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DCG
2011
9 years 1 months ago
A Celtic Framework for Knots and Links
We describe a variant of a method used by modern graphic artists to design what are traditionally called Celtic knots, which are part of a larger family of designs called “mirro...
Jonathan L. Gross, Thomas W. Tucker
DCG
2011
9 years 1 months ago
Prodsimplicial-Neighborly Polytopes
Benjamin Matschke, Julian Pfeifle, Vincent Pilaud
DCG
2011
9 years 4 months ago
Small Grid Embeddings of 3-Polytopes
We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by O(27.55n ) = O(18...
Ares Ribó Mor, Günter Rote, Andr&eacut...
DCG
2011
9 years 4 months ago
The Expected Genus of a Random Chord Diagram
To any generic curve in an oriented surface there corresponds an oriented chord diagram, and any oriented chord diagram may be realized by a curve in some oriented surface. The gen...
Nathan Linial, Tahl Nowik
DCG
2011
9 years 4 months ago
New Classes of Counterexamples to Hendrickson's Global Rigidity Conjecture
We examine the generic local and global rigidity of various graphs in Rd . Bruce Hendrickson showed that some necessary conditions for generic global rigidity are (d + 1)-connected...
Samuel Frank, Jiayang Jiang
DCG
2011
9 years 4 months ago
More Colourful Simplices
We show that any point in the convex hull of each of (d +1) sets of (d +1) points in general position in Rd is contained in at least (d + 1)2/2 simplices with one vertex from each ...
Antoine Deza, Tamon Stephen, Feng Xie
DCG
2011
9 years 4 months ago
Lines Pinning Lines
Boris Aronov, Otfried Cheong, Xavier Goaoc, Gü...
DCG
2011
9 years 4 months ago
Random Geometric Complexes
We study the expected topological properties of ˇCech and Vietoris-Rips complexes built on random points in Rd . We find higher dimensional analogues of known results for connect...
Matthew Kahle
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