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» On the Geometric Dilation of Finite Point Sets
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CCCG
2009
15 years 24 days ago
The Centervertex Theorem for Wedge Depth
There are many depth measures on point sets that yield centerpoint theorems. These theorems guarantee the existence of points of a specified depth, a kind of geometric median. How...
Gary L. Miller, Todd Phillips, Donald Sheehy
IMR
2004
Springer
15 years 5 months ago
Finite Element Mesh Sizing for Surfaces Using Skeleton
The finite element (FE) mesh sizing has great influence on computational time, memory usage, and accuracy of FE analysis. Based on a systematic in-depth study of the geometric com...
William Roshan Quadros, Steven J. Owen, Michael L....
COCOA
2008
Springer
15 years 1 months ago
New Algorithms for k-Center and Extensions
The problem of interest is covering a given point set with homothetic copies of several convex containers C1,...,Ck, while the objective is to minimize the maximum over the dilatat...
René Brandenberg, Lucia Roth
SIGACT
2008
103views more  SIGACT 2008»
14 years 11 months ago
Computational geometry column 50
Two long-open problems have been solved: (1) every sufficiently large planar point set in general position contains the vertices of an empty hexagon; (2) every finite collection o...
Joseph O'Rourke
CORR
2008
Springer
92views Education» more  CORR 2008»
14 years 11 months ago
Bipolarization of posets and natural interpolation
The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of [0, 1]n. We take this basic fact as a starting poin...
Michel Grabisch, Christophe Labreuche