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Journal articles

Lines tangent to four triangles in three-dimensional space

Hervé Brönnimann 1 Olivier Devillers 2 Sylvain Lazard 3 Frank Sottile 4 
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
3 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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
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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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