Skip to main content
SpringerLink
Log in

A novel geometric approach for 3-D geological modelling

Une nouvelle approche géométrique pour la modélisation géologique 3-D

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

This paper presents a graphics system called the prism network and its boundary (PNB) aimed at representing the stratified solids that are formed in the subsurface terrain. It allows full 3D modelling of these types of spaces formed by superimposed layers bounded by stratification surfaces. A set of boreholes in the ground is used to generate a network of prisms that models the solid space and serves as the basis for creating two secondary networks, one of triangles and another of quadrilaterals, which define the model boundaries. This graphics system has been implemented in C++, using the standard OpenGL graphics API. The paper first defines and implements a model in the PNB data structure, the process by means of which it is generated is then described, and, finally, a range of applications to specific cases is presented and graphically illustrated.

Résumé

Cet article présente un système graphique appelé PNB (sigles en anglais de Réseau de Prismes et sa Frontière) qui vise à représenter les solides stratifiés qui sont formés dans le sous-sol. Il permet la modélisation 3D complète de ces types d’espaces formés par des couches superposées délimitées par des surfaces de stratification. À partir d’un ensemble de forages dans le terrain est généré un réseau de prismes qui modélise l’espace solide et sert de base pour la création de deux réseaux secondaires, l’un de triangles et l’autre de quadrilatères, qui définissent les frontières du modèle. Ce système graphique a été implémenté en C++, en utilisant l’API standard graphique OpenGL. Le article définit d’abord le modèle et le met en œuvre dans la structure de données PNB, puis décrit le processus de leur génération, et enfin, présente et illustre graphiquement une gamme d’applications à des cas particuliers.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  • Abdul-Rahman A, Pilouk M (2008) Spatial data modeling for 3D GIS. Springer, Berlin, 290 pp

    Google Scholar 

  • Baojun W, Bin S, Zhen S (2009) A simple approach to 3D geological modelling and visualization. Bull Eng Geol Environ 68:559–565

    Article  Google Scholar 

  • Bartier PM, Keller CP (1996) Multivariate interpolation to incorporate thematic surface data using inverse distance weighting. Comput Geosci 22(7):795–799

    Article  Google Scholar 

  • Baumgart BG (1975) A polyhedron representation for computer vision. In: Proceedings of the national computer conference, AFIPS conference, vol 44, Arlington, VA. AFIPS Press, pp 589–596

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

    Article  Google Scholar 

  • Cheng YM, Liu HT, Wei WB, Au SK (2005) Location of critical three-dimensional non-spherical failure surface by NURBS functions and ellipsoid with applications to highway slopes. Comput Geotech 32:387–399

    Article  Google Scholar 

  • Courrioux G, Nullans S, Guillen A, Boissonnat JD, Repusseau P, Renaud X, Thibaut M (2001) 3D volumetric modelling of Cadomian terranes (Northern Brittany France): an automatic method using Voronoi diagrams. Tectonophysics 331:181–196

    Article  Google Scholar 

  • de Kemp EA (1999) Visualization of complex geological structures using 3-D Bézier construction tools. Comput Geosci 25(5):581–597

    Article  Google Scholar 

  • Delaunay B (1934) Sur la sphere vide. Bull Acad Sci USSR 7:793–800

    Google Scholar 

  • Eberhardt H, Vesa-Klumpp V, Hanebeck UD (2010) Density trees for efficient nonlinear state estimation. In: Proceedings of the 13th international conference on information fusion, Edinburgh, UK

  • Farin G (2001) Curves and surfaces for CAGD, 5th edn: a practical guide. Morgan Kaufmann, San Francisco, 520 pp

    Google Scholar 

  • Farin G, Hoschek J, Kim M-S (2002) Handbook of computer aided geometric design. Elsevier Science BV, Amsterdam, 848 pp

    Google Scholar 

  • Fisher TR, Wales RQ (1991) Three-dimensional solid modeling of geological objects using non-uniform rational B-splines (NURBS). In: Turner AK (ed) Three dimensional modelling with geoscientific information systems. Kluwer, Dordrecht, pp 85–105

    Google Scholar 

  • Galera C, Bennis C, Moretti I, Mallet JL (2003) Construction of coherent 3D geological blocks. Comput Geosci 2(2):69–77

    Google Scholar 

  • Gong J, Cheng P, Wang Y (2004) Three-dimensional modeling and application in geological exploration engineering. Comput Geosci 30(4):391–404

    Article  Google Scholar 

  • Guibas L, Russel D (2004) An empirical comparison of techniques for updating Delaunay triangulations. In: Proceedings of the twentieth annual symposium on computational geometry (SCG ‘04), New York, pp 170–179

  • Hack R, Orlic B, Ozmutlu S, Zhu S, Rengers N (2006) Three and more dimensional modelling in geo-engineering. Bull Eng Geol Environ 65:143–153

    Article  Google Scholar 

  • Hearn D, Baker MP (1997) Computer graphics. C version. Prentice Hall, Upper Saddle River, 652 pp

    Google Scholar 

  • Homer H, Thomas S (1998) A survey of construction and manipulation of octree. Comput Vis Graph Image Process 43:409–431

    Google Scholar 

  • Houlding SW (1994) 3D geoscience modeling computer techniques for geological characterization. Springer, New York, 309 pp

    Book  Google Scholar 

  • Kessler H, Mathers SJ, Sobisch HG (2009) The capture and dissemination of integrated 3D geospatial knowledge at the British geological survey using GSI3D software and methodology. Comput Geosci 35(6):1311–1321

    Article  Google Scholar 

  • Lixin W, Xuexi C, Yanbing W, Kunyang L (2003) 3D geosciences modeling and an universal GTP model for geology, mining and civil engineering. In: International workshop on virtual geographical environment, Hong Kong

  • McConnell JJ (2006) Computer graphics: theory into practice. Jones & Bartlett Learning, Sudbury, 519 pp

    Google Scholar 

  • Nordvik T, Grøneng G, Venkik Ganerød G, Nilsen B, Harding C, Blikra LH (2009) Geovisualization, geometric modelling and volume estimation of the Åknes rockslide, Western Norway. Bull Eng Geol Environ 68:245–256

    Article  Google Scholar 

  • Odgaard A, Andersen K, Melsen F, Gundersen HJG (2011) A direct method for fast three-dimensional serial reconstruction. J Microsc 159(3):335–342 (1990) (article first published online: 2 Aug 2011)

    Google Scholar 

  • Paoluzzi A, Ramella M, Santarelli A (1989) Boolean algebra over linear polyhedra. Comput Aided Des 21:474–484

    Article  Google Scholar 

  • Pouliot J, Bédard K, Kirkwood D, Lachance B (2008) Reasoning about geological space: coupling 3D GeoModels and topological queries as an aid to spatial data selection. Comput Geosci 34(5):529–541

    Article  Google Scholar 

  • PrisModel website http://webs.uvigo.es/igd/PrisModel

  • Refice A, Giachetta E, Capolongo D (2012) SIGNUM: a Matlab, TIN-based landscape evolution model. Comput Geosci 45:293–303

    Article  Google Scholar 

  • Salvini R, Francioni M, Riccucci S, Fantozzi PL, Bonciani F, Mancini S (2011) Stability analysis of “Grotta delle Felci” Cliff (Capri Island, Italy): structural, engineering-geological, photogrammetric surveys and laser scanning. Bull Eng Geol Environ 70:549–557

    Article  Google Scholar 

  • Shaffer CA (2011) Data structures and algorithm analysis in C++, 3rd edn. Dover, New York, 624 pp

    Google Scholar 

  • Shi WZ (1996) A hybrid model for 3D GIS. Geoinformatics 1:400–409

    Google Scholar 

  • Shi WZ (2000) Development of a hybrid model for three-dimensional GIS. Geo Spat Inf Sci 3(2):6–12

    Article  Google Scholar 

  • Stroud I (2006) Boundary representation modelling techniques. Springer, Berlin, 808 pp

    Google Scholar 

  • Tacher L, Pomian-Srzednicki I, Parriaux A (2006) Geological uncertainties associated with 3-D subsurface models. Comput Geosci 32(2):212–221

    Article  Google Scholar 

  • Turner AK (2006) Challenges and trends for geological modelling and visualisation. Bull Eng Geol Environ 65:109–127

    Article  Google Scholar 

  • Wang CX, Bai SW, He HJ (2003) Study on geological modeling in 3D strata visualization. Chin J Rock Mech Eng 22(10):1722–1726

    Google Scholar 

  • Wright RS, Haemel N, Sellers G, Lipchak B (2010) OpenGL SuperBible: comprehensive tutorial and reference, 5th edn. Addison-Wesley Professional, Boston, 1008 pp

    Google Scholar 

  • Zhu L, Zhang C, Li M, Pan X, Sun J (2012) Building 3D solid models of sedimentary stratigraphic systems from borehole data: an automatic method and case studies. Eng Geol 127:1–13

    Article  Google Scholar 

  • Zlatanova S, Abdul-Rahman A, Pilouk M (2002) 3D GIS: current status and perspectives. In: Proceedings of the joint conference on geo-spatial theory, processing and applications, 8–12 July, Ottawa

Download references

Author information

Authors and Affiliations

  1. School of Industrial Engineering, University of Vigo, Maxwell 9, 36310, Vigo, Galicia, Spain

    Benito Bouza-Rodríguez & Alberto Comesaña-Campos

  2. Department of Mining Engineering, Mining Engineering School, University of Oviedo, Independencia 13, 33004, Oviedo, Asturias, Spain

    Agustín Menéndez-Díaz

  3. Department of Mining Engineering, Mining Engineering School, University of Oviedo, Campus de Mieres, 33600, Oviedo, Asturias, Spain

    Silverio Garcia-Cortes

Authors
  1. Benito Bouza-Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alberto Comesaña-Campos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Agustín Menéndez-Díaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Silverio Garcia-Cortes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Agustín Menéndez-Díaz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bouza-Rodríguez, B., Comesaña-Campos, A., Menéndez-Díaz, A. et al. A novel geometric approach for 3-D geological modelling. Bull Eng Geol Environ 73, 551–567 (2014). https://doi.org/10.1007/s10064-013-0545-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10064-013-0545-9

Keywords

Mots clés

Search

Navigation