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DELAUNAY TRIANGULATIONS IN THE PLANE WITH${\mathcal O} (\sqrt{N} \log N)$STORAGE REQUIREMENTS

Author

Listed:
  • A. KARTASHOV

    (Institute for Theoretical Physics, University of Linz, Altenberger Str. 69, A-4040 Linz, Austria)

  • R. FOLK

    (Institute for Theoretical Physics, University of Linz, Altenberger Str. 69, A-4040 Linz, Austria)

Abstract

We present a straightforward iterative algorithm constructing the planar Delaunay triangulation in${\mathcal O} (\sqrt{N} \log N)$time. The algorithm proceeds iteratively by adding new points one by one to a partial point set pre-ordered by one coordinate and adjusting the partial diagram correspondingly. We introduce the techniques ofsafe fragments, showing that the larger part of a partial digram cannot be changed by adding further points; in the average case of a random point set the amount of information which need be stored in memory at any moment does not exceed${\mathcal O} (\sqrt{N} \log N)$. The computational overhead for the memory management is linear inN. In particular, this makes very large Delaunay triangulations (and Voronoi tessellations) accessible for simulations on personal computers.

Suggested Citation

  • A. Kartashov & R. Folk, 1995. "DELAUNAY TRIANGULATIONS IN THE PLANE WITH${\mathcal O} (\sqrt{N} \log N)$STORAGE REQUIREMENTS," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 6(05), pages 639-649.
    • Handle: RePEc:wsi:ijmpcx:v:06:y:1995:i:05:n:s012918319500054x
    DOI: 10.1142/S012918319500054X
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