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Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation

MPS-Authors
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Granados,  Miguel
Computer Graphics, MPI for Informatics, Max Planck Society;
International Max Planck Research School, MPI for Informatics, Max Planck Society;

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Hachenberger,  Peter
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Hert,  Susan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Kettner,  Lutz
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Seel,  Michael
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Granados, M., Hachenberger, P., Hert, S., Kettner, L., Mehlhorn, K., & Seel, M. (2003). Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation. In Algorithms - ESA 2003: 11th Annual European Symposium (pp. 654-666). Berlin, Germany: Springer.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-2C67-A
Abstract
We describe a data structure for three-dimensional Nef complexes, algorithms for boolean operations on them, and our implementation of data structure and algorithms. Nef polyhedra were introduced by W. Nef in his seminal 1978 book on polyhedra. They are the closure of half-spaces under boolean operations and can represent non-manifold situations, open and closed boundaries, and mixed dimensional complexes. Our focus lies on the generality of the data structure, the completeness of the algorithms, and the exactness and efficiency of the implementation. In particular, all degeneracies are handled.