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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}
}
BibTeX

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

ACM SIGMOD Anthology

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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 BibTeX

References

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BibTeX
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Aristides A. G. Requicha: Representations for Rigid Solids: Theory, Methods, and Systems. ACM Comput. Surv. 12(4): 437-464(1980) BibTeX
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Referenced by

  1. Goetz Graefe: Query Evaluation Techniques for Large Databases. ACM Comput. Surv. 25(2): 73-170(1993)
  2. Oliver Günther, Jeff Bilmes: Tree-Based Access Methods for Spatial Databases: Implementation and Performance Evaluation. IEEE Trans. Knowl. Data Eng. 3(3): 342-356(1991)
  3. H. V. Jagadish: Spatial Search with Polyhedra. ICDE 1990: 311-319
  4. Oliver Günther: The Design of the Cell Tree: An Object-Oriented Index Structure for Geometric Databases. ICDE 1989: 598-605
BibTeX
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