Skip to main content
Springer Nature Link
Log in

An irregular triangle mesh buffer analysis method for boundary representation geological object in three-dimension

  • Research Article
  • Published:
Earth Science Informatics Aims and scope Submit manuscript

Abstract

Three-dimensional (3D) buffer analysis is a basic function of spatial analysis used widely in 3D Geographic Information Systems (3DGIS). Current buffer analysis methods for spatial points and curves generally function well. One exception is buffer zone of surface. Previous researchers in this field have used voxel models to overcome this limitation; however, defects with voxel model buffer analysis include redundancies, approximations, and poor visualization characteristics. In this contribution, a surface buffer analysis method is presented for the boundary representation of geological objects. Exact geometric representation is achieved via the construction of irregular triangle meshes in 3D. The results can be used for 3D structural modeling and then form the basis for spatial analysis or model-based quantitative assessment in mineral potential mapping and resource evaluation. Three comparisons between existing voxel methods and our new method, evaluating visualization, precision and redundancy, are conducted. The comparisons show that our proposed method is robust and provides a higher quality output than voxel modeling. Finally, uncertainty analysis of buffer distance in different geological objects was discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  • Agrawala M, Beers A, Levoy M (1995) 3D painting on scanned surfaces. 1995 symposium on interactive

  • Agterberg F, Bonham-Carter G, Wright D (1990) Statistical Pattern Integration for Mineral Exploration. Pergamum Press, Oxford

  • Amenta N, Bern M, Eppstein D (1999) Optimal point placement for mesh smoothing. J Algorithms 30:302–322

    Article  Google Scholar 

  • Bajaj CL, Bernardini F, Xu G (1995) Automatic reconstruction of surfaces and scalar fields from 3d scans. ACM SIGGRAPH 1995, Computer Graphics Proceedings. ACM Press, New York, pp 109–118

  • Bernardini F, Bajaj CL, Chen J, Schikore D (1999) Automatic reconstruction of 3d CAD models from digital scans. Int J Comput Geom Appl 9:327–369

    Article  Google Scholar 

  • Bluscaglia GC, Dari EA (1997) Anisotropic mesh optimization and its application in additivity. Int J Numer Methods Eng 40:4119–4136

    Article  Google Scholar 

  • Bonham-Carter GF (1994) Geographic information systems for geoscientist: modeling with GIS. Oxford Elsevier, 398

  • Borouchaki H, Lo S (1995) Fast Delaunay triangulation in three-dimensions. Comput Methods Appl Mech Eng 128:153–167

    Article  Google Scholar 

  • Bowyer A (1981) Computing Dirichlet tessellations. The compute of. Journal 24:162–166

    Google Scholar 

  • Burtsev S, Kuzmin Y (1993) An efficient flood-filling algorithm. Comput Graph 17(5):549–561

    Article  Google Scholar 

  • Calcagno P, Chiles JP, Courrioux G, Guillen. A (2008) Geological modelling from field data and geological knowledge part I. Modelling method coupling 3D potential-field interpolation and geologica rules. Phys Earth Planet Inter 171:1–11

  • Carranza EJM (2004) Objective selection of suitable unit cell size in data-driven modelling of mineral prospectivity. Comput Geosci 35:2032–2046

  • Carranza EJM, Sadeghi M (2010) Predictive mapping of prospectivity and quantitative estimation of undiscovered VMS deposits in Skellefte district (Sweden). Ore Geol Rev 38(3):219–241

  • Carr C, Beatson K, Cherrie B, Mitchell J, Fright R, McCallum C, Evans R (2001) Reconstruction and representation of 3d objects with radial basis functions. In: ACM SIGGRAPH 2001, Computer Graphics Proceedings, 2001, ACM Press, New York, pp 67–76

  • Caumon G, Collon-Drouaillet P, Le Carlier de Veslud S, Sausse S (2009) Surface-based 3D modeling of geological structures. Math Geo Sci 41:927–945

    Article  Google Scholar 

  • Chan SL, Purisima EO (1998) A new tetrahedral tesselation scheme for isosurface generation. Comput Graph 22(1):83–90

  • Chen J, Lv P, Wu W, Zhao J, Hu Q (2007) A 3D method for predicting blind ore-bodies based on a 3D visualization model and its application. Earth Sci Front 14:54–62

    Article  Google Scholar 

  • Cheng QM, Agterberg FP (1999) Fuzzy weights of evidence method and its application in mineral potential mapping. Nat Resour Res 8:27–35

    Article  Google Scholar 

  • Cheng S, Dey T, Edelsbrunner H, Facello M, Teng S (2000) Sliver Exudation. J ACM 47:883–904

    Article  Google Scholar 

  • Danielsson P (1980) Euclidean distance mapping. Comput Graphics Image Process 14(3):227–248

    Article  Google Scholar 

  • Dari EA, Buscaglia GC (1994) Mesh optimization: how to obtain good unstructured 3-D finite element meshes with not-so-good mesh generators. Struct Optim 8:181–188

    Article  Google Scholar 

  • Du Q, Wang D (2003) Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations. Int J Numer Methods Eng 56:1355–1373

    Article  Google Scholar 

  • Edelsbrumer H, Li X, Miller G, Stathopoulos A, Talmor D, Teng S, Ungor A, Walkington N (2000) Smoothing and cleaning up slivers, Proceedings of the 32nd ACM symposium on Theory and Computing, pp 273–277

  • Fausto B, Joshua M, Holly R, Claudio S (1999) The ball-pivoting algorithm for surface reconstruction. IEEE Trans Vis Comput Graph 5(4):349–359

    Article  Google Scholar 

  • Ford A, Blenkinsop TG (2008) Combining fractal analysis of mineral deposit clustering with weights of evidence to evaluate patterns of mineralization: Application to copper deposits of the Mount Isa Inlier, NW Queensland, Australia. Ore Geol Rev 33(3–4):435–450

  • Frank T, Tertois AL, Mallet JL (2007) 3D-reconstruction of complex geological interfaces from irregularly distributed and noisy point data. Comput Geosci 33:932–943

    Article  Google Scholar 

  • Freitag LA, Ollivier-Gooch C (1997) Tetrahedral mesh improvement using swapping and smoothing. Int J Numer Methods Eng 40:3979–4002

    Article  Google Scholar 

  • George B, J’anos F (2001) Traditional and new ways to handle uncertainty in geology. Nat Resour Res 10(3):179–187

    Article  Google Scholar 

  • Gerritsen BHM, van der Werff K, Veltkamp RC (2002) Modelling natural objects with alpha-complexes. Comput Aided Des 34(12):881–897

    Article  Google Scholar 

  • Grimm CM, Hughes JF (1995) Modeling surfaces of arbitrary topology using manifolds. In: ACM SIGGRAPH 1995, Computer Graphics Proceedings. 1995, ACM Press, New York, pp 359–368

  • Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1992) Surface reconstruction from unorganized points. In: Computer Graphics (Proceedings of ACM SIGGRAPH 92). ACM Press, New York, pp 71–78

  • Hyungjun P, Kwangsoo K (1995) An adaptive method for smooth surface approximation to scattered 3D points. Comput Aided Des 27(12):929–939

    Article  Google Scholar 

  • Li W, McMains S (2001) A GPU-based voxelization approach to 3D minkowski sum computation. 14th Annual ACM Symposium. 131–142

  • Li FY, Pan M, Zhu L (2005) Research on the algorithm for 3D raster buffer-generation. J Computer-Aided Des Comput Graph 17(9):1928–1932

    Google Scholar 

  • Li N, Wu X, Xiao K, Chen X (2013) Rapid voxelization method for complex orebody. J. Huazhong Univ. of Sci & Tech, Natural Science Edition, 41:34–37

  • Lin HW, Wang G (2003) Three dimensional singed Euclidean distance transform and its applications. Chin J Comput 26:1645–1651

    Google Scholar 

  • Lu X, Wang H (2012) An algorithm for 3D vector buffer based on efficient Boolean operation. J China Univ Min Technol 41:481–487

    Google Scholar 

  • Mallet JL (1992) GOCAD: a computer aided design program for geological applications. Three-dimensional modeling with geoscientific. Inf Syst 354:123–141

    Google Scholar 

  • Mallet JL (1997) Discrete modeling for natural objects. Math Geol 29(2):199–219

    Article  Google Scholar 

  • Mederos B, Amenta N, Velho L, deFigueiredo LH (2005) Surface reconstruction for noisy point clouds. In: SGP’05: Proceedings of the 2005 Euro / ACM SIGGRAPH Symposium on Geometry Processing. ACM Press, New York, 53–62

  • Miller G, Talmor D, Teng S, Walkington N (1995) A Delaunay based numerical method for three-dimension: generation, formulation, and partition. In Proceedings of the 27th ACM symposium of Theory and Computing, 683–692

  • Morse S, Yoo S, Chen T, Rheingans P, Subramanian R (2001) Interpolating implicit surfaces from scattered surface data suing compactly supported radial basis functions. In: SMI’01: Proceedings of the International Conference on Shape Modeling & Applications, 2001, IEEE Computer Society Press, Washington, 89–98

  • Okabe A, Boots B, Sugihara K (1992) Spatial tessellations concepts and applications of Voronoi diagrams. John Wiley & Sons Ltd, New York

    Google Scholar 

  • Porwal A (2001) Extended Weights-of-Evidence Modelling for Predictive Mapping of Base Metal Deposit Potential in Aravalli Province, Western India. Explor Min Geol 10(4):273–287

  • Porwal A, Carranza EJM (2015) Introduction to the Special Issue: GIS-based mineral potential modelling and geological data analyses for mineral exploration. Ore Geol Rev 71:477–483

  • Porwal A, González-Álvarez I, Markwitz V, McCuaig TC, Mamuse A (2010) Weights-of-evidence and logistic regression modeling of magmatic nickel sulfide prospectivity in the Yilgarn Craton, Western Australia. Ore Geol Rev 38(3):184–196

  • Porwal A, Hale M (2000) GIS-based weights-of-evidence analysis of multi-class spatial data for predictive mineral mapping: A case study from Aravalli province, western India. Proceedings, XIV International Conference on Applied Geologic Remote Sensing pp 377–384

  • Raines GL (1999) Evaluation of weights of evidence to predict epithermal gold deposits in the Great Basin of the western United States. Nat Resour Res 8:257–276

  • Rajan V (1994) Optimality of the Delaunay triangulation in Rn. Discret Comput Geom 12:189–202

    Article  Google Scholar 

  • Savchenko VV, Pasko AA, Okunev OG, Kunii TL (1995) Function representation of solids reconstructed from scattered surface points and contours. Comput Graphics Forum 14(4):181–188

    Article  Google Scholar 

  • Si H (2010) Constrained Delaunay tetrahedral mesh generation and refinement. Finite Elem Anal Des 46:33–46

    Article  Google Scholar 

  • Tao P, Xu QS, Liu K (2010) The prediction methods and its influencing factors of the sedimentary bauxite resource, taking bauxite resource of Guizhou Province, China as an example. Geol Bull China 10:1533–1538 in Chinese with English Abstract

    Google Scholar 

  • Tangestani MH, Moore F (2001) Porphyry copper potential mapping using the weights-of- evidence model in a GIS, northern Shahr-e-Babak, Iran. Aust J Earth Sci 48(5):695–701

  • Turk G, Brien F (2002) Modelling with implicit surfaces that interpolate. ACM Trans Graph 21(4):855–873

    Article  Google Scholar 

  • Wang X, Guo F, Lv N, Zhou C (2008) Research on novel 3D buffer analysis method based on vector. ICEODPA, 29

  • Watson D (1981) Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. Comput J 24:167–172

    Article  Google Scholar 

  • William EL, Harvey EC (1987) Marching cubes: a high resolution 3D surface construction algorithm. Comput Graph 21(4):163–169

    Article  Google Scholar 

  • Wu H (1997) Problem of buffer zone construction in GIS. J Wuhan Tech Univ Surv Mapp 22:358–364

    Google Scholar 

  • Wu H, Gong J, Li D (1999) Buffer curve and buffer generation algorithm in aid of edge-constrained triangle network. Acta Geodaetica ET Cartographica Sinica 28:355–359

    Google Scholar 

  • Wu L, Liu Y, Zhang J (2001) Geographic information system theory. Science Press, Section 8, Beijing

    Google Scholar 

  • Xiao KY, Zhang XH, Li JC, Chen JP, Ding JH, Lou DB, Wang BL, Ye TZ, Zhang LX (2007) Quantitative assessment method for national important mineral resources prognosis. Earth Sci Front 14:20–26 in Chinese with English Abstract

    Google Scholar 

  • Xiao K, Li N, Porwal A, Holden EJ, Bagas L, Lu YJ (2015) GIS-based 3D prospectivity mapping: a case study of Jiama copper-polymetallic deposit in Tibet, China. Ore Geol Rev 71:611–632

    Article  Google Scholar 

  • Ye TZ, Xiao KY, Yan GS (2007) Methodology of deposit modeling and mineral resource potential assessment using integrated geological information. Earth Sci Front 14:11–19 in Chinese with English Abstract

    Article  Google Scholar 

  • Ye TZ, Lv ZC, Pang ZS (2014) Theory and methodology of prospecting deposits in exploration areas. Geological Publishing House, Beijing

    Google Scholar 

  • Yuan F, Li X, Zhang M, Zhou T, Gao D, Hong D, Liu X, Wang Q, Zhu J (2014) Three-dimensional prospectivity modelling based on integrated Geoinformation for prediction of buried orebodies. Acta Geol Sin 88:630–643

    Google Scholar 

  • Zavattieri PD, Dari EA, Buscaglia GC (1996) Optimization strategies in unstructured mesh generation. Int J Numer Methods Eng 39:2055–2071

    Article  Google Scholar 

  • Zhou Y, Chen W, Tang Z (1995) An elaborate ambiguity detection method for constructing isosurfaces within tetrahedral meshes. Comput Graph 19(3):355–364

    Article  Google Scholar 

Download references

Acknowledgements

This research was financially supported by 41302262 from the National Natural Science Foundation of China (NSFC, http://www.nsfc.gov.cn/), the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (2006BAB01A01), and the Central Non-profit Organization Foundation of China (K1316). The anonymous reviewers are also thanked for their constructive comments regarding the manuscript.

Author information

Authors and Affiliations

  1. MLR Laboratory of Metallogeny and Mineral Resource Assessment, Institute of Mineral Resources, Chinese Academy of Geological Sciences, Beijing, 100037, China

    Nan Li & Xianglong Song

  2. Centre for Exploration Targeting, School of Earth and Environment, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Nan Li, Leon Bagas, Mark Lindsay & Daniel Wedge

  3. Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu, 610059, China

    Lin Bai

Authors
  1. Nan Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Leon Bagas
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Mark Lindsay
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Daniel Wedge
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Lin Bai
    View author publications

    You can also search for this author inPubMed Google Scholar

  6. Xianglong Song
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Nan Li.

Additional information

Responsible editor: H. A. Babaie

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, N., Bagas, L., Lindsay, M. et al. An irregular triangle mesh buffer analysis method for boundary representation geological object in three-dimension. Earth Sci Inform 10, 149–167 (2017). https://doi.org/10.1007/s12145-016-0283-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12145-016-0283-1

Keywords