30 research outputs found
Introduction to Mathematical Programming-Based Error-Correction Decoding
Decoding error-correctiong codes by methods of mathematical optimization,
most importantly linear programming, has become an important alternative
approach to both algebraic and iterative decoding methods since its
introduction by Feldman et al. At first celebrated mainly for its analytical
powers, real-world applications of LP decoding are now within reach thanks to
most recent research. This document gives an elaborate introduction into both
mathematical optimization and coding theory as well as a review of the
contributions by which these two areas have found common ground.Comment: LaTeX sources maintained here: https://github.com/supermihi/lpdintr
Rounding, filleting and smoothing of implicit surfaces
© 2017 CAD Solutions, LLC We describe an approach for performing constant radius offsetting and the related operations of filleting, rounding and smoothing for implicit surfaces. The offsetting operation is used as the basic component for defining the remaining operations. These operations are important operations for any modelling system. While it is known how to perform these operations for parametric representation and polygon meshes, there is limited prior work for implicit surfaces and procedural volumetric objects. The proposed approach is based on repeatedly computing the distance to a given implicit surface and its offset surfaces. We illustrate the results obtained by this approach with several examples, including procedurally defined microstructures and CAD objects
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Self-Assembly of Colloidal Nanocrystals: Surface Ligands Promote the Formation of Unexpected Superlattices
Abstracts for the twentyfirst European workshop on Computational geometry, Technische Universiteit Eindhoven, The Netherlands, March 9-11, 2005
This volume contains abstracts of the papers presented at the 21st European Workshop on Computational Geometry, held at TU Eindhoven (the Netherlands) on March 9–11, 2005. There were 53 papers presented at the Workshop, covering a wide range of topics. This record number shows that the field of computational geometry is very much alive in Europe. We wish to thank all the authors who submitted papers and presented their work at the workshop. We believe that this has lead to a collection of very interesting abstracts that are both enjoyable and informative for the reader. Finally, we are grateful to TU Eindhoven for their support in organizing the workshop and to the Netherlands Organisation for Scientific Research (NWO) for sponsoring the workshop
Large bichromatic point sets admit empty monochromatic 4-gons
We consider a variation of a problem stated by ErdËťos
and Szekeres in 1935 about the existence of a number
fES(k) such that any set S of at least fES(k) points in
general position in the plane has a subset of k points
that are the vertices of a convex k-gon. In our setting
the points of S are colored, and we say that a (not necessarily
convex) spanned polygon is monochromatic if
all its vertices have the same color. Moreover, a polygon
is called empty if it does not contain any points of
S in its interior. We show that any bichromatic set of
n ≥ 5044 points in R2 in general position determines
at least one empty, monochromatic quadrilateral (and
thus linearly many).Postprint (published version