基于轮廓线三维矿体表面重建的一种改进算法
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摘要
基于轮廓线的三维矿体表面建模方法是矿体建模的主流方法,但在实际应用中,传统的建模方法显现出了不足之处,笔者对该方法进行了针对性地改进。对于一组单轮廓线可自动添加矿体趋势线,并且还可以进行人工编辑修改,然后利用中间加密轮廓线的方法实现对矿体形态的控制。通过投影计算封闭轮廓线之间的最短距离自动添加分支点,利用平面的带洞限定三角剖分实现分支的自动构建,大大节省了人力资源,同时保证了分支矿体的准确性。针对初始构建的三维矿体表面模型几何质量差,引入了质量控制,实现了表面模型的重构,保证了模型质量和后续的计算。这些改进在实际的应用中取得了良好的效果。
The 3 D orebody surface modeling method based on contours is the main method of orebody modeling; nevertheless,in practical application,the traditional modeling method has shortcomings,which have been improved with the method in this paper. In general,contour lines of these methods are used to reconstruct the surface model by artificial selection of two contour lines,but it is difficult to grasp the overall trend of the orebody as a whole,and the shape of the three dimensional orebodies is relatively coarse. When researchers deal with the problem of branch,it is very tedious to add the branch point in that it takes a lot of manpower and time,and it is difficult to guarantee the correct result. The surface model of the orebody exhibits a lot of degenerated triangles,even in the situation that the surfaces of the orebodies are self-intersected or overlapped,hence the geometric quality of the model is so poor that it influences subsequent visualization and model calculation. The trend line for a group of contours is introduced,and it can also be edited.Then the encryption method for refining the intermediate contours so as to achieve the control of the orebody shape is used. Through projection,the shortest distance between closed contours is calculated,and branch points are automatically added. The constrained triangulation with holes is used to achieve the building of branch automatically,which greatly saves human resources and ensures the accuracy of branch of orebody. According to the problem of poor geometric quality of the initial 3 D orebody surface model,the quality control to achieve the reconstruction of the surface model is introduced,which ensures the model quality and subsequent calculation. These improvements have achieved good results in practical application.
The 3 D orebody surface modeling method based on contours is the main method of orebody modeling; nevertheless,in practical application,the traditional modeling method has shortcomings,which have been improved with the method in this paper. In general,contour lines of these methods are used to reconstruct the surface model by artificial selection of two contour lines,but it is difficult to grasp the overall trend of the orebody as a whole,and the shape of the three dimensional orebodies is relatively coarse. When researchers deal with the problem of branch,it is very tedious to add the branch point in that it takes a lot of manpower and time,and it is difficult to guarantee the correct result. The surface model of the orebody exhibits a lot of degenerated triangles,even in the situation that the surfaces of the orebodies are self-intersected or overlapped,hence the geometric quality of the model is so poor that it influences subsequent visualization and model calculation. The trend line for a group of contours is introduced,and it can also be edited.Then the encryption method for refining the intermediate contours so as to achieve the control of the orebody shape is used. Through projection,the shortest distance between closed contours is calculated,and branch points are automatically added. The constrained triangulation with holes is used to achieve the building of branch automatically,which greatly saves human resources and ensures the accuracy of branch of orebody. According to the problem of poor geometric quality of the initial 3 D orebody surface model,the quality control to achieve the reconstruction of the surface model is introduced,which ensures the model quality and subsequent calculation. These improvements have achieved good results in practical application.
引文
[1]赵增玉.三维固体矿产资源储量和潜力评价系统关键技术研究[D].北京:北京大学,2011.Zhao Z Y. Research on key technologies of three dimensional solid mineral resources reserves and potential evaluation system[D].Beijing:Peking University,2011.
[2]李梅,毛善君,马蔼乃.平行轮廓线三维矿体重建算法[J].计算机辅助设计与图形学学报,2006,18(7):1017-1021.Li M,Mao S J,Ma A N. Building orebody solid model from planar contours[J]. Journal of Computer-Aided Design&Computer Graphics,2006,18(7):1017-1021.
[3]马洪滨,郭甲腾.一种新的多轮廓线重构三维形体算法:切开—缝合法[J].东北大学学报:自然科学版,2007,28(1):111-114.Ma H B,Guo J T. Cut-and-sew algorithm:a new multi-contour reconstruction algothms[J]. Journal of Northeastern University:Natural Science,2007,28(1):111-114.]
[4]孙立双,毕天平,马运涛,等.一种基于剖面轮廓线进行矿体三维建模的方法[J].沈阳建筑大学学报:自然科学版,2011,27(4):653-658.Sun L S,Bi T P,Ma Y T,et al. An orebody 3D modeling algorithm based on section contour Lines[J]. Journal of Shenyang Jianzhu University:Natural Science,2011,27(4):653-658.
[5]冀晓伟,卢才武,李海波.三维矿体表面建模中的三角剖分技术及其应用[J].金属矿山,2011,2:106-110.Ji X W,Lu C W,Li H B. Triangulation technique and its application in 3D ore body surface modeling[J]. Metal Mine,2011(2):106-110.
[6]曹国林,孟耀伟.复杂地质构造三维地质体建模方法研究[J].矿冶工程,2012,32(3):22-29.Cao G L,Meng Y W. Research on 3D modeling of complex geologic bodies[J]. Mining and Metallurgical Engineering,2012,32(3):22-29.
[7]荆永滨.矿床三维地质混合建模与属性插值技术的研究及应用[D].长沙:中南大学,2010,24-25.Jing Y B. Study and application on 3D hybrid geological modeling and attribute interpolation of mineral deposit[D]. Changsha:Central South University,2010,24-25.
[8]赵攀,田宜平.基于剖面的层状与非层状矿体的三维可视化研究[J].金属矿山,2008,387(9):90-92,96.Zhao P,Tian Y P. Section-based 3D visualization modeling of stratified and non-stratified orebodies[J]. Metal Mine,2008,387(9):90-92,96.
[9]朱良峰,吴信才,刘修国,等.基于钻孔数据的三维地层模型的构建[J].地理与地理信息科学,2004,20(3):26-30.Zhu L F,Wu X C,Liu X G,et al. Reconstruction of 3D strata model based on borehole data[J]. Geography and Geo-Information Science,2004,20(3):26-30.
[10]李兆亮,潘懋,杨洋,等.三维复杂断层网建模方法及应用[J].北京大学学报:自然科学版,2015,51(1):79-85.Li Z L,Pan M,Yang Y,et al. Research and application of the three-dimensional complex fault network modeling[J]. Acta Scientiarum Naturalium Universitatis Pekinensis,2015,51(1):79-85.
[11]李兆亮,潘懋,韩大匡,等.三维构造建模技术[J].地球科学:中国地质大学学报,2016,41(12):2136-2146.Li Z L,Pan M,Han D K,et al. Three-dimensional structural modeling technique[J]. Earth Science,2016,41(12):2136-2146.
[12] Meyers D,Skinner S,Sloan K. Surfaces from Contours[J]. ACM transactions on graphics,1992,11(3):228-258.
[13] Meyers D. Reconstruction of surfaces from planar contours[D].Washington:University of Washington,1994.
[14] Keppel E. Approximating complex surfaces by triangulation of contour lines[J]. IBM Journal of Research and Development,1975,19(1):2-11.
[15] Fuchs H,Kedem Z M,Uselton S P. Optimal surface reconstruction from planar contours[C]//Communications of the ACM,1977,20(10):693-702.
[16] Ekoule A,Peyrin F,Odet C. A triangulation algorithm from arbitrary shaped multiple planar contours[J]. ACM Transactions on Graphics(TOG),1991,10(2):82-99.
[17] Ganapathy S,Dennehy T. A new general triangulation method for planar contours[J]. ACM Siggraph Computer Graphics,1982,16(3):69-75.
[18] Mallet J L. Geomodeling[M]. New York:Oxford University Press,2002.
[19]明镜,颜玫.基于Morphing的三维地质界面生成[J].地理与地理信息科学,2014,30(1):37-40.Ming J,Yan M. Three-dimensional geological surface creation based on morphing[J]. Geography and Geo-Information Science,2014,30(1):37-40.
[20]何金国,查红彬.基于BPLI二维平行轮廓线重建三维表面的新算法[J].北京大学学报:自然科学版,2003,39(3):399-411.He J G,Zha H B. New algorithms based on BPLI Solution for reconstructing 3D surfaces fron parallel contours[J]. Acta Scientiarum Naturalium Universitatis Pekinensis,2003,39(3):399-411.
[21]杨洋,潘懋,吴耕宇,等.一种新的轮廓线三维地质表面重建方法[J].地球信息科学学报,2015,17(3):253-259.Yang Y,Pan M,Wu G Y,et al. High quality geological surface reconstruction from planar contours[J]. Journal of Geo-information Science,2015,17(3):253-259.
[22] Shewchuk J R. Delaunay refinement algorithms for triangular mesh generation[J]. Computational geometry,1997,22(1):21-74.
[23] Pan M,Li Z L,Gao Z B,et al. 3-D geological modeling-concepts,methods and key techniques[J]. Acta Geologica Sinica,2012,86(4):1031-1036.
[24] Shewchuk J R. What is a good linear element? Interpolation,conditioning,and quality measures[C]//Eleventh International Meshing Roundtable(Ithaca,New York),Sandia National Laboratories,2002,115-126.
[25] Caumon G P,Collon Drouaillet,et al. Surface-based 3D modeling of geological structures[J]. Mathematical Geosciences,2009,41(8):927-945.
[26] Hoppe H,DeRose T,Duchamp T,et al. Mesh optimization[C]//SIGGRAPH 93 Conference Proceedings,1993:19-26.
[2]李梅,毛善君,马蔼乃.平行轮廓线三维矿体重建算法[J].计算机辅助设计与图形学学报,2006,18(7):1017-1021.Li M,Mao S J,Ma A N. Building orebody solid model from planar contours[J]. Journal of Computer-Aided Design&Computer Graphics,2006,18(7):1017-1021.
[3]马洪滨,郭甲腾.一种新的多轮廓线重构三维形体算法:切开—缝合法[J].东北大学学报:自然科学版,2007,28(1):111-114.Ma H B,Guo J T. Cut-and-sew algorithm:a new multi-contour reconstruction algothms[J]. Journal of Northeastern University:Natural Science,2007,28(1):111-114.]
[4]孙立双,毕天平,马运涛,等.一种基于剖面轮廓线进行矿体三维建模的方法[J].沈阳建筑大学学报:自然科学版,2011,27(4):653-658.Sun L S,Bi T P,Ma Y T,et al. An orebody 3D modeling algorithm based on section contour Lines[J]. Journal of Shenyang Jianzhu University:Natural Science,2011,27(4):653-658.
[5]冀晓伟,卢才武,李海波.三维矿体表面建模中的三角剖分技术及其应用[J].金属矿山,2011,2:106-110.Ji X W,Lu C W,Li H B. Triangulation technique and its application in 3D ore body surface modeling[J]. Metal Mine,2011(2):106-110.
[6]曹国林,孟耀伟.复杂地质构造三维地质体建模方法研究[J].矿冶工程,2012,32(3):22-29.Cao G L,Meng Y W. Research on 3D modeling of complex geologic bodies[J]. Mining and Metallurgical Engineering,2012,32(3):22-29.
[7]荆永滨.矿床三维地质混合建模与属性插值技术的研究及应用[D].长沙:中南大学,2010,24-25.Jing Y B. Study and application on 3D hybrid geological modeling and attribute interpolation of mineral deposit[D]. Changsha:Central South University,2010,24-25.
[8]赵攀,田宜平.基于剖面的层状与非层状矿体的三维可视化研究[J].金属矿山,2008,387(9):90-92,96.Zhao P,Tian Y P. Section-based 3D visualization modeling of stratified and non-stratified orebodies[J]. Metal Mine,2008,387(9):90-92,96.
[9]朱良峰,吴信才,刘修国,等.基于钻孔数据的三维地层模型的构建[J].地理与地理信息科学,2004,20(3):26-30.Zhu L F,Wu X C,Liu X G,et al. Reconstruction of 3D strata model based on borehole data[J]. Geography and Geo-Information Science,2004,20(3):26-30.
[10]李兆亮,潘懋,杨洋,等.三维复杂断层网建模方法及应用[J].北京大学学报:自然科学版,2015,51(1):79-85.Li Z L,Pan M,Yang Y,et al. Research and application of the three-dimensional complex fault network modeling[J]. Acta Scientiarum Naturalium Universitatis Pekinensis,2015,51(1):79-85.
[11]李兆亮,潘懋,韩大匡,等.三维构造建模技术[J].地球科学:中国地质大学学报,2016,41(12):2136-2146.Li Z L,Pan M,Han D K,et al. Three-dimensional structural modeling technique[J]. Earth Science,2016,41(12):2136-2146.
[12] Meyers D,Skinner S,Sloan K. Surfaces from Contours[J]. ACM transactions on graphics,1992,11(3):228-258.
[13] Meyers D. Reconstruction of surfaces from planar contours[D].Washington:University of Washington,1994.
[14] Keppel E. Approximating complex surfaces by triangulation of contour lines[J]. IBM Journal of Research and Development,1975,19(1):2-11.
[15] Fuchs H,Kedem Z M,Uselton S P. Optimal surface reconstruction from planar contours[C]//Communications of the ACM,1977,20(10):693-702.
[16] Ekoule A,Peyrin F,Odet C. A triangulation algorithm from arbitrary shaped multiple planar contours[J]. ACM Transactions on Graphics(TOG),1991,10(2):82-99.
[17] Ganapathy S,Dennehy T. A new general triangulation method for planar contours[J]. ACM Siggraph Computer Graphics,1982,16(3):69-75.
[18] Mallet J L. Geomodeling[M]. New York:Oxford University Press,2002.
[19]明镜,颜玫.基于Morphing的三维地质界面生成[J].地理与地理信息科学,2014,30(1):37-40.Ming J,Yan M. Three-dimensional geological surface creation based on morphing[J]. Geography and Geo-Information Science,2014,30(1):37-40.
[20]何金国,查红彬.基于BPLI二维平行轮廓线重建三维表面的新算法[J].北京大学学报:自然科学版,2003,39(3):399-411.He J G,Zha H B. New algorithms based on BPLI Solution for reconstructing 3D surfaces fron parallel contours[J]. Acta Scientiarum Naturalium Universitatis Pekinensis,2003,39(3):399-411.
[21]杨洋,潘懋,吴耕宇,等.一种新的轮廓线三维地质表面重建方法[J].地球信息科学学报,2015,17(3):253-259.Yang Y,Pan M,Wu G Y,et al. High quality geological surface reconstruction from planar contours[J]. Journal of Geo-information Science,2015,17(3):253-259.
[22] Shewchuk J R. Delaunay refinement algorithms for triangular mesh generation[J]. Computational geometry,1997,22(1):21-74.
[23] Pan M,Li Z L,Gao Z B,et al. 3-D geological modeling-concepts,methods and key techniques[J]. Acta Geologica Sinica,2012,86(4):1031-1036.
[24] Shewchuk J R. What is a good linear element? Interpolation,conditioning,and quality measures[C]//Eleventh International Meshing Roundtable(Ithaca,New York),Sandia National Laboratories,2002,115-126.
[25] Caumon G P,Collon Drouaillet,et al. Surface-based 3D modeling of geological structures[J]. Mathematical Geosciences,2009,41(8):927-945.
[26] Hoppe H,DeRose T,Duchamp T,et al. Mesh optimization[C]//SIGGRAPH 93 Conference Proceedings,1993:19-26.
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