面向隐伏矿体预测的三维地质建模与空间分析若干技术研究
|
摘要
矿产资源预测与评价逐渐进入基于GIS技术定量预测与评价的新阶段,GIS已成为矿产资源预测与评价定量化的核心技术。传统的二维GIS只能表达面上的信息,对于大比例尺下的隐伏矿体预测中矿床的三维空间信息往往不能很自然地表达与分析。三维GIS和三维地学建模系统的出现弥补了二维GIS的不足,使对地质对象进行真三维表达成为可能。然而在这种真三维空间数据环境下的矿产资源定量预测与评价过程中,需要有高效与稳健的三维地质建模和三维空间分析技术来支撑。
论文首先对隐伏矿体预测中三维地质建模技术进行了研究,讨论了地质对象的空间数据表达,给出了一种通过表面建模建立地质体几何轮廓,由体素模型表达地质体,将体素模型以线性八叉树存储的解决方案。为了满足大规模地质体高分辨率下线性八叉树建模的需要,论文提出了一种硬件加速条件下的由面表示模型动态生成线性八叉树算法。算法利用深度缓存判断体元在实体内外,通过栈结构来存储八叉树分解的情况,在对栈的操作中输出编码,省去了结点的排序和压缩过程。进一步利用深度缓存中的信息,算法对实体进行了分块,并按分块构造线性八叉树达到加速效果。实验结果表明线性八叉树生成过程可以在高分辨率下快速地执行。
为了满足地质控矿指标定量提取的需要,论文对隐伏矿体预测中基于体素模型的空间分析若干技术进行了研究。首先给出了一种适用于离散化三维地质空间的距离分析方法,该方法通过欧式距离变换生成欧式距离场进行量算。基于数学形态学滤波,论文提出了一种地质体趋势形态分析方法;论文利用欧式距离场与数学形态学对地质体形态起伏分析方法进行了研究,提出了一种对地质体形态起伏进行分级定量提取的方法。论文以数学形态学膨胀运算的原理生成空间实体的栅格缓冲体,提出了一种基于GPU的栅格缓冲体生成算法。基于这些空间分析方法,论文还对地质控矿作用模拟进行了研究,模拟了地质体控矿作用,岩体-围岩理想接触带控矿作用和接触面间倾角。
The prediction and evaluation of mineral resources gradually enter a new stage of quantitative prediction and evaluation using GIS techniques, while GIS has become core techniques of quantitative prediction and evaluation of mineral resources. Traditional two-dimensional GIS can only represent information based on face. For three-dimensional spatial information of deposits in the prediction of buried ore bodies at large-scale, 2D GIS can not represent and analysis very well. This shortcoming in 2D GIS can be overcome by three-dimensional GIS and 3D geological modeling system, in which geological objects can be true 3D represented. Under these true 3D spatial data environment, however, the procedure of prediction and evaluation of mineral resources needs the efficient and robust techniques of 3D geological modeling and 3D spatial analysis to support.
First the techniques of 3D geological modeling in the prediction of buried ore bodies were studied. The spatial data representations of geological objects were discussed. The paper gives a solution in which the geometric contours of geological body were built by surface modeling while geological body were represented by voxel model, and stored in linear octrees. In order to meet the needs of high-resolution modeling of massive geological bodies, moreover, a hardware accelerated algorithm which can generate linear octrees dynamically from surface representation models was presented. In the algorithm, depth buffers were used to determine whether a voxel is inside or outside a 3D object, a stack structure were used to store the decomposition status of octree, and the codes are exported during the stack operation so the sort and compression of nodes is avoided. The depth buffers are further used to divide the object. Based on this division, the construction of linear octree can be accelerated. The result shows the process of linear octree generation can be run fairly fast under high resolution.
To meet the needs of quantitative extraction of ore-controlling indicators, the paper studied some techniques on voxel model based spatial analysis in the prediction of buried ore bodies. A distance analysis method is proposed which is suitable in concrete three-dimensional geological space. In this method Euclidean distance transform is employed to generate Euclidean distance field. Moreover, the paper presents a morphological filtering based algorithm which can get trend shape of geological body. Based on Euclidean distance field and mathematical morphology, the method for morphological character of geological body was studied. By using the method given in study, the undulant range of morphological changes of geological body can be sebquential extracted. Furthermore, employing dilation operation in mathematical morphology to generate raster buffer of an objects, the paper presents a GPU based algorithm for raster buffer generation. Based on these techniques for spatial analysis, the study also focused on modeling the geological ore-controlling actions, which included modeling ore-controlling actions of geological bodies, the contact zone of rock and country rocks, and modeling the angles of contact surfaces.
论文首先对隐伏矿体预测中三维地质建模技术进行了研究,讨论了地质对象的空间数据表达,给出了一种通过表面建模建立地质体几何轮廓,由体素模型表达地质体,将体素模型以线性八叉树存储的解决方案。为了满足大规模地质体高分辨率下线性八叉树建模的需要,论文提出了一种硬件加速条件下的由面表示模型动态生成线性八叉树算法。算法利用深度缓存判断体元在实体内外,通过栈结构来存储八叉树分解的情况,在对栈的操作中输出编码,省去了结点的排序和压缩过程。进一步利用深度缓存中的信息,算法对实体进行了分块,并按分块构造线性八叉树达到加速效果。实验结果表明线性八叉树生成过程可以在高分辨率下快速地执行。
为了满足地质控矿指标定量提取的需要,论文对隐伏矿体预测中基于体素模型的空间分析若干技术进行了研究。首先给出了一种适用于离散化三维地质空间的距离分析方法,该方法通过欧式距离变换生成欧式距离场进行量算。基于数学形态学滤波,论文提出了一种地质体趋势形态分析方法;论文利用欧式距离场与数学形态学对地质体形态起伏分析方法进行了研究,提出了一种对地质体形态起伏进行分级定量提取的方法。论文以数学形态学膨胀运算的原理生成空间实体的栅格缓冲体,提出了一种基于GPU的栅格缓冲体生成算法。基于这些空间分析方法,论文还对地质控矿作用模拟进行了研究,模拟了地质体控矿作用,岩体-围岩理想接触带控矿作用和接触面间倾角。
The prediction and evaluation of mineral resources gradually enter a new stage of quantitative prediction and evaluation using GIS techniques, while GIS has become core techniques of quantitative prediction and evaluation of mineral resources. Traditional two-dimensional GIS can only represent information based on face. For three-dimensional spatial information of deposits in the prediction of buried ore bodies at large-scale, 2D GIS can not represent and analysis very well. This shortcoming in 2D GIS can be overcome by three-dimensional GIS and 3D geological modeling system, in which geological objects can be true 3D represented. Under these true 3D spatial data environment, however, the procedure of prediction and evaluation of mineral resources needs the efficient and robust techniques of 3D geological modeling and 3D spatial analysis to support.
First the techniques of 3D geological modeling in the prediction of buried ore bodies were studied. The spatial data representations of geological objects were discussed. The paper gives a solution in which the geometric contours of geological body were built by surface modeling while geological body were represented by voxel model, and stored in linear octrees. In order to meet the needs of high-resolution modeling of massive geological bodies, moreover, a hardware accelerated algorithm which can generate linear octrees dynamically from surface representation models was presented. In the algorithm, depth buffers were used to determine whether a voxel is inside or outside a 3D object, a stack structure were used to store the decomposition status of octree, and the codes are exported during the stack operation so the sort and compression of nodes is avoided. The depth buffers are further used to divide the object. Based on this division, the construction of linear octree can be accelerated. The result shows the process of linear octree generation can be run fairly fast under high resolution.
To meet the needs of quantitative extraction of ore-controlling indicators, the paper studied some techniques on voxel model based spatial analysis in the prediction of buried ore bodies. A distance analysis method is proposed which is suitable in concrete three-dimensional geological space. In this method Euclidean distance transform is employed to generate Euclidean distance field. Moreover, the paper presents a morphological filtering based algorithm which can get trend shape of geological body. Based on Euclidean distance field and mathematical morphology, the method for morphological character of geological body was studied. By using the method given in study, the undulant range of morphological changes of geological body can be sebquential extracted. Furthermore, employing dilation operation in mathematical morphology to generate raster buffer of an objects, the paper presents a GPU based algorithm for raster buffer generation. Based on these techniques for spatial analysis, the study also focused on modeling the geological ore-controlling actions, which included modeling ore-controlling actions of geological bodies, the contact zone of rock and country rocks, and modeling the angles of contact surfaces.
引文
[1]赵鹏大,张寿庭,陈建平.危机矿山可接替资源预测评价若干问题探讨[J].成都理工大学学报(自然科学版),2004,31(2):111-117
[2]毛先成.三维数字矿床与隐伏矿体定量预测研究[D].长沙:中南大学博士学位论文,2006.
[3]刘承祚,地质专家系统与成矿预测.当代矿产资源勘查评价的理论与方法[M],北京:地震出版社,1999.
[4]Bonham-Carter G F,Agterberg F P,Wright D F.Integration of geological datasets for gold exploration in Nova Scotia[J].Photogrammetric Engineering and Remote Sensing,1988,54(11):1585-1592.
[5]Bonham-Carter G F,Agterberg F P,Wright D F.Weights of evidence modelling:a new approach to mapping mineral potential[J].Geological Survey of Canada Paper,1990,89(9):171-183.
[6]Bonham-Carter G F,Reddy R K T,Galley A G.Preliminary results using a forward-chaining inference net with a GIS to map base-metal potential:application to Snow Lake Greenstone Belt,Manitoba,Canada[A].Proceedings of International Workshop on Statistical Prediction of Mineral Resources[C].Wuhan,China,1990.
[7]Agterberg F P.Combining indicator patterns for mineral resource evaluation[A].Proceedings of International Workshop on Statistical Prediction of Mineral Resources[C].Wuhan,China,1990.
[8]Reddy R K T,Bonham-Carter G F.A decision-tree approach to mineral potential mapping in Snow Lake area,Manitoba[J].Canadian Journal of Remote Sensing,1991,17(2):191-200.
[9]Agterberg F P.Combining indicator patterns in weights of evidence modeling for resource evaluation[J].Nonrenewable Resources,1992,1(1):39-50.
[10]Wyborn L A I,Gallacher P,Jagodzinski E A.A conceptual approach to metallogenic modeling using GIS:example from the Pine Greek Inlier[A].Proceedings of A Symposium on Australian Research in Ore Genesis[C],1994:151-155.
[11]Knox-Robinson C M,Wyborn L A I.Towards a holistic exploration strategy:using geographic information systems(GIS)as a tool to enhance exploration[J].Australian Journal of Earth Sciences,1997,44(4):453-463.
[12] Knox-Robinson C M, Gardoll S J. GIS-stereoplot: an interactive stereonet plotting module for ArcView 3.0 geographic information system[J]. Computers & Geosciences, 1998, 24 (3): 243-250.
[13] Harris J. R., Wilkinson L., Grunsky E. C. Effective use and interpretation of lithogeochemical data in regional mineral exploration programs: application of Geographic Information Systems GIS technology[J]. Ore Geology Reviews, 2000,16: 107-143.
[14] Mihalasky M, Cameron E M. Conceptual modelling of major gold deposits, Nevada: use of GIS to integrate a complex geoscience database [A]. In: Proceedings of Canadian Conference on GIS[C] 1991: 481-482.
[15] Rencz AN, Harris J, Watson G P, et al. Data integration for mineral exploration in the Antigonish Highlands, Nova Scotia: application of GIS and RS[J]. Canadian Journal of Remote Sensing, 1994,20 (3): 257-267.
[16] Schmatz D R, Engi M, Lieberman J E. ParaDIS: a relational database for the consistent documentation and analysis of metamorphic mineral assemblages [J]. Computers & Geosciences, 1995, 21 (9): 1031-1041.
[17] Hariri M M, Use of the GIS (Geographic Information Systems) in determining relationship between geology, structures and mineral prospects, southern part of the Arabian shield, Saudi Arabia[J]. Pakistan Journal of Applied Sciences, 2003, 3 (2): 92-96.
[18] Asadi H H, Hale M. A predictive GIS model for mapping potential gold and base metal mineralization in Takab area, Iran[J]. Computers & Geosciences, 2001, 27(8): 901-912.
[19] Qiuming Cheng, Shengyuan Zhang. Fuzzy weights of evidence method implemented in GeoDAS GIS for information extraction and integration for prediction of point events [J]. Proceedings of IEEE International Geoscience and Remote Sensing Symposium, 2002, 5 (5): 2933-2945.
[20] Katz S S. Emulating the Prospector Expert System with a raster GIS [J]. Computers & Geosciences, 1991, 17 (7): 1033-1050.
[21] Chen Y L. Indicator pattern combination for mineral resource potential mapping with the general C-F model [J]. Mathematical Geology, 2003, 35 (3): 301-321.
[22] Chen Y L. MRPM: three visual basic programs for mineral resource potential mapping [J]. Computers & Geosciences, 2004, 30 (7): 969-983.
[23] Yang Wenjiu, Liu Xinji. Integration of multi-geoscience data for mineral resources prediction using GIS methodology[J].Computers,Environment and Urban Systems,1992 16(4):367-374.
[24]朱良峰,吴信才,刘修国.3D GIS支持下的城市三维地质信息系统研究[J].岩土力学,2004,25(6):883-886.
[25]Simon W.Houlding.3D Geoscience Modeling:Computer Techniques for Geological Characterization[M].Springer-Verlag,2000.
[26]Hunter G M.Efficient Computation and Data Structures for Graphics[D].New York:Princeton University,1978.
[27]Jackins C.,Tanimato S.L.Oct-trees and their use in presenting three-dimensional objects[J].Computer Graphics Image Processing,1980,14:249-270.
[28]Meagher D.Octree encoding:a new technique for the representation,manipulation and display of arbitrary 3-D objects[D].Rensselaer Polytechnic Institute,Troy,NY,Oct.1980.
[29]Srihari S.N.,Hierarchical representation for serial section images[A].In Proceedings,5th Intl Conf.Pattern Recognition[C],Miami Beach,F1,Dec.1980,1075-1080.
[30]Chien C.H.,Aggarwal,J.K.,Volume/surface octrees for the representation of three-dimensional objects[J].Computer Graphics and Image Processing,1986,36:100-113.
[31]Wheeler A.J.,Stokes P.C.The use of block and wireframe modeling for undergorund mining[J].Mining Magazine,1988,3:209-213.
[32]Bak P.R.G.,Mill A.J.B.Three dimensional representation in a geo-scientific resource management system for the minerals industry[A].Three dimensional application in geographical information systems[C].Taylor& Francis,London 1989:155-182.
[33]Smith D.R.,Paradis A.R.Three-dimensional GIS for the earth sciences[A].In:Proceedings of 9th international symposiumon computer-assisted cartography[C],1989:324-325.
[34]Raper J.F.The 3-dimensional geo-scientific mapping and modeling systems:a conceptual design[M].London:Taylor & Francis,1989.
[35]Fritsch,D.Towards three-dimensional data structures in geographic information systems[A].EGIS Foundation[C],Utrecht 1990:335-345.
[36]Molenaar M.A topology for 3D vector maps[J].ITC Journal,1992,1:25-33.
[37]Houlding S.W.3D Geoscience Modeling:Computer Techniques for Geological Characterization[M].New York & Heidelburg:Springer-Verlag,1994.
[38]Houlding S.W.Practical geostatistics,modeling and spatial analysis[M].New York & Heidelburg:Springer-Verlag,2000.
[39]Li R.Data structure and application issues in 3-D geographic information systems[J].Geomatica,1994,48(3):209-224.
[40]Zlatanova S.3D GIS for Urban Development[D].Enschede(Netherlands):International Inst.for Aerospace Survey and Earth Sciences,2000:222.
[41]韩国建,郭达志,金学林.矿体信息的八叉树存储和检索技术[J].测绘学报,1992,21(1):13-17.
[42]Shi W.Z.A hybrid model for 3D GIS[J].Geoinformatics,196,1:400-409.
[43]龚健雅,夏宗国.矢量与栅格集成的三维数据模型[J].武汉测绘科技大学学报,1997,22(1):7-15.
[44]李德仁,李清泉.一种三维GIS混合数据结构研究[J].测绘学报,1997,26(2):128-133.
[45]李青元.三维矢量结构GIS拓扑关系及其动态建立[J].测绘学报,1997,26(03):235-240.
[46]李清泉,李德仁.三维空间数据模型集成的概念框架研究[J].测绘学报.1998,27(4):325-330.
[47]Xiao L.B,Zhang,Y.,Luo,J.et al.A 3D GIS four-level vectored octree structure integrating vector and raster features[A].In:The International Archives of Photogrammetry and Remote Sensing[C],1999,32(4W12):265-272.
[48]孙敏,陈军,张学庄.基于表面剖分的3DCM空间数据模型研究[J].测绘学报,2000,29(3):257-265.
[49]程朋根,龚健雅.地勘工程3维空间数据模型及其数据结构设计[J].测绘学报,2001,30(01):74-81.
[50]吴立新,张瑞欣等.三维地学模拟与虚拟矿山系统[J].测绘学报,2002,31(1):28-33.
[51]程朋根,龚健雅,史文中,等.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),2004,29(7):602-607.
[52]Wu,L.X.A generalized tri-prism model for 3D geosciences modeling and topological description[A].In:Advanced Workshop on Spatial Information Technology[C].Hong Kong,PolyU,2002.
[53]Wu L.X.Topological relations included generalized tri-prism(GTP)model for 3D geosciences modeling.Computer and Geosciences,2004,30(4):405-418
[54]Shi W.Z.,Yang,B.S.,Li,Q.Q.An objected-oriented data model for complex objects in three-dimensional geographic information system[J].International Journal of Geographic Information Science,2003,17(5):411-430.
[55]史文中,吴立新,李清泉,王彦兵,杨必胜.三维空间信息系统模型与算法[M].北京:电子工业出版社,2007.
[56]张成才,秦昆,卢艳.GIS空间分析理论与方法[M].武汉:武汉大学出版社,2004.
[57]李清泉.基于混合数据结构的三维GIS数据模型与空问分析研究[D].武汉:武汉测绘科技大学1995.
[58]肖乐斌.基于栅格框架的三维GIS集成数据模型与空间分析研究[D].北京:中国科学院地理科学与资源研究所,1999.
[59]李芳玉,潘懋,朱雷.三维缓冲体生成栅格算法研究.计算机辅助设计与图形学学报[J],2005,17(9):1928-1932.
[60]李邵军,冯夏庭,王威,周辉.岩土工程中基于栅格的三维地层建模及空问分析[J].岩石力学与工程学报,2007,26(3):532-537.
[61]王金贵.地下管线三维空间分析初步研究[D].南京:南京大学,2005.
[62]Spraguea,K.,Kempa,E.Spatial targeting using queries in a 3-D GIS environment with application to mineral exploration[J].Computers &Geosciences,2006,32:396-418.
[63]Yau,M.M.Generation quadtrees of cross section from octrees[J].Computer vision,Graphics and Image Processing,1984,27:211-238.
[64]Thibault,W.C.Naylor,B.F.Set operations on polyhedra using binary space partitioning trees[J].ACM SIGGRAPH Computer Graphics,1987,21(4):153-162.
[65]Samet H.Neighbor finding in images represented by octrees[J],Computer vision,Graphics and Image Processing,1989,46:367-386.
[66]谢传节.虚拟地理信息系统数据模型研究[D].北京:中国科学院地理科学与资源研究所,2000.
[67]赖健清,彭省临,杨牧,邵拥军,杨斌.铜陵凤凰山铜矿南区构造地球化学异常的确定与评价[J].地质与勘探,2007,43(4):51-55.
[68]朱志澄,宋鸿林.构造地质学[M].武汉:中国地质大学出版社,1990.
[69]王家耀.空间信息系统原理[M].北京:科学出版社,2001.
[70]Shekhar S.,Chawla S.Spatial Databases[M]:A Tour.Prentice Hall,2003.
[71]邬伦.地理信息系统原理、方法与应用[M].北京:科学出版社,2001.
[72]江斌,黄波,陆锋.GIS环境下的空间分析和地学视觉化[M].北京:高等教育出版社,2000.
[73]陈立潮,张永梅,刘玉树,张建华.基于栅格的GIS三维空间数据模型[J].计算机工程,2004,30(8):4-6.
[74]吴立新,史文中.地理信息系统原理与算法[M].北京:科学出版社,2003.
[75]Zlatanova S,Rahrnan A.Shi W.Topological models and frameworks for 3D spatial objects[J].Computers and Geosciences,2004,30(4):419-428.
[76]程朋根.地矿三维空间数据模型与算法研究[D].武汉:武汉大学,2005.
[77]Lee D.T.,Schachter B.J.Tow algorithms for constructing a Delaunay Triangulation[J].International Journal of Computer and Information Science,1980,9(3):219-242.
[78]Lawson C.L.Software for C' Surface Interpolation.Mathematical Software Ⅲ[M].New York,Academic press,1977:61-194.
[79]Meyers D.,Skinner S.,Sloan K.Surfaces from Contours[J].ACM Transactions on Graphics,1992,11(3):228-258.
[80]http://www.datamine.co.uk[EB/OL].
[81]http://www.nlm.nih.gov/research/visible/visible_human.html[EB/OL].
[82]Lippert L.,Cross M.H.Fast wavelet based volume rendering by accumulation of transparent texture maps[J].Computer Graphics Forum,1995:14(3):431-443.
[83]Kaufman A.,Cohen D.,YAGEL R.Volume graphics[J].IEEE Computer,1993,26:51-64.
[84]Widjaya H.,Mueller T.,Entezari A.Voxelization in common sampling lattices [A].In:Proceedings of Pacific Graphics 2003[C],Canmore,Alberta,Canada,2003:497-501.
[85]Kaufman A.Efficient algorithms for 3D scan-conversion of parametric curves,surfaces and volumes[J].Computer Graphics,1987,21:171-179.
[86]Kaufman A.Efficient algorithms for scan-conversing 3D polygons[J].Computer Graphics,1988,12:213-219.
[87]Sramek M.,Kaufman,A.Alias-free voxelization of geometric objects[J].IEEE Transactions on Visualization and Computer Graphics,1999,5(3):251-267.
[88]Wang S.W.,Kaufman,A.Volume-sampled 3D modeling[A].IEEE Computer Graphics[C],1994,Appril 14,26-32.
[89]Frisken F.S.Using distance maps for accurate surface representation in sampled volumes[A].In:IEEE Symposium on Volume Visualization[C],1998:23-30.
[90]Jones M.W.The production of volume data from triangular meshes using voxelization[J].Computer Graphics Forum,1996,15,311-318.
[91]Lee Y.T,Requicha,A.Algorithms for computing the volume and other integral properties of solids[J].Commun.ACM,1982,25:635-650.
[92]Rueda A.J.,Segura R.,Feito ER.,Ogayar C.Voxelization of solids using simplicial coverings[A].In:Proceedings of WSCG[C],2004:227-234.
[93]Fang,S.,Chen,H.Hardware accelerated voxelization[J].Computers & Graphics,2000,24(3):433-442.
[94]Beckhaus S.,Wind J.,Strothotte T.Hardware-based voxelization for 3D spatial analysis[A].In:Proceedings of the 5th International Conference on Computer Graphics and Imaging[C].Canmore,Alberta,Canada,2002:15-20.
[95]Dong Z.,Chen W.,Bao H.,Zhang H.,Peng Q.Realtime-time voxelization for complex polygonal models[A].In:Proceedings.12th Pacific Conference on Computer Graphics and Applications[C].Seoul,South Korea,2004:43-50.
[96]Ogayar C.J.,Rueda A.J.,Segura R.J.,Feito F.R.Fast and simple hardware accelerated voxelizations using simplicial coverings[J].Visual Comput.2007,23:535-543.
[97]吕广宪,潘懋,王占刚,兰向荣.基于GPU加速的高分辨率实体体素化研究[J].地理与地理信息科学,2007,23(1):5-9.
[98]Karabassi E.,Papaioannou G,Theoharis T.A fast depth-buffer-based voxelization algorithm[J].ACM Journal of Graphics Tools,2002,4:114-124.
[99]Passalis G.,Kakadiaris I.A.Theoharis T.Efficient hardware voxelization[A].In:Proceedings of the Computer Graphics International 2004[C].2004:374-377.
[100]管伟光,解林,马颂德.体图形学[J].中国图象图形学报,1999,4(6):486-490.
[101]孙家广等.计算机图形学[M].北京:清华大学出版社,1998:499-500.
[102]Chen H.H.,Huang T.S.A survey of construction and manipulation of octrees[J].Computer vision,Graphics and Image Processing,1988,43:409-431.
[103]胡鹏,黄杏元,华一新.地理信息系统教程[M].武汉:武汉大学出版社,2002.
[104]Tu T,O'Hallaron D,Lopez J.Etree:A database-oriented method for generating large Octree meshes[J].Engineering with Computers,2004,20(2):117-128.
[105]吕广宪,潘懋,吴焕萍,丛威青,吴自兴.面向真三维地学建模的海量虚拟八叉树模型研究[J].北京大学学报(自然科学版),2007,43(4):496-501.
[106]Roy U.,Xu Y.3-D object decomposition with extended octree model and its application in geometric simulation of NC machining[J].Robotics and Computer-Integrated Manufacturing,1998,14(4):317-327.
[107]Gargantini I.Linear octtrees for fast processing of three dimensional objects[J].Computer Graphics and Image Processing,1982,20(4):365-374.
[108]李清泉,李德仁.八叉树的三维行程编码[J].武汉测绘科技大学学报,1997,22(2):102-106.
[109]Bak P.R.G,Cram D.L.,Prissag R.Interactive evaluation of linear octree encoded deposit models[A].In:23rd Application of Computers and Operations Research in the Mineral[C].Tucson,USA,1992:691.
[110]张建民,朱均,孙国基,岸野文郎,北村喜文.快速成型中基于立方单元体的三维模型及其应用[J].西安交通大学学报:2000,34(10):62-66.
[111]Ibaroudene D.Representation and display of three-dimensional medical images using a linear octree[J].Computerized Medical Imaging and Graphics,1995,19(1):153-159.
[112]Luccheci B.J.A parallel linear octree collision detection algorithm[D].Reno:University of Nevada Reno,2002.
[113]Hecquard,J.Connected component labeling with linear octree[J].Pattern Recognition,1991,24(6):515-531.
[114]Tamminen M.Efficient octree conversion by connectivity labeling[J].Computers & Graphics,1984,18(3):43-51.
[115]Atkinson H.H.,Gargantini I.,Walsh T.R.S.Filling by quadrants or octants[J].Computer Vision,Graphics,and Image Processing,1986,33(2):138-155.
[116]严蔚敏,吴伟民.数据结构[M].北京:清华大学出版社,1997:279-283.
[117]曹彤,刘臻.用于建立三维GIS的八叉树编码压缩算法[J].中国图像图形学报,2002,7(1):50-54.
[118]周洞汝,杨荣.线性八叉树的一种最优构造算法[J].计算机学报,1993,16(4):281-286.
[119]Kitamura Y.,Kishino F.A Parallel algorithm for octree generation from polyhedral shape representation[A].IEEE Proceedings of ICPR '96[C],1996:303-309.
[120]OpenGL体系结构审核委员会,Dave Shreiner,Mason Woo,Jackie Neider,Tom Davis.OpenGL编程指南[M].邓郑祥译.第四版.北京:人民邮电出版社,2005.
[121]http://graphics.stanford.edu/data/3Dscanrep/[EB/OL].
[122]Serra J.Introduction to mathematical morphology[J].Computer Vision, Graphics,and Image Processing,1986,35:283-305.
[123]唐常青,吕宏伯,黄铮,张方.数学形态学方法及其应用[M].北京:科学出版社,1990.
[124]Rosenfeld A,Pfaltz J.Sequential operations in digital picture processing[J].Journal of Association for Computing Machinery,1966,13(4):471-494.
[125]Rosenfeld A,Pfaltz J.Distance functions on digital pictures[J].Pattern Recognition,1968,1(1):250-255.
[126]Borgefors G.Distance transformations in digital pictures[J].Computer Vision,Graphics,and Image Processing,1986,34:344-371.
[127]Danielsson P.Euclidean distance mapping[J].Computer Graphics and Image Processing,1980,14(3):227-248.
[128]Ye Q-Z.The signed Euclidean distance transform and its applications[A].In:Proceedings of the 9th International Conference of Pattern Recognition[C],Rome,Italy,1988.495-499.
[129]Leymarie F,Levine M D.Fast raster scan distance propagation on the discrete rectangular lattice[J].CVGIP:Image Understanding,1992,55(1):84-94.
[130]陈山菱.完全欧几里德距离变换的最优算法[J].计算机学报,1995,8(18):611-616.
[131]Borgefors G.On digital distance transform s in three dimensions[J].Computer Vision and Image Understanding,1996,64(3):368-376.
[132]Ragnemalm I.The Euclidean distance transform in arbitrary dimensions[J].Patteern Recognition Letter,1993,14:883-888.
[133]蔺宏伟,王国瑾.三维带符号的欧氏距离变换及其应用[J].计算机学报,2003,26(12):1645-1651.
[134]诸葛婴,田捷,王蔚洪.三维欧氏距离变换的一种新方法[J].软件学报.2001,12(3):383-389.
[135]郭仁忠.空间分析(第二版)[M].北京:高等教育出版社,2001.
[136]於崇文.数学地质的方法与应用[M].北京:冶金工业出版社,1980.
[137]Gonzalez R.G,Woods R.E.数字图像处理(第二版)[M]-阮秋琦,阮宇智等译.北京:电子工业出版社,2003:427-430.
[138]Zhuang X-H.Harlick R.M.Morphological structuring element decomposition[J].Computer Graphics and Image Processing,1986,35:370-382.
[139]Sternberg S.R.Grayscale Morphology[J].Computer Graphics and Image Processing,1986,35:333-355.
[140]Meyer F.Automatic screen of cytological specimens[J].Computer Graphics and Image Processing,1986,35:356-369.
[141]毛先成,陈国珧.香花岭锡矿床数学模型及立体定量预测初探[J].地质与勘探.1988,24(10):15-224.
[142]杨善慈,文鸿雁.杨赤中函数的理论公式及其适应力的理论探讨[J].科学探索,1989,20(3):230-237.
[143]毛先成,陈国珧.断层波状构造及其控矿规律的定量研究[J].中南矿冶学院学报,1993,24(1):8-13.
[144]吕妙儿,黄杏元.基于GIS的缓冲区生成模型理论和方法[J].科技通报,2000,16(5):356-360.
[145]毋河海.关于GIS缓冲区的建立问题[J].武汉测绘科技大学学报,1997,22(4):358-364.
[146]乔彦友.缓冲区生成的一种新算法[A].中国地理信息系统协会第三届年会论文集[C].北京:测绘出版社,1997.
[147]吴华意,龚健雅,李德仁.缓冲曲线和边约束三角网辅助的缓冲区生成算法[J].测绘学报,1999,28(4):355-359.
[148]Gonzalez R.G,Woods R.E.数字图像处理(第二版).阮秋琦,阮宇智等译[M].北京:电子工业出版社,2003:463-474.
[2]毛先成.三维数字矿床与隐伏矿体定量预测研究[D].长沙:中南大学博士学位论文,2006.
[3]刘承祚,地质专家系统与成矿预测.当代矿产资源勘查评价的理论与方法[M],北京:地震出版社,1999.
[4]Bonham-Carter G F,Agterberg F P,Wright D F.Integration of geological datasets for gold exploration in Nova Scotia[J].Photogrammetric Engineering and Remote Sensing,1988,54(11):1585-1592.
[5]Bonham-Carter G F,Agterberg F P,Wright D F.Weights of evidence modelling:a new approach to mapping mineral potential[J].Geological Survey of Canada Paper,1990,89(9):171-183.
[6]Bonham-Carter G F,Reddy R K T,Galley A G.Preliminary results using a forward-chaining inference net with a GIS to map base-metal potential:application to Snow Lake Greenstone Belt,Manitoba,Canada[A].Proceedings of International Workshop on Statistical Prediction of Mineral Resources[C].Wuhan,China,1990.
[7]Agterberg F P.Combining indicator patterns for mineral resource evaluation[A].Proceedings of International Workshop on Statistical Prediction of Mineral Resources[C].Wuhan,China,1990.
[8]Reddy R K T,Bonham-Carter G F.A decision-tree approach to mineral potential mapping in Snow Lake area,Manitoba[J].Canadian Journal of Remote Sensing,1991,17(2):191-200.
[9]Agterberg F P.Combining indicator patterns in weights of evidence modeling for resource evaluation[J].Nonrenewable Resources,1992,1(1):39-50.
[10]Wyborn L A I,Gallacher P,Jagodzinski E A.A conceptual approach to metallogenic modeling using GIS:example from the Pine Greek Inlier[A].Proceedings of A Symposium on Australian Research in Ore Genesis[C],1994:151-155.
[11]Knox-Robinson C M,Wyborn L A I.Towards a holistic exploration strategy:using geographic information systems(GIS)as a tool to enhance exploration[J].Australian Journal of Earth Sciences,1997,44(4):453-463.
[12] Knox-Robinson C M, Gardoll S J. GIS-stereoplot: an interactive stereonet plotting module for ArcView 3.0 geographic information system[J]. Computers & Geosciences, 1998, 24 (3): 243-250.
[13] Harris J. R., Wilkinson L., Grunsky E. C. Effective use and interpretation of lithogeochemical data in regional mineral exploration programs: application of Geographic Information Systems GIS technology[J]. Ore Geology Reviews, 2000,16: 107-143.
[14] Mihalasky M, Cameron E M. Conceptual modelling of major gold deposits, Nevada: use of GIS to integrate a complex geoscience database [A]. In: Proceedings of Canadian Conference on GIS[C] 1991: 481-482.
[15] Rencz AN, Harris J, Watson G P, et al. Data integration for mineral exploration in the Antigonish Highlands, Nova Scotia: application of GIS and RS[J]. Canadian Journal of Remote Sensing, 1994,20 (3): 257-267.
[16] Schmatz D R, Engi M, Lieberman J E. ParaDIS: a relational database for the consistent documentation and analysis of metamorphic mineral assemblages [J]. Computers & Geosciences, 1995, 21 (9): 1031-1041.
[17] Hariri M M, Use of the GIS (Geographic Information Systems) in determining relationship between geology, structures and mineral prospects, southern part of the Arabian shield, Saudi Arabia[J]. Pakistan Journal of Applied Sciences, 2003, 3 (2): 92-96.
[18] Asadi H H, Hale M. A predictive GIS model for mapping potential gold and base metal mineralization in Takab area, Iran[J]. Computers & Geosciences, 2001, 27(8): 901-912.
[19] Qiuming Cheng, Shengyuan Zhang. Fuzzy weights of evidence method implemented in GeoDAS GIS for information extraction and integration for prediction of point events [J]. Proceedings of IEEE International Geoscience and Remote Sensing Symposium, 2002, 5 (5): 2933-2945.
[20] Katz S S. Emulating the Prospector Expert System with a raster GIS [J]. Computers & Geosciences, 1991, 17 (7): 1033-1050.
[21] Chen Y L. Indicator pattern combination for mineral resource potential mapping with the general C-F model [J]. Mathematical Geology, 2003, 35 (3): 301-321.
[22] Chen Y L. MRPM: three visual basic programs for mineral resource potential mapping [J]. Computers & Geosciences, 2004, 30 (7): 969-983.
[23] Yang Wenjiu, Liu Xinji. Integration of multi-geoscience data for mineral resources prediction using GIS methodology[J].Computers,Environment and Urban Systems,1992 16(4):367-374.
[24]朱良峰,吴信才,刘修国.3D GIS支持下的城市三维地质信息系统研究[J].岩土力学,2004,25(6):883-886.
[25]Simon W.Houlding.3D Geoscience Modeling:Computer Techniques for Geological Characterization[M].Springer-Verlag,2000.
[26]Hunter G M.Efficient Computation and Data Structures for Graphics[D].New York:Princeton University,1978.
[27]Jackins C.,Tanimato S.L.Oct-trees and their use in presenting three-dimensional objects[J].Computer Graphics Image Processing,1980,14:249-270.
[28]Meagher D.Octree encoding:a new technique for the representation,manipulation and display of arbitrary 3-D objects[D].Rensselaer Polytechnic Institute,Troy,NY,Oct.1980.
[29]Srihari S.N.,Hierarchical representation for serial section images[A].In Proceedings,5th Intl Conf.Pattern Recognition[C],Miami Beach,F1,Dec.1980,1075-1080.
[30]Chien C.H.,Aggarwal,J.K.,Volume/surface octrees for the representation of three-dimensional objects[J].Computer Graphics and Image Processing,1986,36:100-113.
[31]Wheeler A.J.,Stokes P.C.The use of block and wireframe modeling for undergorund mining[J].Mining Magazine,1988,3:209-213.
[32]Bak P.R.G.,Mill A.J.B.Three dimensional representation in a geo-scientific resource management system for the minerals industry[A].Three dimensional application in geographical information systems[C].Taylor& Francis,London 1989:155-182.
[33]Smith D.R.,Paradis A.R.Three-dimensional GIS for the earth sciences[A].In:Proceedings of 9th international symposiumon computer-assisted cartography[C],1989:324-325.
[34]Raper J.F.The 3-dimensional geo-scientific mapping and modeling systems:a conceptual design[M].London:Taylor & Francis,1989.
[35]Fritsch,D.Towards three-dimensional data structures in geographic information systems[A].EGIS Foundation[C],Utrecht 1990:335-345.
[36]Molenaar M.A topology for 3D vector maps[J].ITC Journal,1992,1:25-33.
[37]Houlding S.W.3D Geoscience Modeling:Computer Techniques for Geological Characterization[M].New York & Heidelburg:Springer-Verlag,1994.
[38]Houlding S.W.Practical geostatistics,modeling and spatial analysis[M].New York & Heidelburg:Springer-Verlag,2000.
[39]Li R.Data structure and application issues in 3-D geographic information systems[J].Geomatica,1994,48(3):209-224.
[40]Zlatanova S.3D GIS for Urban Development[D].Enschede(Netherlands):International Inst.for Aerospace Survey and Earth Sciences,2000:222.
[41]韩国建,郭达志,金学林.矿体信息的八叉树存储和检索技术[J].测绘学报,1992,21(1):13-17.
[42]Shi W.Z.A hybrid model for 3D GIS[J].Geoinformatics,196,1:400-409.
[43]龚健雅,夏宗国.矢量与栅格集成的三维数据模型[J].武汉测绘科技大学学报,1997,22(1):7-15.
[44]李德仁,李清泉.一种三维GIS混合数据结构研究[J].测绘学报,1997,26(2):128-133.
[45]李青元.三维矢量结构GIS拓扑关系及其动态建立[J].测绘学报,1997,26(03):235-240.
[46]李清泉,李德仁.三维空间数据模型集成的概念框架研究[J].测绘学报.1998,27(4):325-330.
[47]Xiao L.B,Zhang,Y.,Luo,J.et al.A 3D GIS four-level vectored octree structure integrating vector and raster features[A].In:The International Archives of Photogrammetry and Remote Sensing[C],1999,32(4W12):265-272.
[48]孙敏,陈军,张学庄.基于表面剖分的3DCM空间数据模型研究[J].测绘学报,2000,29(3):257-265.
[49]程朋根,龚健雅.地勘工程3维空间数据模型及其数据结构设计[J].测绘学报,2001,30(01):74-81.
[50]吴立新,张瑞欣等.三维地学模拟与虚拟矿山系统[J].测绘学报,2002,31(1):28-33.
[51]程朋根,龚健雅,史文中,等.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),2004,29(7):602-607.
[52]Wu,L.X.A generalized tri-prism model for 3D geosciences modeling and topological description[A].In:Advanced Workshop on Spatial Information Technology[C].Hong Kong,PolyU,2002.
[53]Wu L.X.Topological relations included generalized tri-prism(GTP)model for 3D geosciences modeling.Computer and Geosciences,2004,30(4):405-418
[54]Shi W.Z.,Yang,B.S.,Li,Q.Q.An objected-oriented data model for complex objects in three-dimensional geographic information system[J].International Journal of Geographic Information Science,2003,17(5):411-430.
[55]史文中,吴立新,李清泉,王彦兵,杨必胜.三维空间信息系统模型与算法[M].北京:电子工业出版社,2007.
[56]张成才,秦昆,卢艳.GIS空间分析理论与方法[M].武汉:武汉大学出版社,2004.
[57]李清泉.基于混合数据结构的三维GIS数据模型与空问分析研究[D].武汉:武汉测绘科技大学1995.
[58]肖乐斌.基于栅格框架的三维GIS集成数据模型与空间分析研究[D].北京:中国科学院地理科学与资源研究所,1999.
[59]李芳玉,潘懋,朱雷.三维缓冲体生成栅格算法研究.计算机辅助设计与图形学学报[J],2005,17(9):1928-1932.
[60]李邵军,冯夏庭,王威,周辉.岩土工程中基于栅格的三维地层建模及空问分析[J].岩石力学与工程学报,2007,26(3):532-537.
[61]王金贵.地下管线三维空间分析初步研究[D].南京:南京大学,2005.
[62]Spraguea,K.,Kempa,E.Spatial targeting using queries in a 3-D GIS environment with application to mineral exploration[J].Computers &Geosciences,2006,32:396-418.
[63]Yau,M.M.Generation quadtrees of cross section from octrees[J].Computer vision,Graphics and Image Processing,1984,27:211-238.
[64]Thibault,W.C.Naylor,B.F.Set operations on polyhedra using binary space partitioning trees[J].ACM SIGGRAPH Computer Graphics,1987,21(4):153-162.
[65]Samet H.Neighbor finding in images represented by octrees[J],Computer vision,Graphics and Image Processing,1989,46:367-386.
[66]谢传节.虚拟地理信息系统数据模型研究[D].北京:中国科学院地理科学与资源研究所,2000.
[67]赖健清,彭省临,杨牧,邵拥军,杨斌.铜陵凤凰山铜矿南区构造地球化学异常的确定与评价[J].地质与勘探,2007,43(4):51-55.
[68]朱志澄,宋鸿林.构造地质学[M].武汉:中国地质大学出版社,1990.
[69]王家耀.空间信息系统原理[M].北京:科学出版社,2001.
[70]Shekhar S.,Chawla S.Spatial Databases[M]:A Tour.Prentice Hall,2003.
[71]邬伦.地理信息系统原理、方法与应用[M].北京:科学出版社,2001.
[72]江斌,黄波,陆锋.GIS环境下的空间分析和地学视觉化[M].北京:高等教育出版社,2000.
[73]陈立潮,张永梅,刘玉树,张建华.基于栅格的GIS三维空间数据模型[J].计算机工程,2004,30(8):4-6.
[74]吴立新,史文中.地理信息系统原理与算法[M].北京:科学出版社,2003.
[75]Zlatanova S,Rahrnan A.Shi W.Topological models and frameworks for 3D spatial objects[J].Computers and Geosciences,2004,30(4):419-428.
[76]程朋根.地矿三维空间数据模型与算法研究[D].武汉:武汉大学,2005.
[77]Lee D.T.,Schachter B.J.Tow algorithms for constructing a Delaunay Triangulation[J].International Journal of Computer and Information Science,1980,9(3):219-242.
[78]Lawson C.L.Software for C' Surface Interpolation.Mathematical Software Ⅲ[M].New York,Academic press,1977:61-194.
[79]Meyers D.,Skinner S.,Sloan K.Surfaces from Contours[J].ACM Transactions on Graphics,1992,11(3):228-258.
[80]http://www.datamine.co.uk[EB/OL].
[81]http://www.nlm.nih.gov/research/visible/visible_human.html[EB/OL].
[82]Lippert L.,Cross M.H.Fast wavelet based volume rendering by accumulation of transparent texture maps[J].Computer Graphics Forum,1995:14(3):431-443.
[83]Kaufman A.,Cohen D.,YAGEL R.Volume graphics[J].IEEE Computer,1993,26:51-64.
[84]Widjaya H.,Mueller T.,Entezari A.Voxelization in common sampling lattices [A].In:Proceedings of Pacific Graphics 2003[C],Canmore,Alberta,Canada,2003:497-501.
[85]Kaufman A.Efficient algorithms for 3D scan-conversion of parametric curves,surfaces and volumes[J].Computer Graphics,1987,21:171-179.
[86]Kaufman A.Efficient algorithms for scan-conversing 3D polygons[J].Computer Graphics,1988,12:213-219.
[87]Sramek M.,Kaufman,A.Alias-free voxelization of geometric objects[J].IEEE Transactions on Visualization and Computer Graphics,1999,5(3):251-267.
[88]Wang S.W.,Kaufman,A.Volume-sampled 3D modeling[A].IEEE Computer Graphics[C],1994,Appril 14,26-32.
[89]Frisken F.S.Using distance maps for accurate surface representation in sampled volumes[A].In:IEEE Symposium on Volume Visualization[C],1998:23-30.
[90]Jones M.W.The production of volume data from triangular meshes using voxelization[J].Computer Graphics Forum,1996,15,311-318.
[91]Lee Y.T,Requicha,A.Algorithms for computing the volume and other integral properties of solids[J].Commun.ACM,1982,25:635-650.
[92]Rueda A.J.,Segura R.,Feito ER.,Ogayar C.Voxelization of solids using simplicial coverings[A].In:Proceedings of WSCG[C],2004:227-234.
[93]Fang,S.,Chen,H.Hardware accelerated voxelization[J].Computers & Graphics,2000,24(3):433-442.
[94]Beckhaus S.,Wind J.,Strothotte T.Hardware-based voxelization for 3D spatial analysis[A].In:Proceedings of the 5th International Conference on Computer Graphics and Imaging[C].Canmore,Alberta,Canada,2002:15-20.
[95]Dong Z.,Chen W.,Bao H.,Zhang H.,Peng Q.Realtime-time voxelization for complex polygonal models[A].In:Proceedings.12th Pacific Conference on Computer Graphics and Applications[C].Seoul,South Korea,2004:43-50.
[96]Ogayar C.J.,Rueda A.J.,Segura R.J.,Feito F.R.Fast and simple hardware accelerated voxelizations using simplicial coverings[J].Visual Comput.2007,23:535-543.
[97]吕广宪,潘懋,王占刚,兰向荣.基于GPU加速的高分辨率实体体素化研究[J].地理与地理信息科学,2007,23(1):5-9.
[98]Karabassi E.,Papaioannou G,Theoharis T.A fast depth-buffer-based voxelization algorithm[J].ACM Journal of Graphics Tools,2002,4:114-124.
[99]Passalis G.,Kakadiaris I.A.Theoharis T.Efficient hardware voxelization[A].In:Proceedings of the Computer Graphics International 2004[C].2004:374-377.
[100]管伟光,解林,马颂德.体图形学[J].中国图象图形学报,1999,4(6):486-490.
[101]孙家广等.计算机图形学[M].北京:清华大学出版社,1998:499-500.
[102]Chen H.H.,Huang T.S.A survey of construction and manipulation of octrees[J].Computer vision,Graphics and Image Processing,1988,43:409-431.
[103]胡鹏,黄杏元,华一新.地理信息系统教程[M].武汉:武汉大学出版社,2002.
[104]Tu T,O'Hallaron D,Lopez J.Etree:A database-oriented method for generating large Octree meshes[J].Engineering with Computers,2004,20(2):117-128.
[105]吕广宪,潘懋,吴焕萍,丛威青,吴自兴.面向真三维地学建模的海量虚拟八叉树模型研究[J].北京大学学报(自然科学版),2007,43(4):496-501.
[106]Roy U.,Xu Y.3-D object decomposition with extended octree model and its application in geometric simulation of NC machining[J].Robotics and Computer-Integrated Manufacturing,1998,14(4):317-327.
[107]Gargantini I.Linear octtrees for fast processing of three dimensional objects[J].Computer Graphics and Image Processing,1982,20(4):365-374.
[108]李清泉,李德仁.八叉树的三维行程编码[J].武汉测绘科技大学学报,1997,22(2):102-106.
[109]Bak P.R.G,Cram D.L.,Prissag R.Interactive evaluation of linear octree encoded deposit models[A].In:23rd Application of Computers and Operations Research in the Mineral[C].Tucson,USA,1992:691.
[110]张建民,朱均,孙国基,岸野文郎,北村喜文.快速成型中基于立方单元体的三维模型及其应用[J].西安交通大学学报:2000,34(10):62-66.
[111]Ibaroudene D.Representation and display of three-dimensional medical images using a linear octree[J].Computerized Medical Imaging and Graphics,1995,19(1):153-159.
[112]Luccheci B.J.A parallel linear octree collision detection algorithm[D].Reno:University of Nevada Reno,2002.
[113]Hecquard,J.Connected component labeling with linear octree[J].Pattern Recognition,1991,24(6):515-531.
[114]Tamminen M.Efficient octree conversion by connectivity labeling[J].Computers & Graphics,1984,18(3):43-51.
[115]Atkinson H.H.,Gargantini I.,Walsh T.R.S.Filling by quadrants or octants[J].Computer Vision,Graphics,and Image Processing,1986,33(2):138-155.
[116]严蔚敏,吴伟民.数据结构[M].北京:清华大学出版社,1997:279-283.
[117]曹彤,刘臻.用于建立三维GIS的八叉树编码压缩算法[J].中国图像图形学报,2002,7(1):50-54.
[118]周洞汝,杨荣.线性八叉树的一种最优构造算法[J].计算机学报,1993,16(4):281-286.
[119]Kitamura Y.,Kishino F.A Parallel algorithm for octree generation from polyhedral shape representation[A].IEEE Proceedings of ICPR '96[C],1996:303-309.
[120]OpenGL体系结构审核委员会,Dave Shreiner,Mason Woo,Jackie Neider,Tom Davis.OpenGL编程指南[M].邓郑祥译.第四版.北京:人民邮电出版社,2005.
[121]http://graphics.stanford.edu/data/3Dscanrep/[EB/OL].
[122]Serra J.Introduction to mathematical morphology[J].Computer Vision, Graphics,and Image Processing,1986,35:283-305.
[123]唐常青,吕宏伯,黄铮,张方.数学形态学方法及其应用[M].北京:科学出版社,1990.
[124]Rosenfeld A,Pfaltz J.Sequential operations in digital picture processing[J].Journal of Association for Computing Machinery,1966,13(4):471-494.
[125]Rosenfeld A,Pfaltz J.Distance functions on digital pictures[J].Pattern Recognition,1968,1(1):250-255.
[126]Borgefors G.Distance transformations in digital pictures[J].Computer Vision,Graphics,and Image Processing,1986,34:344-371.
[127]Danielsson P.Euclidean distance mapping[J].Computer Graphics and Image Processing,1980,14(3):227-248.
[128]Ye Q-Z.The signed Euclidean distance transform and its applications[A].In:Proceedings of the 9th International Conference of Pattern Recognition[C],Rome,Italy,1988.495-499.
[129]Leymarie F,Levine M D.Fast raster scan distance propagation on the discrete rectangular lattice[J].CVGIP:Image Understanding,1992,55(1):84-94.
[130]陈山菱.完全欧几里德距离变换的最优算法[J].计算机学报,1995,8(18):611-616.
[131]Borgefors G.On digital distance transform s in three dimensions[J].Computer Vision and Image Understanding,1996,64(3):368-376.
[132]Ragnemalm I.The Euclidean distance transform in arbitrary dimensions[J].Patteern Recognition Letter,1993,14:883-888.
[133]蔺宏伟,王国瑾.三维带符号的欧氏距离变换及其应用[J].计算机学报,2003,26(12):1645-1651.
[134]诸葛婴,田捷,王蔚洪.三维欧氏距离变换的一种新方法[J].软件学报.2001,12(3):383-389.
[135]郭仁忠.空间分析(第二版)[M].北京:高等教育出版社,2001.
[136]於崇文.数学地质的方法与应用[M].北京:冶金工业出版社,1980.
[137]Gonzalez R.G,Woods R.E.数字图像处理(第二版)[M]-阮秋琦,阮宇智等译.北京:电子工业出版社,2003:427-430.
[138]Zhuang X-H.Harlick R.M.Morphological structuring element decomposition[J].Computer Graphics and Image Processing,1986,35:370-382.
[139]Sternberg S.R.Grayscale Morphology[J].Computer Graphics and Image Processing,1986,35:333-355.
[140]Meyer F.Automatic screen of cytological specimens[J].Computer Graphics and Image Processing,1986,35:356-369.
[141]毛先成,陈国珧.香花岭锡矿床数学模型及立体定量预测初探[J].地质与勘探.1988,24(10):15-224.
[142]杨善慈,文鸿雁.杨赤中函数的理论公式及其适应力的理论探讨[J].科学探索,1989,20(3):230-237.
[143]毛先成,陈国珧.断层波状构造及其控矿规律的定量研究[J].中南矿冶学院学报,1993,24(1):8-13.
[144]吕妙儿,黄杏元.基于GIS的缓冲区生成模型理论和方法[J].科技通报,2000,16(5):356-360.
[145]毋河海.关于GIS缓冲区的建立问题[J].武汉测绘科技大学学报,1997,22(4):358-364.
[146]乔彦友.缓冲区生成的一种新算法[A].中国地理信息系统协会第三届年会论文集[C].北京:测绘出版社,1997.
[147]吴华意,龚健雅,李德仁.缓冲曲线和边约束三角网辅助的缓冲区生成算法[J].测绘学报,1999,28(4):355-359.
[148]Gonzalez R.G,Woods R.E.数字图像处理(第二版).阮秋琦,阮宇智等译[M].北京:电子工业出版社,2003:463-474.