pages 454-464. Springer-Verlag, 2003. Extended version to appear in Graphical Models
106. Sang-Hun Lee, Kunwoo Lee: Partial entity structure: a compact non-manifold boundary representation based on partial topological entities. Symposium on Solid Modeling and Applications 2001: 159-170
107. Suzana Djurcilor, Visualizing Gridded Datasets with Larger Number of Missing Value, A dissertation for the degree of doctor of philosophy, University of California, June 2001
108．石教英，蔡文立．科学计算可视化算法与系统．科学出版社，1996．
109．洪歧．张树生，王静，刘雪梅．体绘制技术．计算机应用研究，2004年
110．唐泽圣，孙延奎，邓俊辉．科学计算可视化理论与应用研究进展．清华大学学报(自然科学版)，2001年，第41卷，第45期
111. Neider, Jackie, Davis, Tom. Title. OpenGL Programming Guide Second Edition The Official Guide to Learning OpenGL, Version 1.1 1996 Addison-Wesley Publishing Company
112. T. M. MURALI AND T. A. FUNKHOUSER, Consistent solid and boundary representations from arbitrary polygonal data, Proc. 1997 Symposium on Interactive 3D Graphics, (1997), pp. 155-162.
113. B. G. Baumgart, A Polyhedron Representation for Computer Vision, National Computer Conference, Anaheim, CA, 1975, pp 589-596.
114. K. Weiler, Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments, IEEE Computer Graphics and Application, 1985, 5(1): 21-40
115. Lutz Kettner, Using Generic Programming for Designing a Data Structure for Polyhedral Surfaces, in Proc. 14th Annual ACM Symp. on Computational Geometry, 1998.
116. L. Guibas and J. Stolfi, Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams, ACM Transactions on Graphics, 4(2):74-123, April 1985.
117. D. Lischinski, Incremental Delaunay triangulation, Graphics Gems Ⅳ, ed. P. Heckbert (Academic Press, Boston, 1994), pp. 47～59.
118. Weiler, K The Radial Edge Structure: a Topological Representation for Non-manifold Geometric Boundary Modeling, Wozny, M.J., McLauhlin,H.W and Encamcao, J.L., editors, Geometric Modeling for CAD Applications, Noth-Holland, pp.3-36, 1988
119. Choi, Y., Vertex-based Boundary Representation of Nonmanifold Geometric Models, PhD. Thesis, Carnegie Mellon University, August 1989
120. Gursoz, E.L., Choi, Y., and Prinz, F.B., Vertex-based Boundary Representation of Non-manifold Boundaries, Wozny, M.J., Turner, J.U., and Preiss, K., editors, Geometric Modeling for Product Engineering, North-Holland, pp. 107-130, 1990
121. Rossignac, J. and O'Conner, M.A., SGC: A Dimensional independent Model for Pointsets with Internal Structures and Incomplete Boundaries, Geometric Modeling for Product Engineering, North-Holland, pp. 145-180, 1990
122. Marcelo Kallmann, Hanspeter Bieri, and Daniel Thalmann, Fully Dynamic Constrained Delaunay Triangulations. in Geometric Modelling for Scientific Visualization. 2003. Heidelberg, Germany
123. Mir Abolfazl Mostafavia, Christopher Goldb, Maciej Dakowicz, Delete and insert operations in Voronoi/Delaunay methods and applications. Computers & Geosciences 29 (2003) 523-530
124．包世泰，夏斌，崔学军，黎华．地质三维信息模型研究及其应用[J]．大地构造与成矿学，2004，28(4)：470～476
125. Dubrule O., C. Basire, S. Bombarde. Reservoir Geology using 3-D modelling tools, SPE38659, October 1997
126．中国科学院重点项目结题报告：三维地层信息系统与岩土工程实用软件集成系统．中国科学院武汉岩土力学研究所，2001
127. Michael Garland, Paul S. Heckbert. Fast Polygonal Approximation of Terrains and Height Fields. School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213. 1995
128. James H. Clark. Hierarchical geometric models for visible surface algorithms. CACM, 1976, 19(10): 547～554.
129. Paul S. Heckbert and Michael Garland. Multiresolution modeling for fast rendering. In Proc. Graphics Interface, 1994, pages 43～50, Ban_, Canada, May. Canadian Inf. Proc. Soc.
130. Houlding S W. 3D geosciences modeling-computer techniques for geological characterization[M]. New York: Springer-Verlag, 1994
131．李青元．三维矢量结构GIS混合数据结构研究．中国矿业大学博士学位论文，1996
132．张煜，白世伟．一种基于三棱柱体体元的三维地层建模方法及应用[J]．中国图象图形学报，2001，6(3)：285～29
133. Wu L X. Topological relations embodied in a generalized tri-prism (GTP) model for a 3D geoscience modeling system[J]. Computers and Geosciences, 2004, 30(4): 405～41
134．朱良峰，吴信才，刘修国，尚建嘎．基于钻孔数据的三维地层模型的构建．地理与地理信息科学，2004，20(3)：26～30
135．陈学习，吴立新，车德福，郝海森，徐磊．基于钻孔数据的含断层地质体三维建模方法．煤田地质与勘探，2005，33(5)：5～8
136. http://www.cs.cmu.edu/～quake/triangle.html
137. http://tetgen.berlios.de/
2．沈芳，黄润秋，苗放．地理信息系统与地质环境评价[J]．地质灾害与环境保护，2000，11(1)：6～10
3. Jean Benoit, Pedro A de Alba, Stephen M Sawyer. National geotechnical experimentation sites center data repository [A]. David Frost J, Jean2Lou A Chameau. Proceedings of Geographic Information Systems and Their Application in Geotechnical Earthquake Engineering [C]. Atlanta: American Society of Civil Engineers, 1993. 17～21.
4．方海东，施斌，王宝军．GIS在环境岩十工程中应用的回顾与展望[J]．桂林工学院学报．2001，21(4)：371～375
5. Gupta R P and Joshi B C. Landslide Hazard Zoning Using the GIS Approach. Engineering Geology, 1990(2): 119～133
6. Van Dijke J J and Van Westen C J, Rockfall hazard: A geomorphological application of neighbourhood analysis with ILWIS. ITC Journal, 1990(1): 40～44
7. Emmi Jose Macari, James R Martin, Thomas L. Brandon (ASCE A. M.). Liquefaction potential of puertorico [A]. David Frost J, Jean2Lou A Chameau. Proceedings of Geographic Information Systems and Their Application in Geotechnical Earthquake Engineering [C]. Atlanta: American Society y of Civil Engineers, 1993, 72～77
8. James R Martin. Development of geographical information system (GIS) for seismic hazard study of Charleston. SC[A]. David Frost J, Jean2Lou A Chameau. Proceedings of Geographic Information Systems and Their Application in Geotechnical Earthquake Engineering [C]. Atlanta: American Society of Civil Engineers, 1993, 77～82
9．梅希亚—纳瓦罗M著，石宏仁编译．用GIS进行的地质灾害、易损性与风险评价：科罗拉多州伍德斯普林斯市的模式．地质科技动态，1997(6)：15～21
10. Fell R. Landslide risk assessment and acceptable risk. Canadian Geotechnical Journal. 1994(2): 261～272
11. Carlson E. Three Dimensional Conceptual Modeling of Subsurface Structures. ASPRS ACSM, Annual Convention, 1987(4): 188～200
12. Carl Youngmann. Spatial Data Structures for Modeling Subsurface Features. Three Dimensional Applications in GIS, 1989
13. Molenaar Martien. A Formal Data Structure for Three Dimensional Vector Maps. In:Proceedings of 4th Int. Sympo-siumon Spatial Data Handing, Zurich, 1990:830-843
14. Raper J F. Key 3D modeling concepts for geoscientific analysis. In: Turner A K(ed), Three-Dimensional Modeling with Geoscientific Information Systems. NATO ASI 354, Dordrecht, Kluwer Academic Publishers, 1992:215～232
15. Turner A.K. Three-dimensional modeling with geoscientific information systems. NATO ASI 354, Dordrecht: Kluwer Academic Publishers, 1992
16. Thomas R.Fisher. Use of 3D Geographic Information Systems in Hazardous Waste Site Investigations. Oxford University Press. Environmental Modeling with GIS, 1993
17. Rongxing Li. Data structures and application issues in 3D geographic information systems. GEOMATICA, 1994, 48(3): 209～224
18. Pack R T, Tarboton D G, Goodwin C N. The SINMAP approach to terrain stability mapping. In: Moore D, Hungr O, eds. Proceedings of 8th Congress of the International Association of Engineering Geology, RotterDam, Netherlands: AA Balkema Publisher, 1998, 1157～1165
19．李咸亨，谢浩明，郭祺华．应用分散式系统架构于台湾省大地工程资料库之建立．土木水利(台)．1991(4)：37～51
20．陈雷．地理信息系统(GIS)在工程勘察中的应用．工程勘察．1998(2)：10～12
21．孙国庆，郑先昌．城市工程勘察信息系统建设的思路和方法．城市勘测1999(2)：42～48
22．雷明堂，蒋小珍．地理信息系统在岩溶塌陷评价中的运用．中国岩溶．1994，13(4)：351～356
23．江东，王建华，陈佩佩．RS、GIS技术在煤矿地质灾害预测中的应用[J]．遥感信息，1999，(2)：19～21
24．张凌，施斌，王宝军．GIS环境中砂土液化评价方法[J]．水文地质工程地质，2000，27(5)：15～16．
25．张菊明．三维地质模型得设计和显示．中国数学地质进展，1995(7)：189～195
26．柴贺军，黄地龙，黄润秋等．岩体结构三维可视化及其工程应用研究．岩土工程学报，2001(2)：217～220
27．齐安文，吴立新，李冰等．一种新的三维地学空间构模方法——类三棱柱法．煤炭学报，2002(2)：158～163
28．何满潮，刘斌，徐能雄．工程岩体三维可视化构模系统的开发．中国矿业大学学报，2003(1)：38～43
29．李冬田．岩坡摄影地质测量与岩坡空间信息系统．河海大学学报，1999(1)：25～28
30．王笑海．基于三维拓扑格网结构的GIS地层模型研究．中国科学院武汉岩土力学研究所博士学位论文，1999
31．陈健．三维地层信息系统的建模与分析研究．中国科学院武汉岩土力学研究所博士学位论文，2001
32．李先华，林珲，陈晓清等．GIS支持下降雨滑坡的启动机制研究与数字仿真．工程地质学报，2001(1)：133～140
33．李先华，管群，杨武年等．数字地形图上滑坡动态方向稳定性系数的确定与滑坡滑动方向的确定，岩石力学与工程学报．1999(3)：308～311
34．李先华，陈晓清，胡凯衡等．GIS支持下的滑坡运动过程数字仿真．岩石力学与工程学报，2001(2)：175～179
35．王旭春，何满潮，蒋宁静等．在GIS中实现基于力学原理的滑坡稳定性计算．岩石力学与工程学报，2003(6)：977～980
36．谢谟文，江崎哲郎，周国云等．基于GIS空间数据库的三维边坡稳定性分析．岩石力学与工程学报，2002(10)：1494～1499
37．李冬田，余运华．岩坡稳定的层分析方法与抗滑系数图谱．岩土工程学报，200l(1)：18～22
38．陈昌彦，张菊明，杜永廉等．边坡工程地质信息的三维可视化及其在三峡船闸边坡工程中的应用．岩土工程学报，1998(4)：1～6
39．赵晓东，宋振骐．开采沉陷预测的GIS面元栅格数字化模型及其应用．煤炭学报，2000(5)：472～477
40．赵晓东，蒋宇静，宋振骐等．基于GIS平台开采沉陷预测模型的构建与应用．岩石力学与工程学报，2003(6)：981～984
41．王纯祥，白世伟，贺怀建．三维地层可视化中地质建模研究．岩石力学与工程学报，2003(11)：1722～1726
42. Kelk B. 3-D modelling with geoscientific infromation systems: the problem[A]. In: Turner A. K. (ed), Three-Dimensional Modeling with Geoscientific Information Systems[C], NATO ASI 354, 1992, 29-37, Kluwer Academic Publishers, Dordrecht
43. Turner A. K.. Three-Dimensional Modeling with Geoscientific Information Systems [M], 1992, NATO ASI 354, Kluwer Academic Publishers, Dordrecht
44．吴立新，史文中．地理信息系统原理与算法．科学出版社，2003．
45. Ho-Le K. Finite Element Mesh Generation Methods: a Review and Classification. CAD, 20,1988,27-38
46．肖乐斌，钟耳顺，刘纪远，宋关福．三维GIS的基本问题探讨中国图象图形学报．2001，09
47．方海东，施斌，王宝军．GIS在环境岩土工程中应用的回顾与展望[J]．桂林工学院学报，2001，21(4)：371-375．
48．吴立新，史文中．论三维地学空间构模．地理与地理信息科学，2005，第21卷，第1期
49．王纯祥．三维地层信息系统及其力学分析功能研究．中国科学院武汉岩土力学研究所博士学位论文，2003
50．王明华．工程岩体三维地质建模与可视化研究．中国科学院武汉岩土力学研究所博士学位论文，2004．6
51. G.L. Dirichlet, Uber die reductoin der positiven quadratischen formen mit drei underestimm-ten ganzen zahlen. Z. Reine Angew. Math. 40 209-227, 1850.
52. G. Voronoi. Nouvelles applications des patametre continus a la theorie des formes quadratiques. Recherches sur les parallelloedres primitifs, J. Reinie angew. Math. 134, 1908
53 F.P.普雷帕拉塔，M.I.沙莫斯著．计算几何导论．科学出版社，1990．
54. Lee,D.T. and Schachter, B.J. Two Algorithms for Constructing a Delaunay Triangulation. Int'J.of Comp. And Info. Sci.vol.9,no.3,1980,219-242.
55. Shamos M I. and Hoey D. Closest Point Problems. In: Proceedings of the 16th Annual Symposium on the Foundations of Computer Science, 1975. 151～162
56. Lewis B A. and Robinson J S. Triangulation of Planar Regions with Applications. The Computer Journal, 1978, 21 (4): 324～332
57. Sibson R. Locally Equiangular Triangulations. Computer Journal, 1978, 21 (3): 243～245
58. Dawy'er R A. A fast divide and conquer algorithm for constructing Delaunay triangulations[J]. Algorithmica, 1987, (2): 137～151
59. Lawson C L Generation of a triangular grid with application to contour plotting[A]. In: Technical Memorandum [c], Institute of Technology, Jet Pollution Laboratory, California, 1972: 299.
60. Charles L. Lawson. Software for Surface Interpolation. Mathematical Software III (John R. Rice, editor), pages 161-194. Academic Press, New York, 1977.
61. Adrian Bowyer. Computing Dirichlet Tessellations. Computer Journal 24(2): 162-166, 1981.
62. David F. Watson. Computing the n-dimensional Delaunay Tessellation with Application to Voronoi Polytopes. Computer Journal 24(2): 167-172, 1981.
63. Green P J. and Sibson R. Computing Dirichlet Tesselat ions in the Plane. The Computer Journal, 1978, 21 (2): 168— 173
64. Brassel K E. and Reif D. Procedure to Generate Thiessen Polygons. Geophysical Analysis, 1979(11) : 289— 303
65. McCaullaghM T. and Ross C G. Delaunay Triangulat ion of a Random Data Set For Iirarithmic Mapping. The Cartographic Journal, 1980 (17): 93— 99
66. Maus A. Delaunay Triangulation and the Convex Hull of n Points in Expected Linear Time. B IT, 1984 (24): 151— 163
67. 凌海滨,吴兵. 改进的自连接 Delaunay 三角网生成算法[J]. 计算机应用, 1999, 19(12)
68. Blacker Ted D. Paving : a New Approach to Automated Quadrilateral Mesh Generation [ J ] . International Journal for Numerical Methods in Engineering ,1991 ,32 :811 - 8471.
69. Bih - Yaw Shih ,Hiroshi Sakurai. Automated Hexahedral Mesh Generation by Swept Volume Decomposition and Recomposition [ A ] . 5th International Meshing Roundtable [ C ] . Sandia National Laboratories , 1996. 273 - 2801.
70. Schneiders R ,Weiler F. Octree - based Generation of Hexahedral Element Mesher [A ] 15th International Meshing Roundtable[C] . Sandia National Laboratories ,1996. 205 - 2161
71. L. Paul Chew. Constrained Delaunay Triangulations. Algorithmica 4(1):97—108, 1989.
72 Hazlewood C.Approximating Constrained Tetrahedrizations. Computer Aided Geometric Design, 1993, (10): 67-87
73 Weatherill N P, Hassan O. Efficient Three-dimensional Delaunay Triangulation with Automatic Point Creation and Imposed Boundary Constraints. International Journal of Numerical Methods in Engineering, 1994,.37: 2005-2039
74. Lin, M. C., Manocha, D., And Gottschalk, S. Collision detection between geometric models: a survey. In IMA Conference on Mathematics of Surfaces. 1998, vol. 1,602～608.
75. Held, M., Klosowski, J. T., And Mitchell, J. Evaluation of collision detection methods for virtual reality fly-throughs. In Proc. Seventh Canadian Conf. Computer Geometry, 1995, vol. 3,205～210.
76. Jimenez, P., And Torras, C. Collision detection: a geometric approach. In modeling and planning for sensor based intelligent robot systems. World Scientific Pub. Co. 1995, 68～85
77. Gottschalk S, Lin M C, Manoeha D. OBBTree: A Hierarchical structure for rapid interference detection. Computer Graphics, 1996, 30(8): 171～180
78. Moller, Tomas. A fast triangle-triangle intersection test. Journal of Graphics Tools, 1997, 2(2):25-30.
79. Moller, Tomas, and EricHaines. Real-Time Rendering. A.K. Peters, Ltd., Natick, MA. 1999.
80. Lam NSN Spatial interpolation methods: a review[J], the American Cartographer, 1983, 10(2): 129～149
81．李培军，层状地质体的三维模拟与可视化，地学前缘，2002，7，271～277
82. Houlding SW. 3D geoscience modeling computer techniques for geological characterization [M]. Berlin Heidelberg: Springer Verlag, 1994
83．龚健雅 当代GIS的若干理论与技术[M]武汉：武汉测绘科技大学出版社，19991
84．熊伟，毛善君，马蔼乃，沈大勇．面向地质应用的三维数据模型研究．煤田地质与勘探，2002年06期
85．王继周，李成名，林宗坚．三维GIS的基本问题与研究进展．计算机工程与应用，2003年24期
86．李青元，朱小弟，曹代勇．三维地质模型的数据模型研究．中国煤田地质，2000年，第12卷，第3期
87 Shephard MS, Georges MK. Reliability of automatic 3D mesh generation. Computer Methods in Applied Mechanics and Engineering 1992; 101 (1-3):443～462
88. Jonathan Richard Shewchuk, Delaunay refinement algorithms for triangular mesh generation. Computational Geometry 22 (2002) 21-74
89. J. R. Shewchuk, Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery. Eleventh International Meshing Roundtable (Ithaca, New York), pages 193-204. Sandia National Laboratories, September 2002.
90. Gary L. Miller, Dafna Talmor, Shang-Hua Teng, Noel Walkington, and Han Wang. Control Volume Meshes using Sphere Packing: Generation, Refinement and Coarsening. Fifth International Meshing Roundtable (Pittsburgh, Pennsylvania), pages 47-61, October 1996.
91. Delaunay Boris N., Sur la Sph'ere Vide. Izvestia Akademia Nauk SSSR, Ⅶ Seria, Otdelenie Matematicheskii i Estestvennyka Nauk 7:793-800, 1934.
92. Lemon A M, Jones N L. Building solid models from boreholes and user-defined cross-section[J]. Computers and Geosciences, 2003, 29(3): 547—555
93. Shephard M. S. and Georges M. K., Three-dimensional Mesh Generation by Finite Octree Technique. J. Numer. Methods in Engineer. 32: 709-749, 1991.
94. Shewchuk J. R., A Condition Guaranteeing the Existence of Higher-Dimensional Constrained Delaunay Triangulations. Proceedings of the Fourteenth Annual Symposium on Computational Geometry (Minneapolis, Minnesota), pages 76-85, 1998
95．颜七笙．郑盛贵与距离成反比加权法的数据插值方法及程序实现．东华理工学院学报，第28卷，第1期，2005年3月
96．周小文，付晖，吴昌瑜．地层特性随机场插值方法应用研究．岩土力学，第26卷，第2期．2005年2月
97．朱求安，张万昌，余钧辉．基于GIS的空间插值方法研究．江西师范大学学报(自然科学版)，第28卷，第2期，2004年3月
98．吴春发，李星．地质模拟中数据插值方法的应用．地球信息科学，第6卷，第2期，2004年6月
99．王明强，朱永梅，刘文欣．有限元网格划分方法应用研究．机械设计与制造，Feb．2004．No 1
100．黄志超，包忠诩，周天瑞，陈泽中．有限元网格划分技术研究．南昌大学学报(工科版)，第23卷，第4期，2001年12月
101．杜平安．有限元网格划分的基本原则．机械设计与制造，Feb．2000，No 1
102．王华侨．结构有限元分析中的网格划分技术及其应用实例．CAD／CAM与制造业信息化．2005，01
103．郑贵洲，申永利．地质特征三维分析及三维地质模拟现状研究．地球科学进展，第19卷，第2期，2004年4月
104. L. De Floriani, M.M. Mesmoudi, E. Puppo, and F. Morando. Non-manifold decomposition in arbitrary dimensions. In A. Vialard A. Braquelaire, J.O. Lachaud, editor, Discrete Geometry for Computer Imagery, volume 2301 of Lecture Notes in Computer Science, pages 69-80. Springer-Verlag, 2002. Extended version to appear in Graphical Models
105. L. De Floriani, Franco Morando, and Enrico Puppo. A Representation for Abstract Simplicial Complexes: An Analysis and a Comparison. Discrete Geometry for Computer Imagery, volume 2886 of Lecture Notes in Computer Science, pages 454-464. Springer-Verlag, 2003. Extended version to appear in Graphical Models
106. Sang-Hun Lee, Kunwoo Lee: Partial entity structure: a compact non-manifold boundary representation based on partial topological entities. Symposium on Solid Modeling and Applications 2001: 159-170
107. Suzana Djurcilor, Visualizing Gridded Datasets with Larger Number of Missing Value, A dissertation for the degree of doctor of philosophy, University of California, June 2001
108．石教英，蔡文立．科学计算可视化算法与系统．科学出版社，1996．
109．洪歧．张树生，王静，刘雪梅．体绘制技术．计算机应用研究，2004年
110．唐泽圣，孙延奎，邓俊辉．科学计算可视化理论与应用研究进展．清华大学学报(自然科学版)，2001年，第41卷，第45期
111. Neider, Jackie, Davis, Tom. Title. OpenGL Programming Guide Second Edition The Official Guide to Learning OpenGL, Version 1.1 1996 Addison-Wesley Publishing Company
112. T. M. MURALI AND T. A. FUNKHOUSER, Consistent solid and boundary representations from arbitrary polygonal data, Proc. 1997 Symposium on Interactive 3D Graphics, (1997), pp. 155-162.
113. B. G. Baumgart, A Polyhedron Representation for Computer Vision, National Computer Conference, Anaheim, CA, 1975, pp 589-596.
114. K. Weiler, Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments, IEEE Computer Graphics and Application, 1985, 5(1): 21-40
115. Lutz Kettner, Using Generic Programming for Designing a Data Structure for Polyhedral Surfaces, in Proc. 14th Annual ACM Symp. on Computational Geometry, 1998.
116. L. Guibas and J. Stolfi, Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams, ACM Transactions on Graphics, 4(2):74-123, April 1985.
117. D. Lischinski, Incremental Delaunay triangulation, Graphics Gems Ⅳ, ed. P. Heckbert (Academic Press, Boston, 1994), pp. 47～59.
118. Weiler, K The Radial Edge Structure: a Topological Representation for Non-manifold Geometric Boundary Modeling, Wozny, M.J., McLauhlin,H.W and Encamcao, J.L., editors, Geometric Modeling for CAD Applications, Noth-Holland, pp.3-36, 1988
119. Choi, Y., Vertex-based Boundary Representation of Nonmanifold Geometric Models, PhD. Thesis, Carnegie Mellon University, August 1989
120. Gursoz, E.L., Choi, Y., and Prinz, F.B., Vertex-based Boundary Representation of Non-manifold Boundaries, Wozny, M.J., Turner, J.U., and Preiss, K., editors, Geometric Modeling for Product Engineering, North-Holland, pp. 107-130, 1990
121. Rossignac, J. and O'Conner, M.A., SGC: A Dimensional independent Model for Pointsets with Internal Structures and Incomplete Boundaries, Geometric Modeling for Product Engineering, North-Holland, pp. 145-180, 1990
122. Marcelo Kallmann, Hanspeter Bieri, and Daniel Thalmann, Fully Dynamic Constrained Delaunay Triangulations. in Geometric Modelling for Scientific Visualization. 2003. Heidelberg, Germany
123. Mir Abolfazl Mostafavia, Christopher Goldb, Maciej Dakowicz, Delete and insert operations in Voronoi/Delaunay methods and applications. Computers & Geosciences 29 (2003) 523-530
124．包世泰，夏斌，崔学军，黎华．地质三维信息模型研究及其应用[J]．大地构造与成矿学，2004，28(4)：470～476
125. Dubrule O., C. Basire, S. Bombarde. Reservoir Geology using 3-D modelling tools, SPE38659, October 1997
126．中国科学院重点项目结题报告：三维地层信息系统与岩土工程实用软件集成系统．中国科学院武汉岩土力学研究所，2001
127. Michael Garland, Paul S. Heckbert. Fast Polygonal Approximation of Terrains and Height Fields. School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213. 1995
128. James H. Clark. Hierarchical geometric models for visible surface algorithms. CACM, 1976, 19(10): 547～554.
129. Paul S. Heckbert and Michael Garland. Multiresolution modeling for fast rendering. In Proc. Graphics Interface, 1994, pages 43～50, Ban_, Canada, May. Canadian Inf. Proc. Soc.
130. Houlding S W. 3D geosciences modeling-computer techniques for geological characterization[M]. New York: Springer-Verlag, 1994
131．李青元．三维矢量结构GIS混合数据结构研究．中国矿业大学博士学位论文，1996
132．张煜，白世伟．一种基于三棱柱体体元的三维地层建模方法及应用[J]．中国图象图形学报，2001，6(3)：285～29
133. Wu L X. Topological relations embodied in a generalized tri-prism (GTP) model for a 3D geoscience modeling system[J]. Computers and Geosciences, 2004, 30(4): 405～41
134．朱良峰，吴信才，刘修国，尚建嘎．基于钻孔数据的三维地层模型的构建．地理与地理信息科学，2004，20(3)：26～30
135．陈学习，吴立新，车德福，郝海森，徐磊．基于钻孔数据的含断层地质体三维建模方法．煤田地质与勘探，2005，33(5)：5～8
136. http://www.cs.cmu.edu/～quake/triangle.html
137. http://tetgen.berlios.de/