Engineering with Computers

, Volume 28, Issue 3, pp 225–239 | Cite as

Boolean operations on multi-region solids for mesh generation

  • André Maués Brabo Pereira
  • Marcos Chataignier de Arruda
  • Antônio Carlos de O. Miranda
  • William Wagner M. Lira
  • Luiz Fernando Martha
Original Article


An algorithm for Boolean operations on non-manifold models is proposed to allow the treatment of solids with multiple regions (internal interfaces) and degenerate portions (shells and wires), in the context of mesh generation. In a solid modeler, one of the most powerful tools to create three-dimensional objects with any level of geometric complexity is the Boolean set operators. They are intuitive and popular ways to combine solids, based on the operations applied to point sets. To assure that the resulting objects have the same dimension as the original objects, without loose or dangling parts, a regularization process is usually applied after a Boolean operation. In practice, the regularization is performed classifying the topological elements and removing internal or lower-dimensional structures. However, in many engineering applications, the adopted geometric model may contain idealized internal parts, as in the case of multi-region models, or lower-dimensional parts, as in the case of solids that contain dangling slabs that are represented as zero-thickness surfaces or wireframes in the model. Therefore, the aim of this work is the development of a generic algorithm that allows the application of the Boolean set operations in a geometric modeling environment applied to finite and boundary element mesh generation. This environment adopts a non-manifold boundary representation that considers an undefined number of topological entities (group concept), and works with objects of different dimensions and with objects not necessarily plane or polyhedral (parametric curved surfaces). Numerical examples are presented to illustrate the proposed methodology.


Geometric modeling Non-manifold solids Boolean operations Boundary representation Mesh generation Degenerate portions 



The authors would like to thank the Computer Graphics Technology Group (Tecgraf) and Pontifical Catholic University of Rio de Janeiro (PUC-Rio) for the financial support and for providing the necessary space and resources used during the development of this work.


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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • André Maués Brabo Pereira
    • 1
    • 2
  • Marcos Chataignier de Arruda
    • 2
  • Antônio Carlos de O. Miranda
    • 3
  • William Wagner M. Lira
    • 4
  • Luiz Fernando Martha
    • 2
  1. 1.Departamento de Engenharia CivilUniversidade Federal FluminenseNiteroiBrazil
  2. 2.Departamento de Engenharia CivilPontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil
  3. 3.Departamento de Engenharia Civil e AmbientalUniversidade de Brasilia, Campus Universitario Darcy RibeiroBrasiliaBrazil
  4. 4.Centro de TecnologiaUniversidade Federal de AlagoasMaceióBrazil

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