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DCG
2006
102views more  DCG 2006»
13 years 11 months ago
Three-Dimensional Delaunay Mesh Generation
We propose an algorithm to compute a conforming Delaunay mesh of a bounded domain specified by a piecewise linear complex. Arbitrarily small input angles are allowed, and the inpu...
Siu-Wing Cheng, Sheung-Hung Poon
DCG
2006
163views more  DCG 2006»
13 years 11 months ago
Isometry-Invariant Valuations on Hyperbolic Space
Abstract. Hyperbolic area is characterized as the unique continuous isometry invariant simple valuation on convex polygons in H2 . We then show that continuous isometry invariant s...
Daniel A. Klain
DCG
2006
101views more  DCG 2006»
13 years 11 months ago
Isodiametric Problems for Polygons
The maximal area of a polygon with n = 2m edges and unit diameter is not known when m 5, nor is the maximal perimeter of a convex polygon with n = 2m edges and unit diameter known...
Michael J. Mossinghoff
DCG
2006
69views more  DCG 2006»
13 years 11 months ago
How Neighborly Can a Centrally Symmetric Polytope Be?
Abstract. We show that there exist k-neighborly centrally symmetric ddimensional polytopes with 2(n + d) vertices, where k(d, n) = ,, d 1 + log((d + n)/d)
Nathan Linial, Isabella Novik
DCG
2006
78views more  DCG 2006»
13 years 11 months ago
A Geometric Study of the Split Decomposition
This paper sheds a new light on the split decomposition theory and T-theory from the viewpoint of convex analysis and polyhedral geometry. By regarding finite metrics as discrete ...
Hiroshi Hirai
DCG
2006
59views more  DCG 2006»
13 years 11 months ago
Tverberg-Type Theorems for Separoids
Juan José Montellano-Ballesteros, Attila P&...
DCG
2006
97views more  DCG 2006»
13 years 11 months ago
k-Sets in Four Dimensions
We show, with an elementary proof, that the number of halving simplices in a set of n points in R4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/13...
Jirí Matousek, Micha Sharir, Shakhar Smorod...
DCG
2006
96views more  DCG 2006»
13 years 11 months ago
Elementary Moves on Triangulations
It is proved that a triangulation of a polyhedron can always be transformed into any other triangulation of the polyhedron using only elementary moves. One consequence is that an ...
Monika Ludwig, Matthias Reitzner