DCG
2011
13 years 3 months ago
2011
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...
DCG
2011
13 years 3 months ago
2011
DCG
2011
13 years 6 months ago
2011
DCG
2011
13 years 6 months ago
2011
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...
DCG
2011
13 years 6 months ago
2011
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...
DCG
2011
13 years 6 months ago
2011
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...
DCG
2011
13 years 6 months ago
2011
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 ...
DCG
2011
13 years 6 months ago
2011
DCG
2011
13 years 6 months ago
2011
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...