Towards Compatible Triangulations
We state the following conjecture: any two planar n-point sets (that agree on the number of convex hull points) can be triangulated in a compatible manner, i.e., such that the resulting two planar graphs are isomorphic. The conjecture is proved true for point sets with at most three interior points. We further exhibit a class of point sets which can be triangulated compatibly with any other set (that satis?es the obvious size and hull restrictions). Finally, we prove that adding a small number of Steiner points (the number of interior points minus two) always allows for compatible triangulations.
KeywordsExtreme Point Interior Point Convex Polygon Order Type Steiner Point
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- 1.O. Aichholzer, F. Aurenhammer, H. Krasser, Enumerating order types for small point sets with applications. 17th Ann. ACM Symp. Computational Geometry, Medford, MA, 2001 (to be presented).Google Scholar
- 3.M. Bern, A. Sahai, Isomorphic triangulations and map conflaation. Personal communication, 2000.Google Scholar
- 6.H. Krasser, Kompatible Triangulierungen ebener Punktmengen. Master Thesis, Institute for Theoretical Computer Science, Graz University of Technology, Graz, Austria, 1999.Google Scholar
- 7.A. Saalfeld, Joint triangulations and triangulation maps. Proc. 3rd Ann. ACM Sympos. Computational Geometry, Waterloo, Canada, 1987, 195–204.Google Scholar