# A Dual Space Representation for Geometric Data.

Oliver Günther, Eugene Wong:
A Dual Space Representation for Geometric Data.
VLDB 1987: 501-506@inproceedings{DBLP:conf/vldb/GuntherW87,
author = {Oliver G{\"u}nther and
Eugene Wong},
editor = {Peter M. Stocker and
William Kent and
Peter Hammersley},
title = {A Dual Space Representation for Geometric Data},
booktitle = {VLDB'87, Proceedings of 13th International Conference on Very
Large Data Bases, September 1-4, 1987, Brighton, England},
publisher = {Morgan Kaufmann},
year = {1987},
isbn = {0-934613-46-X},
pages = {501-506},
ee = {db/conf/vldb/GuntherW87.html},
crossref = {DBLP:conf/vldb/87},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

## Abstract

This paper presents a representation scheme for
polyhedral objects in arbitrary dimensions. Each object
is represented as the algebraic sum of convex polyhedra
(*cells*). Each cell in turn is represented as the
intersection of halfspaces and encoded in a vector. The notion of
vertices is abandoned completely as it is not needed for
the set and search operators we intend to support. We
show how this approach allows us to decompose set
operations (such as intersection) on polyhedral objects
into two steps. The first step consists of a collection of
vector operations; the second step is a garbage collection
where vectors that represent empty celle are eliminated.
*Copyright © 1987 by the VLDB Endowment.
Permission to copy without fee all or part of this material is granted provided that the copies are not made or
distributed for direct commercial advantage, the VLDB
copyright notice and the title of the publication and
its date appear, and notice is given that copying
is by the permission of the Very Large Data Base
Endowment. To copy otherwise, or to republish, requires
a fee and/or special permission from the Endowment.*

## Online Paper

CDROM Version: Load the CDROM "**Volume 1 Issue 4, VLDB '75-'88**" and ...
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## Printed Edition

Peter M. Stocker, William Kent, Peter Hammersley (Eds.):
VLDB'87, Proceedings of 13th International Conference on Very Large Data Bases, September 1-4, 1987, Brighton, England.
Morgan Kaufmann 1987, ISBN 0-934613-46-X

Contents

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Copyright © Tue Mar 16 02:21:59 2010
by Michael Ley (ley@uni-trier.de)