Drawing $K_n$ in Three Dimensions with One Bend per Edge

Olivier Devillers (1) , Hazel Everett (2) , Sylvain Lazard (2) , Maria Pentcheva (2) , Stephen Wismath (3)

1 GEOMETRICA - Geometric computing
2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
3 Department of Mathematics and Computer Science

We give a drawing of $K_n$ in 3D in which vertices are placed at integer grid points and edges are drawn crossing-free with at most one bend per edge in a volume bounded by $O(n^{2.5})$.

Domains: Computational Geometry [cs.CG]

Olivier Devillers, Hazel Everett, Sylvain Lazard, Maria Pentcheva, Stephen Wismath. Drawing $K_n$ in Three Dimensions with One Bend per Edge. 13th International Symposium on Graph Drawing - GD'2005, Sep 2005, University of Limerick, Ireland. ⟨inria-00000374⟩