Abstract
Let \( \mathcal{L} \) be a set of line segments in three dimensional Euclidean space. In this paper, we prove several characterizations of tetrahe-dralizations. We present an O(nm log n) algorithm to determine whether \( \mathcal{L} \) is the edge set of a tetrahedralization, where m is the number of segments and n is the number of endpoints in \( \mathcal{L} \). We show that it is NP-complete to decide whether \( \mathcal{L} \) contains the edge set of a tetrahedralization. We also show that it is NP-complete to decide whether \( \mathcal{L} \) is tetrahedralizable.
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© 2002 Springer-Verlag Berlin Heidelberg
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Yang, B., Wang, C.A., Chin, F. (2002). Algorithms and Complexity for Tetrahedralization Detections. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_27
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DOI: https://doi.org/10.1007/3-540-36136-7_27
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