基于空间离散点的三维地质体精细建模
|
摘要
三维地质建模是运用计算机在三维环境下进行地质分析的技术。传统的地质信息模拟与表达只是将三维空间信息在某一平面上进行呈现,存在空间信息损失与失真、制图过程繁杂和更新信息困难的缺陷。地质体三维空间模型能够获得直观的地下地质体,在指导地质找矿和矿业开发等方面具有重要的实用价值。
本文在研究凸壳算法和Delaunay三角剖分算法的基础上,结合四面体剖分算法和快速凸包技术进行离散点集的凸壳求取,实现了凸壳地质体的建模和体积计算。生成的三维文件可在蓝光三维可视化系统中直接打开和编辑。数据量大和数据精度高是地质体的两大特点,鉴于以上特点,本文对算法进行了两方面的优化:一是结合快速凸包技术,利用一维和二维极值点构造最大初始凸壳,使尽可能多的点包含其中;二是利用向量数量积判断点和凸壳的位置关系,排除初始凸壳的内部点。
本文在凸壳地质体建模研究的基础上,给出了由离散点生成最大体积非凸壳地质体构建算法,并对算法进行了优化处理。该算法适用于给定点必须是生成的地质体的顶点的情况。在研究平面两个三角形不相交判定定理的基础上,本文总结出三维空间两个三角形不相交的判断方法,并给出了相应的证明。
通过在山东某矿的实际应用表明,本模块构建的地质体模型能直观的再现地下地质体的形状,并可准确计算出地质体的体积,在深部找矿预测和矿业开发中起到较好的指导作用,具有较大的实用价值。
3D Geologic modeling is a geological analysis technology in 3D environment by computer. The traditional simulation and expression of geological information put the 3D space information on a plane. There is space information loss and distortion, making process complicated and difficult to update the information deficiencies. 3D geologic body space model can be directly get underground geologic body. It has important practical value in geological prospecting and mining development.
Based on the study of the convex hull and Delaunay triangulation algorithm, the paper calculate the convex hull of discrete points combining tetrahedron subdivision algorithm and fast convex hull technology. It achieved the convex hull geological modeling and volume calculation. The 3D file generated by system can be directly opened and edited by Lion King 3D Visualization System. Large volume data and accuracy is the two major of geological features. In view of the above characteristics, the algorithm is optimized in two. First, Use one and two dimensional extreme point to construct maximum initial convex hull in order to put the as much as point in it by rapid convex Hull. Second, check point and the convex hull position by vector scalar product in order to excluding the internal point of the initial convex hull.
Based on the study of convex hull geological modeling, the paper gives a maximum volume non-convex hull geological construction algorithm generated by discrete points and optimizes the algorithm. The algorithm applies to a given point must be generated in the geological situation of the vertices. It summarizes a judging method which can judge two triangles do not intersect in 3D space and proved it.
Through the practical application of a coal mine in Shandong Province shows that geological body model generated by the module can reproduction subsurface geological body shape intuitively, and can accurately calculate the volume of geological bodies. It plays a better guide and practical value in the deep exploration and mining development, with great practical value.
本文在研究凸壳算法和Delaunay三角剖分算法的基础上,结合四面体剖分算法和快速凸包技术进行离散点集的凸壳求取,实现了凸壳地质体的建模和体积计算。生成的三维文件可在蓝光三维可视化系统中直接打开和编辑。数据量大和数据精度高是地质体的两大特点,鉴于以上特点,本文对算法进行了两方面的优化:一是结合快速凸包技术,利用一维和二维极值点构造最大初始凸壳,使尽可能多的点包含其中;二是利用向量数量积判断点和凸壳的位置关系,排除初始凸壳的内部点。
本文在凸壳地质体建模研究的基础上,给出了由离散点生成最大体积非凸壳地质体构建算法,并对算法进行了优化处理。该算法适用于给定点必须是生成的地质体的顶点的情况。在研究平面两个三角形不相交判定定理的基础上,本文总结出三维空间两个三角形不相交的判断方法,并给出了相应的证明。
通过在山东某矿的实际应用表明,本模块构建的地质体模型能直观的再现地下地质体的形状,并可准确计算出地质体的体积,在深部找矿预测和矿业开发中起到较好的指导作用,具有较大的实用价值。
3D Geologic modeling is a geological analysis technology in 3D environment by computer. The traditional simulation and expression of geological information put the 3D space information on a plane. There is space information loss and distortion, making process complicated and difficult to update the information deficiencies. 3D geologic body space model can be directly get underground geologic body. It has important practical value in geological prospecting and mining development.
Based on the study of the convex hull and Delaunay triangulation algorithm, the paper calculate the convex hull of discrete points combining tetrahedron subdivision algorithm and fast convex hull technology. It achieved the convex hull geological modeling and volume calculation. The 3D file generated by system can be directly opened and edited by Lion King 3D Visualization System. Large volume data and accuracy is the two major of geological features. In view of the above characteristics, the algorithm is optimized in two. First, Use one and two dimensional extreme point to construct maximum initial convex hull in order to put the as much as point in it by rapid convex Hull. Second, check point and the convex hull position by vector scalar product in order to excluding the internal point of the initial convex hull.
Based on the study of convex hull geological modeling, the paper gives a maximum volume non-convex hull geological construction algorithm generated by discrete points and optimizes the algorithm. The algorithm applies to a given point must be generated in the geological situation of the vertices. It summarizes a judging method which can judge two triangles do not intersect in 3D space and proved it.
Through the practical application of a coal mine in Shandong Province shows that geological body model generated by the module can reproduction subsurface geological body shape intuitively, and can accurately calculate the volume of geological bodies. It plays a better guide and practical value in the deep exploration and mining development, with great practical value.
引文
[1]吴健生,朱谷昌等.三维技术在固体矿产勘探和开发中的研究与应用[J].地质与勘探. 2004, 40(1):628~632
[2]苗小平,杨永国,奚砚涛.一种基于三棱柱的三维地质体可视化方法研究[J].中国矿业大学学报.2004,33(5):584~588
[3]曹代勇,李青元,朱小弟,周云霞.地质构造三维可视化模型探讨[J].地质与勘探. 2002, 37(4): 60~62
[4]程朋根,龚健雅,史文中,刘少华.基于似三棱柱体的地质体三维建模与应用研究[J].武汉大学学报.信息科学版.2004,7(7):602~607
[5] Jessell M.Three-dimensional geologieal modeling of Potential field data[J].ComPuters & Geoscienees,2001,27(4):455~465
[6] EhlenJ,Harmon R.S. GeoComp 99:GeoComPutation and thegeosciences[J].Computer & Geosciences.2001,27(8):899~900
[7] Mareshallinger R, Johnson S.E.Guest editorial[J].ComPuter & Geoseiences. 2001, 27(4): 379~379
[8]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[J].地球科学进展. 2004, 19(2): 218~223
[9]孟小红,王卫民,姚长利,胡朝顺.地质模型计算辅助设计原理与应用[M].北京:地质出版社,2001
[10]柴贺军,黄地龙,黄润秋,刘浩吾.岩体结构三维可视化及其工程应用研究[J].岩土工程学报.2001,23(2):217~220
[11] White M.J.Visualization of the El Berrocal granite:application to rock Engineering[J]. Engineering Geology.1998,49:185~194
[12]曾钱帮,刘大安,张菊明,潘炜.浅谈工程地质三维建模与可视化[J].西部探矿工程.2005,(3):72~74
[13] Smaet H. Neighbor finding in images represented by octrees[J].Computer Vision, Graphics and Image Processing.1989,46(3):367~386
[14]潘炜,刘大安,钟辉亚,李拍,刘新中,曾钱帮.三维地质建模以及在边坡工程中的应用[J].岩石力学与工程学报.2004,23(4):597~602
[15] Egan S.S,Kane S,Buddin T.S,etc.Computer modeling and visualization of the structural deformation caused by movement along geological faults[J].Computer & Geosciences, 1999,25(3):283~297
[16] Chand D R, Kapur S S. An algorithm for convex polytopes[J] . JACM, 1970,17(1) : 78~86
[17] Jarvis R A. On the identification of the convex hull of a finite set of points in the plane [J].Information Processing Letters,1973, 2(1) :18~21
[18] Graham R L. An efficient algorithm for determine the convex hull of a finite linear set [J].Information Processing Letters,1972(1):132~133
[19] Preparata F P,Hong S J.Convex hulls of finite sets of points in two and three dimensions [J].CACM,1977,20(2):87~93
[20] Chan T. Optimal output-sensitive convex hull algorithms in two and three dimensions [J]. Discrete Comput. Geom,1996,16(3) :361~368
[21]崔国华,洪帆,余祥宣.确定平面点集凸包的一类最优算法[J].计算机学报, 1997,20(4): 330~334
[22]金文华,何涛,刘晓平等.基于有序简单多边形的平面点集凸包快速求取算法[J].计算机学报,1998,21(6):533~539
[23]蒋红斐.平面点集凸包快速构建算法的研究[J].计算机工程与应用,2002,38(20):48~49
[24]郝晓军.凸包算法的加速与改进研究[D].天津:河北工业大学,2003
[25]樊广佺,张桂云,杨炳儒.海量平面点集凸壳的快速算法[J] .计算机工程,2006,32(21): 64-66.
[26]袁兵.三维栅格地质建模及其空间分析方法研究[D].西安:西安科技大学,2005
[27]杨东来,张永波,王新春等著.地质体三维建模方法和技术指南[M].地质出版社,2007
[28] Clarkson, K. and Shor P. Applications of random sampling in computational geometry, ii. Discr. Comput. Geom.1989,9(4):387~421
[29]周培德.计算几何—算法设计与分析(第三版)[M].清华大学出版社,2008
[30] Lawson C. Software for C1 Surface Interpolation Mathematical Software[M].1977
[31] Preprata F P.Shamos M I. Computational Geometry An Introduction[M] .New York: Springer Verlag,1985
[32]夏松,朱宜萱,杜志强.一种新的空间凸多面体的生成算法[J] .测绘通报, 2006(1) : 21~23
[33]石露,白冰,李小春.判断点和多面体位置关系的一个新算法[J].第十届全国岩石力学与工程学术大会论文集,2008:296
[34]裘怿楠著.裘怿楠石油开发地质文集[M].石油工业出版社,1997
[35]陈传波,何大华.两个三角形不相交的充要条件[J].应用数学,2002,15 (增) :28~30
[36] Chen T.Optimal output-sensilive convex hull algorithms in two and three dimensions. Discrete Comput Geom,1996.16(3) :361~368
[37] LIU G H,CHEN C B. A New Algorithm for Computing the Convex Hull of a Planar Point Set[J].Journal of Zhejiang University(SCIENCE A),2007(8):1210~1217
[38]孙家广,杨长贵.计算机图形学(第2版)[M].北京:清华大学出版社,1995
[39] Simon W.Houlding.Practical geostatistics,modeling and spatial analysis[M].New York and Heidelburg,Springer-Verlag,2000
[40]蒋红斐.离散点集实时Delaunay三角网剖分算法的研究[J].中国铁道科学,2003,24(2) : 44~47
[41]武强,徐华.三维地质建模与可视化方法研究[J].中国科学(D辑,地球科学), 2004,34(1): 54~60
[42] Garey,et al.Triangulating a simple polygon[J].Information Processing Letters,2003,7(4) : 25~30
[43]候恩科.三维地质模拟的若干关键问题研究[D].中国矿业大学北京校区博士论文. 2002
[2]苗小平,杨永国,奚砚涛.一种基于三棱柱的三维地质体可视化方法研究[J].中国矿业大学学报.2004,33(5):584~588
[3]曹代勇,李青元,朱小弟,周云霞.地质构造三维可视化模型探讨[J].地质与勘探. 2002, 37(4): 60~62
[4]程朋根,龚健雅,史文中,刘少华.基于似三棱柱体的地质体三维建模与应用研究[J].武汉大学学报.信息科学版.2004,7(7):602~607
[5] Jessell M.Three-dimensional geologieal modeling of Potential field data[J].ComPuters & Geoscienees,2001,27(4):455~465
[6] EhlenJ,Harmon R.S. GeoComp 99:GeoComPutation and thegeosciences[J].Computer & Geosciences.2001,27(8):899~900
[7] Mareshallinger R, Johnson S.E.Guest editorial[J].ComPuter & Geoseiences. 2001, 27(4): 379~379
[8]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[J].地球科学进展. 2004, 19(2): 218~223
[9]孟小红,王卫民,姚长利,胡朝顺.地质模型计算辅助设计原理与应用[M].北京:地质出版社,2001
[10]柴贺军,黄地龙,黄润秋,刘浩吾.岩体结构三维可视化及其工程应用研究[J].岩土工程学报.2001,23(2):217~220
[11] White M.J.Visualization of the El Berrocal granite:application to rock Engineering[J]. Engineering Geology.1998,49:185~194
[12]曾钱帮,刘大安,张菊明,潘炜.浅谈工程地质三维建模与可视化[J].西部探矿工程.2005,(3):72~74
[13] Smaet H. Neighbor finding in images represented by octrees[J].Computer Vision, Graphics and Image Processing.1989,46(3):367~386
[14]潘炜,刘大安,钟辉亚,李拍,刘新中,曾钱帮.三维地质建模以及在边坡工程中的应用[J].岩石力学与工程学报.2004,23(4):597~602
[15] Egan S.S,Kane S,Buddin T.S,etc.Computer modeling and visualization of the structural deformation caused by movement along geological faults[J].Computer & Geosciences, 1999,25(3):283~297
[16] Chand D R, Kapur S S. An algorithm for convex polytopes[J] . JACM, 1970,17(1) : 78~86
[17] Jarvis R A. On the identification of the convex hull of a finite set of points in the plane [J].Information Processing Letters,1973, 2(1) :18~21
[18] Graham R L. An efficient algorithm for determine the convex hull of a finite linear set [J].Information Processing Letters,1972(1):132~133
[19] Preparata F P,Hong S J.Convex hulls of finite sets of points in two and three dimensions [J].CACM,1977,20(2):87~93
[20] Chan T. Optimal output-sensitive convex hull algorithms in two and three dimensions [J]. Discrete Comput. Geom,1996,16(3) :361~368
[21]崔国华,洪帆,余祥宣.确定平面点集凸包的一类最优算法[J].计算机学报, 1997,20(4): 330~334
[22]金文华,何涛,刘晓平等.基于有序简单多边形的平面点集凸包快速求取算法[J].计算机学报,1998,21(6):533~539
[23]蒋红斐.平面点集凸包快速构建算法的研究[J].计算机工程与应用,2002,38(20):48~49
[24]郝晓军.凸包算法的加速与改进研究[D].天津:河北工业大学,2003
[25]樊广佺,张桂云,杨炳儒.海量平面点集凸壳的快速算法[J] .计算机工程,2006,32(21): 64-66.
[26]袁兵.三维栅格地质建模及其空间分析方法研究[D].西安:西安科技大学,2005
[27]杨东来,张永波,王新春等著.地质体三维建模方法和技术指南[M].地质出版社,2007
[28] Clarkson, K. and Shor P. Applications of random sampling in computational geometry, ii. Discr. Comput. Geom.1989,9(4):387~421
[29]周培德.计算几何—算法设计与分析(第三版)[M].清华大学出版社,2008
[30] Lawson C. Software for C1 Surface Interpolation Mathematical Software[M].1977
[31] Preprata F P.Shamos M I. Computational Geometry An Introduction[M] .New York: Springer Verlag,1985
[32]夏松,朱宜萱,杜志强.一种新的空间凸多面体的生成算法[J] .测绘通报, 2006(1) : 21~23
[33]石露,白冰,李小春.判断点和多面体位置关系的一个新算法[J].第十届全国岩石力学与工程学术大会论文集,2008:296
[34]裘怿楠著.裘怿楠石油开发地质文集[M].石油工业出版社,1997
[35]陈传波,何大华.两个三角形不相交的充要条件[J].应用数学,2002,15 (增) :28~30
[36] Chen T.Optimal output-sensilive convex hull algorithms in two and three dimensions. Discrete Comput Geom,1996.16(3) :361~368
[37] LIU G H,CHEN C B. A New Algorithm for Computing the Convex Hull of a Planar Point Set[J].Journal of Zhejiang University(SCIENCE A),2007(8):1210~1217
[38]孙家广,杨长贵.计算机图形学(第2版)[M].北京:清华大学出版社,1995
[39] Simon W.Houlding.Practical geostatistics,modeling and spatial analysis[M].New York and Heidelburg,Springer-Verlag,2000
[40]蒋红斐.离散点集实时Delaunay三角网剖分算法的研究[J].中国铁道科学,2003,24(2) : 44~47
[41]武强,徐华.三维地质建模与可视化方法研究[J].中国科学(D辑,地球科学), 2004,34(1): 54~60
[42] Garey,et al.Triangulating a simple polygon[J].Information Processing Letters,2003,7(4) : 25~30
[43]候恩科.三维地质模拟的若干关键问题研究[D].中国矿业大学北京校区博士论文. 2002