Home | Issues | About JGAA | Instructions for Authors |
Special Issue on Selected Papers from the Seventeenth International Symposium on Graph Drawing, GD 2009
DOI: 10.7155/jgaa.00216
Drawing 3-Polytopes with Good Vertex Resolution
Vol. 15, no. 1, pp. 33-52, 2011. Regular paper.
Abstract We study the problem how to obtain a small drawing of a 3-polytope with Euclidean distance between any two points at least 1.
The problem can be reduced to a one-dimensional problem, since it is sufficient to guarantee distinct integer x-coordinates. We develop
an algorithm that yields an embedding with the desired property such that the polytope is contained inside a 2(n−2)×2 ×1 box.
The constructed embedding can be scaled to a grid embedding whose x-coordinates are contained in [0,2(n−2)].
Furthermore, the point set of the embedding has a small spread, which differs from the best possible spread only by a multiplicative constant.
|
Submitted: December 2009.
Reviewed: September 2010.
Revised: October 2010.
Accepted: November 2010.
Final: November 2010.
Published: February 2011.
|
Journal Supporters
|