Lines Tangent to Four Triangles in Three-Dimensional Space

Authors:
H. Bronnimann;O. Devillers;S. Lazard;F. Sottile
Affiliations:
Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201, USA;INRIA Sophia-Antipolis, 2004 Rte des Lucioles, B.P. 93, 06902 Sophia-Antipolis Cedex, France;INRIA Lorraine (LORIA), 615 Rue du Jardin Botanique, 54602 Villers-les-Nancy, France;Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
Venue:
Discrete & Computational Geometry
Year:
2007

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Abstract

We investigate the lines tangent to four triangles in R3. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.