一个以“移动立方体法”为关键技术的人机交互三维地质建模系统
|
摘要
三维地质建模理论的研究是3DGIS的一项基础性工作，三维地质模型是3DGIS的重要组成部分，是研制三维地学可视化软件和三维地学信息系统的基础和核心。
由于地质现象的复杂性，三维地学模拟的理论方法和技术仍处于研究阶段，还有许多问题有待解决。目前国外在采矿和地球物理领域的三维地学模拟已进入实用阶段，有了一些较成熟的软件，但国内尚无相应水平独立版权的三维地学模拟软件。
不同的建模方法决定了不同的数据结构及可进行的操作，本次论文将现有的地质模型分为两大类：体元充填模型和边界模型。体元充填模型用于描述非均质地质体，边界模型用于描述均质地质体。
实际的地质体都是复杂的、非均质的，在对地质对象进行模拟时，需要对其进行简化。目前，通过使用一定数目的均质模型来表示非均质地质体是一种实际、有效的手段。
本次论文使用的模型是用来表示均质地质体的边界模型，因为本次论文完成软件的侧重点是在模型的编辑方面，而表示非均质地质体的体元充填模型极不适合人机交互的情形。
“八五”期间，我们完成了PandaCAEX计算机辅助勘查系统的研制。这个系统使用多面体表示的边界模型，成功地实现了三维地质模型的计算机交互建模及人机联作重磁反演，达到了国际先进水平，并获得地矿部科技进步二等奖。这个系统对三维地质建模的主要贡献，是针对三维地质模型在交互修改时的困难，独创了一种所谓的“橡皮膜技术”。使用这种技术可以灵活、交互地构制任意形状的三维地质模型。
PandaCAEX的设计目的是解决金属矿的重磁正反演问题，而金属矿多是一个个孤立的地质体，所以模型算法是针对设计单个复杂的地质体的目标设计的，这在当时被认为是够用了。因此这种算法没有处理相邻模型的能力，相邻的模型间会产生不应有的重叠现象。
但地质体不可能都是分离的，不但金属矿有相邻的情形，更重要的是另一类地质体——层状地质体的存在。PandaCAEX系统完全没有处理层状地质体的能力，因为层状地质体其实就是一层层紧密相邻的地质体。
本次论文的研究目的就是解决PandaCAEX系统的相邻模型重叠问题，它独创了一种新的建模技术，既可以表达块状的金属矿模型又可以表达层状模型，重要的是它完全避免了重叠现象的发生。
这种算法的关键是在所定义的空间中，建立了一个辅助的三维网格，通过网格建立起模型之间的联系，以消除模型的重叠现象。其中的关键技术是多面体模型的光栅化和三维光栅数据的多面体化。多面体的光栅化是二维多边形光栅化的直接推广，本次论文的关键创新是解决了三维光栅数据的多面体化问题。
Marching Cubes技术是科学可视化中用于从三维规则数据场中抽取等值面的技术，本次论文对其进行了改造，将其用于三维光栅数据的多面体化，从而实现了从多面体到光栅，再从光栅到多面体的循环，为解决多面体模型的重叠问题提供了算法基础。
本次论文的成果是以本次论文提出的算法为基础，完成了一个人机交互三维地质建模系统。这个系统使用Visual C++从底层开发，具有良好的用户界面，用户可以从多个窗门中从不同角度同时对模型进行编辑。利用这个系统用户可以借助不同种类的数据，在所定义的三维空间中，交互地对各种复杂的地质对象进行模拟，包括模型的相邻、交叉、层状地质模型及断层。事实上在所定义的网格分辨率的精度下，理论上用户可以构造出任意复
d一内地质体。
本论文对此软个1八旬小儿和限制条个1。进行了了详细的说明。并指山了今后的改进力一向。为
例寺理论的完整性，本次论文还对二：维地质建模中攸川的一些关键技术，如：约人三角剖
分技术；离散光滑插值 n引）技术；非均匀有理Bfy条（＊＊＊BS）技术等进行了较详细
的论述。
The study of the theory of three-dimensional geological modeling is one of the fundamental works in
3DGIS. for 3D geological modeling is a very important component of 3DG1S. It is the foundation and
kernel of 3D geosciences visualization software and 3D geosciences information system.
Due to the complexity of geological conditions, the theory and techniques of 3D geological simulation
are still in the phase of research, many problems are still unresolved. These days, in the field of mining
and geophysics, 3D geological simulation has entered the practical stage in the west, having some
experienced software. But in our country there is no such software of our own.
Different methods of modeling decide different data structure and the operations that can be carried out,
this dissertation classifies the existed geological models into two general types: the volume-filling model
and the boundary model. The volume-filling model is used for the heterogeneous geological bodies and
the boundary model used for the homogeneous geological bodies.
In fact, all of the geological bodies are complicated and heterogeneous. While simulating geological
objects, simplification must be done. At present, using some homogeneous geological bodies to
represent the heterogeneous geological bodies is a practical and efficient method.
This dissertation use the boundary model representing homogeneous geological body, since the software
finished this time is focused on the editing of model and the volume-filling model representing
heterogeneous geological bodies is completely not suitable for this situation.
In the period of 8n 5-year-plan, we finished a software of computer aided exploration system named
PandaCAEX. This system used the boundary model represented by polyhedron, and successfully
achieved the interactive modeling of 3D geological model and the inversion of gravity and magnetic
anomalies. This system reached the advanced international standard in some aspects and acquired the 2nd
level award of science and technology from the ministry of geology. The main contribution of the
system to the 3D geological modeling is the original creation of the technique so called "rubber
membrane" aimed to overcome the difficulty of interactive modeling of 3D geological model. Using this
technique, users can easily make arbitrary shaped 3D geological model interactively.
The design target of PandaCAEX is to carry out the inversion of 3D gravity and magnetism of metal
mine model, so the modeling algorithm is aimed to animate the isolated complex geological body, at that
time, that is thought to be OK. Therefore this modeling algorithm has no the ability to deal with adjoined
models, the adjoined models will has unwilling overlap.
But not all of the geological models are isolated, the metal mine model has adjoining situation, and the
more important situation is the existence of layer geological body. PandaCAEX system has no any
ability to deal with such situation, for the layer geological body is some adjoined geological body
indeed.
The purpose of this dissertation is solving the overlapping problem in PandaCAEX when models
adjoined, it creates a new modeling technique that can represent both the metal mine model and the layer
model, the most important is that it completely solve the overlapping problem.
The key of the algorithm is the setup of an accessory 3D grid in the defined 3D space. Models can have
some relationship depending on the grid, resulting that the overlap problem be solved. The core
techniques are the rasterization of polyhedron and the polyhedronization of the 3D raster. Among these techniques, the rasterization of polyhedron is the direct extension of the rasterization of polygon in 2D space, the major creation of this dissertation is the solution of the polyhedronization of the 3D raster. Marching Cubes is the technique that extracts isosurface from 3D raster in scientific visualization. This dissertation modifies it, and then uses the modification to ma
由于地质现象的复杂性，三维地学模拟的理论方法和技术仍处于研究阶段，还有许多问题有待解决。目前国外在采矿和地球物理领域的三维地学模拟已进入实用阶段，有了一些较成熟的软件，但国内尚无相应水平独立版权的三维地学模拟软件。
不同的建模方法决定了不同的数据结构及可进行的操作，本次论文将现有的地质模型分为两大类：体元充填模型和边界模型。体元充填模型用于描述非均质地质体，边界模型用于描述均质地质体。
实际的地质体都是复杂的、非均质的，在对地质对象进行模拟时，需要对其进行简化。目前，通过使用一定数目的均质模型来表示非均质地质体是一种实际、有效的手段。
本次论文使用的模型是用来表示均质地质体的边界模型，因为本次论文完成软件的侧重点是在模型的编辑方面，而表示非均质地质体的体元充填模型极不适合人机交互的情形。
“八五”期间，我们完成了PandaCAEX计算机辅助勘查系统的研制。这个系统使用多面体表示的边界模型，成功地实现了三维地质模型的计算机交互建模及人机联作重磁反演，达到了国际先进水平，并获得地矿部科技进步二等奖。这个系统对三维地质建模的主要贡献，是针对三维地质模型在交互修改时的困难，独创了一种所谓的“橡皮膜技术”。使用这种技术可以灵活、交互地构制任意形状的三维地质模型。
PandaCAEX的设计目的是解决金属矿的重磁正反演问题，而金属矿多是一个个孤立的地质体，所以模型算法是针对设计单个复杂的地质体的目标设计的，这在当时被认为是够用了。因此这种算法没有处理相邻模型的能力，相邻的模型间会产生不应有的重叠现象。
但地质体不可能都是分离的，不但金属矿有相邻的情形，更重要的是另一类地质体——层状地质体的存在。PandaCAEX系统完全没有处理层状地质体的能力，因为层状地质体其实就是一层层紧密相邻的地质体。
本次论文的研究目的就是解决PandaCAEX系统的相邻模型重叠问题，它独创了一种新的建模技术，既可以表达块状的金属矿模型又可以表达层状模型，重要的是它完全避免了重叠现象的发生。
这种算法的关键是在所定义的空间中，建立了一个辅助的三维网格，通过网格建立起模型之间的联系，以消除模型的重叠现象。其中的关键技术是多面体模型的光栅化和三维光栅数据的多面体化。多面体的光栅化是二维多边形光栅化的直接推广，本次论文的关键创新是解决了三维光栅数据的多面体化问题。
Marching Cubes技术是科学可视化中用于从三维规则数据场中抽取等值面的技术，本次论文对其进行了改造，将其用于三维光栅数据的多面体化，从而实现了从多面体到光栅，再从光栅到多面体的循环，为解决多面体模型的重叠问题提供了算法基础。
本次论文的成果是以本次论文提出的算法为基础，完成了一个人机交互三维地质建模系统。这个系统使用Visual C++从底层开发，具有良好的用户界面，用户可以从多个窗门中从不同角度同时对模型进行编辑。利用这个系统用户可以借助不同种类的数据，在所定义的三维空间中，交互地对各种复杂的地质对象进行模拟，包括模型的相邻、交叉、层状地质模型及断层。事实上在所定义的网格分辨率的精度下，理论上用户可以构造出任意复
d一内地质体。
本论文对此软个1八旬小儿和限制条个1。进行了了详细的说明。并指山了今后的改进力一向。为
例寺理论的完整性，本次论文还对二：维地质建模中攸川的一些关键技术，如：约人三角剖
分技术；离散光滑插值 n引）技术；非均匀有理Bfy条（＊＊＊BS）技术等进行了较详细
的论述。
The study of the theory of three-dimensional geological modeling is one of the fundamental works in
3DGIS. for 3D geological modeling is a very important component of 3DG1S. It is the foundation and
kernel of 3D geosciences visualization software and 3D geosciences information system.
Due to the complexity of geological conditions, the theory and techniques of 3D geological simulation
are still in the phase of research, many problems are still unresolved. These days, in the field of mining
and geophysics, 3D geological simulation has entered the practical stage in the west, having some
experienced software. But in our country there is no such software of our own.
Different methods of modeling decide different data structure and the operations that can be carried out,
this dissertation classifies the existed geological models into two general types: the volume-filling model
and the boundary model. The volume-filling model is used for the heterogeneous geological bodies and
the boundary model used for the homogeneous geological bodies.
In fact, all of the geological bodies are complicated and heterogeneous. While simulating geological
objects, simplification must be done. At present, using some homogeneous geological bodies to
represent the heterogeneous geological bodies is a practical and efficient method.
This dissertation use the boundary model representing homogeneous geological body, since the software
finished this time is focused on the editing of model and the volume-filling model representing
heterogeneous geological bodies is completely not suitable for this situation.
In the period of 8n 5-year-plan, we finished a software of computer aided exploration system named
PandaCAEX. This system used the boundary model represented by polyhedron, and successfully
achieved the interactive modeling of 3D geological model and the inversion of gravity and magnetic
anomalies. This system reached the advanced international standard in some aspects and acquired the 2nd
level award of science and technology from the ministry of geology. The main contribution of the
system to the 3D geological modeling is the original creation of the technique so called "rubber
membrane" aimed to overcome the difficulty of interactive modeling of 3D geological model. Using this
technique, users can easily make arbitrary shaped 3D geological model interactively.
The design target of PandaCAEX is to carry out the inversion of 3D gravity and magnetism of metal
mine model, so the modeling algorithm is aimed to animate the isolated complex geological body, at that
time, that is thought to be OK. Therefore this modeling algorithm has no the ability to deal with adjoined
models, the adjoined models will has unwilling overlap.
But not all of the geological models are isolated, the metal mine model has adjoining situation, and the
more important situation is the existence of layer geological body. PandaCAEX system has no any
ability to deal with such situation, for the layer geological body is some adjoined geological body
indeed.
The purpose of this dissertation is solving the overlapping problem in PandaCAEX when models
adjoined, it creates a new modeling technique that can represent both the metal mine model and the layer
model, the most important is that it completely solve the overlapping problem.
The key of the algorithm is the setup of an accessory 3D grid in the defined 3D space. Models can have
some relationship depending on the grid, resulting that the overlap problem be solved. The core
techniques are the rasterization of polyhedron and the polyhedronization of the 3D raster. Among these techniques, the rasterization of polyhedron is the direct extension of the rasterization of polygon in 2D space, the major creation of this dissertation is the solution of the polyhedronization of the 3D raster. Marching Cubes is the technique that extracts isosurface from 3D raster in scientific visualization. This dissertation modifies it, and then uses the modification to ma
引文
[1] 李培军．层状地质体的三维模拟与可视化．地学前缘．2000，7(增刊)：271～277
[2] 龚健雅．GIS中面向对象时空数据模型．测绘学报．1997，26(4)：290～299
[3] Simon W. Houlding. 3D Geoscience modeling: computer techniques for geological characterization. Berlin: Springer-Verlag. 1994
[4] 侯恩科，吴立新．三维地学模拟几个方面的研究现状与发展趋势．煤田地质与勘探．2000，28(6)：5～8
[5] 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．2000，12(3)：57～61
[6] 孟小红，王卫民，姚长利，胡朝顺．地质模型计算机辅助设计原理与应用．地质出版社．2001
[7] 孙洪泉．地质统计学及其应用．中国矿业大学出版社．1990
[8] 牛文杰，朱大培，陈其明．滑动邻域克里金插值法的改进．计算机辅助设计与图形学学报．2001，Vol．13，No．8：752～756
[9] 王靖波等．基于Kriging方法的空间散乱点插值．计算机辅助设计与图形学学报．1999，Vol．11，No．6：525～529
[10] 普雷帕拉塔，沙莫斯．计算几何导论．科学出版社，1990年11月
[11] A. K. Cline, R. J. Renka. A constrained two-dimensional triangulation and the solution of closest node problem in the presence of barriers. Society for Industrial and Applied Mathematics. 1990, 27(5), 1305～1321
[12] 李伟青，彭群生．一个通用的快速三角化算法．计算机辅助设计与图形学学报．2001，Vol．13，No．9：769～773
[13] 马小虎，潘志庚，石教英．基于凸凹顶点判定的简单多边形Delaunay三角剖分．计算机辅助设计与图形学学报．1999，Vol．11，No．1：1～3
[14] 孙宏伟，王健，杨百龙，张树生．一种适合VRML应用的平面三角剖分快速算法．计算机辅助设计与图形学学报．2001，Vol．13，No．4：324～327
[15] 迟元林，李斌，苏勇．地质体的二维数值剖分．大庆石油地质与开发．1999，18(1)
[16] 梁力，张奇志，林韵梅．一种有效的三维网格自动划分方法．东北大学学报(自然科学版)．1999，2
[17] 栾茹，白保东，谢德馨．基于正四面体的八叉树法三维有限元网格生成．沈阳工业大学学报．1999，21(5)
[18] Mallet J. L.. Discrete smooth interpolation in Geometric Modeling. Computer aided design. 1992, 24(4): 178～190
[19] Mallet J. L. Discrete Modeling for nature objects. Mathematical Geology. 1997, 29(2): 199-218
[20] 施法中．计算机辅助几何设计与非均匀有理B样条(CAGD & NURBS)．北京航空航天大学出版．1994
[21] T. R. Fisher, R. Q. Wales. Rational splines and multidimensional geologic modeling. Computer graphics in geology. Pages 17～28, 1992
[22] Herring John R.. Using Spline Functions to Represent Distributed Attributes. Auto-Carto 10: Technical Papers of the 1991 ACSM-ASPRS Annual Convention. Baltimore:ACSM-ASPRS. 1991, 6:46～58
[23] 乔林，费广正等编著．OpenGL程序设计．清华大学出版社．2000
[24] 廖朵朵，张华军编著．OpenGL三维图形程序设计．星球地图出版社．1996
[25] 唐泽圣，周嘉玉，李新友．计算机图形学基础．清华大学出版社．1996
[26] 孙家广，许隆文．计算机图形学．高等教育出版社．1986
[27] 林振民，陈少强．三维重磁交互解释及区域与局部异常的分离．地球物理学报．1996，39(5)：705～711
[28] 林振民，陈少强．计算机上的橡皮膜技术．物探化探计算技术．1996，18(1)：6～16
[29] SURFACE CONSTRUCTION ALGORITHM. Computer Graphics, 1987, 21(4): 163～170
[30] Cline H. E., Lorensen W. E., Ludke S.. Two Algorithms for Three-Dimensional Reconstruction of Tomograms. Medical Physics. 1988, 15(3)
[31] Durst M. J. Letters: Additional Reference to "Marching Cubes". Computer Graphics. 22(2), 1988
[32] G. M. Nielsin, B. Hamann. The Asymptotic Decider: Resulving the Ambiguity in Marching Cubes. Proc. Visualization 91: 83～91. Oct, 1991
[33] 秦绪佳．医学图象三维重建及可视化技术研究．大连理工大学博士论文．2001
[34] Barnnet C. T.. Theoretical modeling of the magnetic and gravitational fields of an arbitrarily shaped three-dimensional body. Geophysics. 1976, 41: 1353～1364
[35] M. Okabe. Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies. Geophysics. 1979, 44(4): 730～741
[36] V. Pohanka. Optimum expression for computation of the gravity field of a homogeneous polyhedral body. Geophysical Prospecting. 1988, 36:733～751
[37] Yufu Chai, William J. Hinze. Gravity inversion of an interface above which the density contrast varies exponentially with depth. Geophysics. Vol.53, June, 1988: 837～845
[38] P. Ramarao, I. V. Radhakrishna Murthy. TWO FORTRAN 77 FUNCTION SUBPROGRAMS TO CALCULATE GRAVITY ANOMALIES OF BODIES OF FINITE AND INFINITE STRIKE LENGTH WITH THE DENSITY CONTRAST DEFFERING WITH DEPTH. Computers & Geosciences. Vol. 15, No.8: 1265～1277
[39] V. Pinto, A. Casas. AN INTERACTIVE 2D AND 3D GRAVITY MODELING PROGRAM OF IBM-COMPATABLE PERSONAL COMPUTERS. Computers & Geosciences. Vol.22, No.5: 535～546
[40] H. -J. Gotze, Bernd Lahmeyerv. Application of three-dimensional interactive modeling in gravity and magnetics. Geophysics. VOL.53, NO.8, 1988: 1096-1108
[41] 楼海，王椿镛．三维连续密度分布的重力计算及应用．地震学报．1999，21(3)：297～304
[42] 冯锐．三维物性分布的位场计算．地球物理学报．1986，29(4)：399～406
[43] 冯锐，陶裕录．地震-重力联合反演中的非块状一致性模型．地球物理学报．1993，36(4)：463～475
[44] W. Schroeder et al.. Decimation of Triangle Meshes. Computer Graphics. Vol. 26, No.2,1992
[45] 郜延红，周云轩，刘万崧．地球物理位场可视化建模初步探讨．长春科技大学学报．2000，30(2)：185～189
[46] 张剑秋，张福炎．地球物理勘探可视化工作的挑战与机遇．石油地球物理勘探．1997，32(6)：884～889
[47] 陈少强，黄毓瑜．一个微机上的可视化系统及其在地球物理中的应用．工程图学学报．2000，21(3)：103～107
[48] 林振民，陈少强．三维可视化技术在固体矿产中的应用。物探化探计算技术．1994，16(4)：338～344
[49] 林振民，陈少强．平面及直线与多面体相交算法．物探化探计算技术．1996，18(3)：215～218
[50] 戴上平，黄革新．空间数据模型研究．武汉冶金工业大学学报．1999，22(1)
[51] 孙敏，陈军．基于几何元素的三维景观实体建模研究．武汉测绘科技大学学报．2000，25(3)：233～277
[52] 《数学手册》编写组．数学手册．人民教育出版社．1977
[53] David J．Kruglinski 著，潘爱民，王国印译．Visual C++技术内幕(第四版)．清华大学出版社．1999
[54] 侯俊杰．深入浅出MFC(第二版)．华中科技大学出版社．2001
[55] 南开大学数学系《空间解析几何引论》编写组．空间解析几何引论．人民教育出版社．1978
[56] Huang-Yungao-G, Mallet-Jean-Laurent. Conversion of 3D grid into T-surfaces. Computer graphics in geology. Pages 3～16, 1992
[57] Philippe Renard, Gabriel Courrioux. Three-Dimensional Geometric Modeling of a Faulted Domain: The Soultz Horst Example (Alsace, France). Computer & Geosciences. 1994, 20(9): 1379～1390
[58] Ruber O.. Interactive design of faulted geological surface[J]. Geol Jb. 1988, A104: 281～293.
[59] Pflug R.. Solid modeling of geological objects with 3D raster[J]. Geol Jb.. 1988, A104: 213～219
[60] M. Breunig. An approach to the integration of spatial data and systems for a 3D geo-informationsystem. Computers & Geosciences. 1999, 25:39～48
[61] Thomas A. Jones. Using flowpaths and vector fields in object-based modeling. Computers & Geosciences. 2001,27:133～138
[62] Arnaud de la Losa, Bernard Cervelle. 3D Topological modeling and visualization for 3D GIS. Computers & Graphics. 1999, 23:469～478
[63] D. W. Fellner, S. Havemann, G. Muller. Modeling of and navigation in complex 3D
documents. Comput. & Graphics. 1998, 22 (6) : 647-653
[64] Ryutarou Ohbuchi, Yoshiyuki Kokojima, Shigeo Takahashi. Blending shapes by using subdivision surfaces. Computers & Graphics. 2001, 25: 41-58
[65] Xiang Fang, Hujun Bao, Pheng Ann Heng, Tien Tsin Wong, Qunsheng Peng. Continuous field based free-form surface modeling and morphing. Computers & Graphics. 2001, 25: 235-243
[66] Gabriela Garza, Luis Pineda. Synthesis of solid models of polyhedra from their orthogonal views using logical representations. Expert Systems with Applications. 1998, 14: 91-108
[67] Ryutarou Ohbuchi, Hiroshi Masuda, Masaki Aono. Data embedding algorithms for geometrical and non-geometrical targets in three-dimensional polygonal models. Computer Communications. 1998, 21: 1344-1354
[68] U. Labsik, L. Kobbelt, R. Schneider, H. P. Seidel. Progressive transmission of subdivision surfaces. Computational Geometry. 2000, 15: 25-39
[69] M. H. Kuo . Automatic extraction of quadric surfaces from wire-frame models. Computers & Graphics. 2001, 25: 109-119
[70] Dinesh Shikhare, S. Gopalsamy, etc. Zeus: surface modeling, surface grid generation, tetrahedral volume discretization. Computers & Graphics. 1999, 23: 59-72
[71] Marco Viceconti, Cinzia Zannoni, DeboraTesti, Angelo Cappello. CT data sets surface extraction for biomechanical modeling of long bones. Computer Methods and Programs in Biomedicine. 1999, 59:159-166
[72] S. W. Houlding. Real time grade control in mine-planning & production. Computer Applications in the mineral industry. 1991: 507-518
[73] P. S. Campbell, B. F. Smith. An integrated mine planning system for geology, surveying, and engineering. Computer Applications in the mineral industry. 1991: 115-127
[74] N. M. Sirakov , F. M. Muge . A system for reconstructing and visualizing three-dimensional objects. Computers & Geosciences. 2001, 1: 59
[75] D. Seifert , J. L. Soson. Object and Pixel-Based Reservoir Modeling of a Braided Fluvial Reservoir. Mathematical Geology. July, 2000 , Volume 32, Number 5, P581
[76] Otto Ruber. Interactive Design of Faulted Geological Surfaces. Geol. Jb.. Hannover 1988． P.281-293
[77] Reinhard Pflug . Solid Modeling of Geological Objects with 3D Rasters. Geol.Jb. Hannover 1988, P.213-219
[78] Philippe Renard, Gabrel Courrioux. Three-Dimensional geometric modeling of a faulted domain:The Soultz Horst example(Alsace, France). Computers & Geosciences. 1994, Vol.20, No.9: 1379-1390
[2] 龚健雅．GIS中面向对象时空数据模型．测绘学报．1997，26(4)：290～299
[3] Simon W. Houlding. 3D Geoscience modeling: computer techniques for geological characterization. Berlin: Springer-Verlag. 1994
[4] 侯恩科，吴立新．三维地学模拟几个方面的研究现状与发展趋势．煤田地质与勘探．2000，28(6)：5～8
[5] 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．2000，12(3)：57～61
[6] 孟小红，王卫民，姚长利，胡朝顺．地质模型计算机辅助设计原理与应用．地质出版社．2001
[7] 孙洪泉．地质统计学及其应用．中国矿业大学出版社．1990
[8] 牛文杰，朱大培，陈其明．滑动邻域克里金插值法的改进．计算机辅助设计与图形学学报．2001，Vol．13，No．8：752～756
[9] 王靖波等．基于Kriging方法的空间散乱点插值．计算机辅助设计与图形学学报．1999，Vol．11，No．6：525～529
[10] 普雷帕拉塔，沙莫斯．计算几何导论．科学出版社，1990年11月
[11] A. K. Cline, R. J. Renka. A constrained two-dimensional triangulation and the solution of closest node problem in the presence of barriers. Society for Industrial and Applied Mathematics. 1990, 27(5), 1305～1321
[12] 李伟青，彭群生．一个通用的快速三角化算法．计算机辅助设计与图形学学报．2001，Vol．13，No．9：769～773
[13] 马小虎，潘志庚，石教英．基于凸凹顶点判定的简单多边形Delaunay三角剖分．计算机辅助设计与图形学学报．1999，Vol．11，No．1：1～3
[14] 孙宏伟，王健，杨百龙，张树生．一种适合VRML应用的平面三角剖分快速算法．计算机辅助设计与图形学学报．2001，Vol．13，No．4：324～327
[15] 迟元林，李斌，苏勇．地质体的二维数值剖分．大庆石油地质与开发．1999，18(1)
[16] 梁力，张奇志，林韵梅．一种有效的三维网格自动划分方法．东北大学学报(自然科学版)．1999，2
[17] 栾茹，白保东，谢德馨．基于正四面体的八叉树法三维有限元网格生成．沈阳工业大学学报．1999，21(5)
[18] Mallet J. L.. Discrete smooth interpolation in Geometric Modeling. Computer aided design. 1992, 24(4): 178～190
[19] Mallet J. L. Discrete Modeling for nature objects. Mathematical Geology. 1997, 29(2): 199-218
[20] 施法中．计算机辅助几何设计与非均匀有理B样条(CAGD & NURBS)．北京航空航天大学出版．1994
[21] T. R. Fisher, R. Q. Wales. Rational splines and multidimensional geologic modeling. Computer graphics in geology. Pages 17～28, 1992
[22] Herring John R.. Using Spline Functions to Represent Distributed Attributes. Auto-Carto 10: Technical Papers of the 1991 ACSM-ASPRS Annual Convention. Baltimore:ACSM-ASPRS. 1991, 6:46～58
[23] 乔林，费广正等编著．OpenGL程序设计．清华大学出版社．2000
[24] 廖朵朵，张华军编著．OpenGL三维图形程序设计．星球地图出版社．1996
[25] 唐泽圣，周嘉玉，李新友．计算机图形学基础．清华大学出版社．1996
[26] 孙家广，许隆文．计算机图形学．高等教育出版社．1986
[27] 林振民，陈少强．三维重磁交互解释及区域与局部异常的分离．地球物理学报．1996，39(5)：705～711
[28] 林振民，陈少强．计算机上的橡皮膜技术．物探化探计算技术．1996，18(1)：6～16
[29] SURFACE CONSTRUCTION ALGORITHM. Computer Graphics, 1987, 21(4): 163～170
[30] Cline H. E., Lorensen W. E., Ludke S.. Two Algorithms for Three-Dimensional Reconstruction of Tomograms. Medical Physics. 1988, 15(3)
[31] Durst M. J. Letters: Additional Reference to "Marching Cubes". Computer Graphics. 22(2), 1988
[32] G. M. Nielsin, B. Hamann. The Asymptotic Decider: Resulving the Ambiguity in Marching Cubes. Proc. Visualization 91: 83～91. Oct, 1991
[33] 秦绪佳．医学图象三维重建及可视化技术研究．大连理工大学博士论文．2001
[34] Barnnet C. T.. Theoretical modeling of the magnetic and gravitational fields of an arbitrarily shaped three-dimensional body. Geophysics. 1976, 41: 1353～1364
[35] M. Okabe. Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies. Geophysics. 1979, 44(4): 730～741
[36] V. Pohanka. Optimum expression for computation of the gravity field of a homogeneous polyhedral body. Geophysical Prospecting. 1988, 36:733～751
[37] Yufu Chai, William J. Hinze. Gravity inversion of an interface above which the density contrast varies exponentially with depth. Geophysics. Vol.53, June, 1988: 837～845
[38] P. Ramarao, I. V. Radhakrishna Murthy. TWO FORTRAN 77 FUNCTION SUBPROGRAMS TO CALCULATE GRAVITY ANOMALIES OF BODIES OF FINITE AND INFINITE STRIKE LENGTH WITH THE DENSITY CONTRAST DEFFERING WITH DEPTH. Computers & Geosciences. Vol. 15, No.8: 1265～1277
[39] V. Pinto, A. Casas. AN INTERACTIVE 2D AND 3D GRAVITY MODELING PROGRAM OF IBM-COMPATABLE PERSONAL COMPUTERS. Computers & Geosciences. Vol.22, No.5: 535～546
[40] H. -J. Gotze, Bernd Lahmeyerv. Application of three-dimensional interactive modeling in gravity and magnetics. Geophysics. VOL.53, NO.8, 1988: 1096-1108
[41] 楼海，王椿镛．三维连续密度分布的重力计算及应用．地震学报．1999，21(3)：297～304
[42] 冯锐．三维物性分布的位场计算．地球物理学报．1986，29(4)：399～406
[43] 冯锐，陶裕录．地震-重力联合反演中的非块状一致性模型．地球物理学报．1993，36(4)：463～475
[44] W. Schroeder et al.. Decimation of Triangle Meshes. Computer Graphics. Vol. 26, No.2,1992
[45] 郜延红，周云轩，刘万崧．地球物理位场可视化建模初步探讨．长春科技大学学报．2000，30(2)：185～189
[46] 张剑秋，张福炎．地球物理勘探可视化工作的挑战与机遇．石油地球物理勘探．1997，32(6)：884～889
[47] 陈少强，黄毓瑜．一个微机上的可视化系统及其在地球物理中的应用．工程图学学报．2000，21(3)：103～107
[48] 林振民，陈少强．三维可视化技术在固体矿产中的应用。物探化探计算技术．1994，16(4)：338～344
[49] 林振民，陈少强．平面及直线与多面体相交算法．物探化探计算技术．1996，18(3)：215～218
[50] 戴上平，黄革新．空间数据模型研究．武汉冶金工业大学学报．1999，22(1)
[51] 孙敏，陈军．基于几何元素的三维景观实体建模研究．武汉测绘科技大学学报．2000，25(3)：233～277
[52] 《数学手册》编写组．数学手册．人民教育出版社．1977
[53] David J．Kruglinski 著，潘爱民，王国印译．Visual C++技术内幕(第四版)．清华大学出版社．1999
[54] 侯俊杰．深入浅出MFC(第二版)．华中科技大学出版社．2001
[55] 南开大学数学系《空间解析几何引论》编写组．空间解析几何引论．人民教育出版社．1978
[56] Huang-Yungao-G, Mallet-Jean-Laurent. Conversion of 3D grid into T-surfaces. Computer graphics in geology. Pages 3～16, 1992
[57] Philippe Renard, Gabriel Courrioux. Three-Dimensional Geometric Modeling of a Faulted Domain: The Soultz Horst Example (Alsace, France). Computer & Geosciences. 1994, 20(9): 1379～1390
[58] Ruber O.. Interactive design of faulted geological surface[J]. Geol Jb. 1988, A104: 281～293.
[59] Pflug R.. Solid modeling of geological objects with 3D raster[J]. Geol Jb.. 1988, A104: 213～219
[60] M. Breunig. An approach to the integration of spatial data and systems for a 3D geo-informationsystem. Computers & Geosciences. 1999, 25:39～48
[61] Thomas A. Jones. Using flowpaths and vector fields in object-based modeling. Computers & Geosciences. 2001,27:133～138
[62] Arnaud de la Losa, Bernard Cervelle. 3D Topological modeling and visualization for 3D GIS. Computers & Graphics. 1999, 23:469～478
[63] D. W. Fellner, S. Havemann, G. Muller. Modeling of and navigation in complex 3D
documents. Comput. & Graphics. 1998, 22 (6) : 647-653
[64] Ryutarou Ohbuchi, Yoshiyuki Kokojima, Shigeo Takahashi. Blending shapes by using subdivision surfaces. Computers & Graphics. 2001, 25: 41-58
[65] Xiang Fang, Hujun Bao, Pheng Ann Heng, Tien Tsin Wong, Qunsheng Peng. Continuous field based free-form surface modeling and morphing. Computers & Graphics. 2001, 25: 235-243
[66] Gabriela Garza, Luis Pineda. Synthesis of solid models of polyhedra from their orthogonal views using logical representations. Expert Systems with Applications. 1998, 14: 91-108
[67] Ryutarou Ohbuchi, Hiroshi Masuda, Masaki Aono. Data embedding algorithms for geometrical and non-geometrical targets in three-dimensional polygonal models. Computer Communications. 1998, 21: 1344-1354
[68] U. Labsik, L. Kobbelt, R. Schneider, H. P. Seidel. Progressive transmission of subdivision surfaces. Computational Geometry. 2000, 15: 25-39
[69] M. H. Kuo . Automatic extraction of quadric surfaces from wire-frame models. Computers & Graphics. 2001, 25: 109-119
[70] Dinesh Shikhare, S. Gopalsamy, etc. Zeus: surface modeling, surface grid generation, tetrahedral volume discretization. Computers & Graphics. 1999, 23: 59-72
[71] Marco Viceconti, Cinzia Zannoni, DeboraTesti, Angelo Cappello. CT data sets surface extraction for biomechanical modeling of long bones. Computer Methods and Programs in Biomedicine. 1999, 59:159-166
[72] S. W. Houlding. Real time grade control in mine-planning & production. Computer Applications in the mineral industry. 1991: 507-518
[73] P. S. Campbell, B. F. Smith. An integrated mine planning system for geology, surveying, and engineering. Computer Applications in the mineral industry. 1991: 115-127
[74] N. M. Sirakov , F. M. Muge . A system for reconstructing and visualizing three-dimensional objects. Computers & Geosciences. 2001, 1: 59
[75] D. Seifert , J. L. Soson. Object and Pixel-Based Reservoir Modeling of a Braided Fluvial Reservoir. Mathematical Geology. July, 2000 , Volume 32, Number 5, P581
[76] Otto Ruber. Interactive Design of Faulted Geological Surfaces. Geol. Jb.. Hannover 1988． P.281-293
[77] Reinhard Pflug . Solid Modeling of Geological Objects with 3D Rasters. Geol.Jb. Hannover 1988, P.213-219
[78] Philippe Renard, Gabrel Courrioux. Three-Dimensional geometric modeling of a faulted domain:The Soultz Horst example(Alsace, France). Computers & Geosciences. 1994, Vol.20, No.9: 1379-1390