Boolean operations on multi-region solids for mesh generation
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-dimens...
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| Veröffentlicht in: | Engineering with computers Jg. 28; H. 3; S. 225 - 239 |
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| Abstract | 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. |
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| AbstractList | Issue Title: Special Issue: The Mesh Trends Symposium 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.[PUBLICATION ABSTRACT] 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. |
| Author | Martha, Luiz Fernando Miranda, Antônio Carlos de O. de Arruda, Marcos Chataignier Lira, William Wagner M. Pereira, André Maués Brabo |
| Author_xml | – sequence: 1 givenname: André Maués Brabo surname: Pereira fullname: Pereira, André Maués Brabo email: brabo@tecgraf.puc-rio.br, andremaues@id.uf.br organization: Departamento de Engenharia Civil, Universidade Federal Fluminense, Departamento de Engenharia Civil, Pontifícia Universidade Católica do Rio de Janeiro – sequence: 2 givenname: Marcos Chataignier surname: de Arruda fullname: de Arruda, Marcos Chataignier organization: Departamento de Engenharia Civil, Pontifícia Universidade Católica do Rio de Janeiro – sequence: 3 givenname: Antônio Carlos de O. surname: Miranda fullname: Miranda, Antônio Carlos de O. organization: Departamento de Engenharia Civil e Ambiental, Universidade de Brasilia, Campus Universitario Darcy Ribeiro – sequence: 4 givenname: William Wagner M. surname: Lira fullname: Lira, William Wagner M. organization: Centro de Tecnologia, Universidade Federal de Alagoas – sequence: 5 givenname: Luiz Fernando surname: Martha fullname: Martha, Luiz Fernando organization: Departamento de Engenharia Civil, Pontifícia Universidade Católica do Rio de Janeiro |
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| Keywords | Boolean operations Non-manifold solids Boundary representation Degenerate portions Geometric modeling Mesh generation |
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| References | CoelhoLCGGattassMFigueiredoLHIntersecting and trimming parametric meshes on finite-element shellsInt J Numer Methods Eng2000477778000979.6858310.1002/(SICI)1097-0207(20000210)47:4<777::AID-NME797>3.0.CO;2-6 RossignacJRRequichaAGConstructive non-regularized geometryComput Aided Des19912321320754.65130 ShewchukJRAdaptive precision floating-point arithmetic and fast robust geometric predicatesDiscrete Comput Geometry19971830536314876470892.6809810.1007/PL00009321 SenDSrikanthTKEfficient computation of volume fractions for multi-material cell complexes in a grid by slicingComput Geosci20083475478210.1016/j.cageo.2007.09.016 ColyerBProject MIDAS: magnet integrated design and analysis systemIEEE Trans Magn1997331143114810.1109/20.582457 De BergMVan KreveldMOvermarsMSchwarzkopfOComputational geometry: algorithms and applications1997BerlinSpringer0877.68001 ShapiroVVosslerDLSeparation for boundary to CSG conversionACM Trans Graph199312335510.1145/169728.169723 KouXYTanSTSzeWSModeling complex heterogeneous objects with non-manifold heterogeneous cellsComput Aided Des20063845747410.1016/j.cad.2005.11.009 Weiler K (1988) The radial-edge structure: a topological representation for non-manifold geometric boundary representation. Geometric modeling for CAD applications. North Holland, Amsterdam, pp 3–36 Keyser JC (2000) Exact boundary evaluation for curved solids. Dissertation, University of North Carolina Miranda ACO, Martha LF (2002) Mesh generation on high-curvature surfaces based on a background quadtree structure. In: Proceedings of 11th international meshing roundtable, Ithaca, pp 333–341 QianXDuttaDHeterogeneous object modeling through direct face neighborhood alterationComput Graph20032794396110.1016/j.cag.2003.08.001 Gursoz EL, Choi Y, Prinz FB (1990) Vertex-based representation of non-manifold boundaries. In: Wozny M, Turner J, Preiss K (eds) Geometric modeling for product engineering. 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| References_xml | – reference: Keyser JC (2000) Exact boundary evaluation for curved solids. Dissertation, University of North Carolina – reference: Gardan Y, Minich C, Perrin E (2003) Boolean operations on feature-based models. J WSCG (Winter School of Computer Graphics) – reference: ColyerBProject MIDAS: magnet integrated design and analysis systemIEEE Trans Magn1997331143114810.1109/20.582457 – reference: LienhardtPTopological models for boundary representation: a comparison with n-dimensional generalized mapsComput Aided Des19912359820754.65018 – reference: KouXYTanSTSzeWSModeling complex heterogeneous objects with non-manifold heterogeneous cellsComput Aided Des20063845747410.1016/j.cad.2005.11.009 – reference: Weiler K (1986) Topological structures for geometric modeling. Dissertation, Rensselaer Polytechnic Institute, Troy, NY – reference: MillerJRArchitectural issues in solid modelersIEEE Comput Graph Appl19899728710.1109/38.35539 – reference: RequichaAGVoelckerHBBoolean operations in solid modeling: boundary evaluation and merging algorithmsProc IEEE198573304410.1109/PROC.1985.13108 – reference: SenDSrikanthTKEfficient computation of volume fractions for multi-material cell complexes in a grid by slicingComput Geosci20083475478210.1016/j.cageo.2007.09.016 – reference: GursozELChoiYPrinzFBBoolean set operations on non-manifold boundary representation objectsComput Aided Des19912333390725.65156 – reference: Miranda ACO, Martha LF (2002) Mesh generation on high-curvature surfaces based on a background quadtree structure. In: Proceedings of 11th international meshing roundtable, Ithaca, pp 333–341 – reference: HoffmannCMGeometric and solid modeling: an introduction1989San FransiscoMorgan Kaufmann – reference: GardanYPerrinEAn algorithm for reducing 3D Boolean operations to a 2D problem: concepts and resultsComput Aided Des19952827728710.1016/0010-4485(95)00050-X – reference: Rossignac JR, O’Connor MA (1989) A dimensional-independent model for pointsets with internal structures and incomplete boundaries. Geometric modeling for product engineering. 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