On triangulating three-dimensional polygons

A three-dimensional polygon is triangulable if it has a non-self-intersecting triangulation which definea 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 sufhcient conditions for a polygon to be triangttlable, providing special cases when the de cision problem may be answered in polynomial time. We also discuss optimal triangulations of

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