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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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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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  2. Mustafa 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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