Detecting tetrahedralizations of a set of line segments

Authors:
Boting Yang;Cao An Wang
Affiliations:
Department of Computer Science, University of Regina, Canada and Memorial University of Newfoundland;Department of Computer Science, Memorial University of Newfoundland, Canada
Venue:
Journal of Algorithms
Year:
2004

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Abstract

Let L be a set of line segments in three dimensional Euclidean space. In this paper, we prove several characterizations of tetrahedralizations. We present an O(mn log n) algorithm to determine whether L is the edge set of a tetrahedralization, where m is the number of segments and n is the number of distinct endpoints of segments in L. We show that it is NP-complete to decide whether L contains the edge set of a tetrahedralization. We also show that it is NP-complete to decide whether L is a subset of the edge set of a tetrahedralization.