On Triangulating Three-Dimensional Polygons (1996) [19 citations — 2 self]
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author = {Gill Barequet and Matthew Dickerson and David Eppstein},
title = {On Triangulating Three-Dimensional Polygons},
booktitle = {Computational Geometry: Theory and Applications},
year = {1996},
pages = {38--47}
}
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Abstract:
A three-dimensional polygon is triangulable if it has a non-self-intersecting triangulation which defines a simply-connected 2-manifold. We show that the problem of deciding whether a 3D polygon is triangulable is an NP-complete problem. We then establish some necessary conditions and some sufficient conditions for a polygon to be triangulable, providing special cases when the decision problem may be answered in polynomial time. We also discuss optimal triangulations of 3D polygons. Keywords: three-dimensions, triangulation. 1 Introduction A 3-dimensional polygon is a closed chain of straight segments, where every two successive segments share exactly one point and the intersection of every non-successive pair of segments is empty. A triangulation of a 3-dimensional Work on this paper by the first author has been supported by the Israeli Ministry of Science and the Arts, Eshkol Grant 0562-1-94. Work by the second author has been supported by the funds of the National Science Founda...
