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CCCG
2010
13 years 11 months ago
On the variance of random polygons
A random polygon is the convex hull of uniformly distributed random points in a convex body K R2 . General upper bounds are established for the variance of the area of a random p...
William L. Steiger, Imre Bárány
DAGSTUHL
2010
13 years 11 months ago
Exploring Visualization Methods for Complex Variables
Applications of complex variables and related manifolds appear throughout mathematics and science. Here we review a family of basic methods for applying visualization concepts to ...
Andrew J. Hanson, Ji-Ping Sha
SODA
1993
ACM
119views Algorithms» more  SODA 1993»
13 years 11 months ago
Iterated Nearest Neighbors and Finding Minimal Polytopes
We introduce a new method for nding several types of optimal k-point sets, minimizing perimeter, diameter, circumradius, and related measures, by testing sets of the O(k) nearest ...
David Eppstein, Jeff Erickson
ADCM
2007
134views more  ADCM 2007»
13 years 10 months ago
Barycentric coordinates for convex sets
In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous appli...
Joe D. Warren, Scott Schaefer, Anil N. Hirani, Mat...
JC
2007
109views more  JC 2007»
13 years 10 months ago
Cubature formulas for function spaces with moderate smoothness
We construct simple algorithms for high-dimensional numerical integration of function classes with moderate smoothness. These classes consist of square-integrable functions over t...
Michael Gnewuch, René Lindloh, Reinhold Sch...