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A reliable triangular mesh intersection algorithm and its application in geological modelling

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Abstract

We introduce a reliable intersection algorithm for manifold surface meshes. The proposed algorithm builds conforming surface meshes from a set of intersecting triangulated surfaces. This algorithm effectively handles all degenerate triangle–triangle intersection cases. The key idea of the algorithm is based on an extensive set of triangle–edge intersection cases, combined with an intersection curve tracking method. The intersection operations do not rely on global spatial search operations and no remeshing steps are needed. The intersection curves are introduced into each surface mesh using a unique curve imprinting algorithm. The imprinting algorithm naturally handles degenerate intersection cases of many surfaces at an edge or at a point. The algorithm produces a consistent mesh data structure for subsequent mesh optimization operations. The mesh intersection algorithm is used within a general framework for modelling and meshing of geological formations, which are essential for reliable mathematical modelling of oil reservoirs.

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References

  1. Carette J, Elsheikh M, Smith S (2011) A generative geometric kernel. In: Khoo S-C, Siek JG (eds) Proceedings of the 2011 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation, PEPM 2011, Austin, TX, USA, 24–25 Jan 2011, ACM, New York, pp 53–62. doi:10.1145/1929501.1929510

  2. Caumon G, Lepage F, Sword C, Mallet JL (2004) Building and editing a sealed geological model. Math Geol 36:405–424

    Article  MATH  Google Scholar 

  3. 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  MATH  Google Scholar 

  4. Coelho LCG, Gattass M, de Figueiredo LH (2000) Intersecting and trimming parametric meshes on finite element shells. Int J Numer Methods Eng 47(4):777–800

    Article  MATH  Google Scholar 

  5. ElSheikh AH, Smith S, Chidiac SE (2004) Semi-formal design of reliable mesh generation systems. Advances in Engineering Software 35(12):827–841. doi:10.1016/j.advengsoft.2004.06.012

  6. Gottschalk S, Lin MC, Manocha D (1996) OBBTree: a hierarchical structure for rapid interference detection. In: Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, SIGGRAPH ’96, pp 171–180

  7. Guo K, Zhang L, Wang C, Huang S (2007) Boolean operations of stl models based on loop detection. Int J Adv Manuf Technol 33:627–633

    Article  Google Scholar 

  8. Halbwachs Y, Courrioux G, Renaud X, Repusseau P (1996) Topological and geometric characterization of fault networks using 3-dimensional generalized maps. Math Geol 28:625–656

    Article  Google Scholar 

  9. Lienhardt P (1989) Subdivisions of n-dimensional spaces and n-dimensional generalized maps. In: Proceedings of the fifth annual symposium on computational geometry, ACM, New York, NY, USA, SCG ’89, pp 228–236

  10. Lindenbeck C, Ebert H, Ulmer H, Lavorante LP, Pflug R (2002) Tricut: a program to clip triangle meshes using the rapid and triangle libraries and the visualization toolkit. Comput Geosci 28(7):841–850

    Article  Google Scholar 

  11. Lira WM, Coelho LCG, Martha LF (2002) Multiple intersections of finite-element surface meshes. In: 11th international meshing roundtable, Ithaca, New York, USA, pp 355–363

  12. Lo S, Wang W (2003) An algorithm for the intersection of quadrilateral surfaces by tracing of neighbours. Comput Methods Appl Mech Eng 192(20–21):2319–2338

    Article  MATH  Google Scholar 

  13. Lo S, Wang W (2004) A fast robust algorithm for the intersection of triangulated surfaces. Eng Comput 20:11–21

    Article  Google Scholar 

  14. Lo SH (1995) Automatic mesh generation over intersecting surfaces. Int J Numer Methods Eng 38(6):943–954

    Article  MATH  Google Scholar 

  15. Lohner R, Parikh P (1988) Generation of three-dimensional unstructured grids by the advancing-front method. Int J Numer Methods Fluids 8(10):1135–1149

    Article  Google Scholar 

  16. Mücke EP (1993) Shapes and implementations in three-dimensional geometry. PhD thesis, Department of Computer Science, University of Illinois at Urbana-Champaign

  17. Schroeder WJ, Avila LS, Hoffman W (2000) Visualizing with vtk: a tutorial. IEEE Comput Graph Appl 20:20–27

    Article  Google Scholar 

  18. Shewchuk JR (1996) Robust adaptive floating-point geometric predicates. In: Proceedings of the twelfth annual symposium on computational geometry, ACM, New York, NY, USA, SCG ’96, pp 141–150

  19. Shewchuk JR (1996) Triangle: engineering a 2d quality mesh generator and delaunay triangulator. In: Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering, Springer-Verlag, London, UK, FCRC ’96/WACG ’96, pp 203–222

  20. Shostko AA, Lohner R, Sandberg WC (1999) Surface triangulation over intersecting geometries. Int J Numer Methods Eng 44(9):1359–1376

    Article  MATH  Google Scholar 

  21. Wang D, Hassan O, Morgan K, Weatherill N (2006) Eqsm: an efficient high quality surface grid generation method based on remeshing. Comput. Methods Appl Mech Eng 195(41–43):5621–5633

    Article  MATH  MathSciNet  Google Scholar 

  22. Wang D, Hassan O, Morgan K, Weatherill N (2007) Enhanced remeshing from stl files with applications to surface grid generation. Commun Numer Methods Eng 23(3):227–239

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

The authors would like to thank the anonymous reviewers for their insightful and constructive comments which helped enhance this manuscript. Major Parts of this work was carried out while the authors were employed at Al-Azhar University, Cairo, Egypt.

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Authors and Affiliations

  1. Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 201 East 24th Street, Campus Mail C0200, Austin, TX, 78712, USA

    Ahmed H. Elsheikh

  2. Cheriton School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

    Mustafa Elsheikh

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  1. Ahmed H. Elsheikh
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Correspondence to Ahmed H. Elsheikh.

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Elsheikh, A.H., Elsheikh, M. A reliable triangular mesh intersection algorithm and its application in geological modelling. Engineering with Computers 30, 143–157 (2014). https://doi.org/10.1007/s00366-012-0297-3

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  • DOI: https://doi.org/10.1007/s00366-012-0297-3

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