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.
Work on this paper has been partially supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST-2000-26473 (ECG – Effective Computational Geometry for Curves and Surfaces), and by the ESPRIT IV LTR Project No. 28155 (GALIA). We thank Sven Havemann and Peter Hoffmann for helpful discussions.
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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: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_59
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DOI: https://doi.org/10.1007/978-3-540-39658-1_59
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