Skip to Main content Skip to Navigation

# Lines tangent to four triangles in three-dimensional space

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [15 references]

https://hal.inria.fr/inria-00000598
Contributor : Sylvain Lazard <>
Submitted on : Friday, November 4, 2005 - 4:23:39 PM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM

### Citation

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⟩

Record views

Files downloads