Lines tangent to four triangles in three-dimensional space

Abstract : We investigate the lines tangent to four triangles in $\mathbb{R}^3$. 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.
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Submitted on : Friday, November 4, 2005 - 4:23:39 PM
Last modification on : Tuesday, October 30, 2018 - 10:27:43 AM

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Hervé Brönnimann, Olivier Devillers, Sylvain Lazard, Frank Sottile. Lines tangent to four triangles in three-dimensional space. Discrete and Computational Geometry, Springer Verlag, 2007, 37 (3), pp.369-380. ⟨10.1007/s00454-006-1278-3⟩. ⟨inria-00000598⟩

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