On the Realizable Weaving Patterns of Polynomial Curves in \(\mathbb R^3\)

  • Saugata Basu
  • Raghavan Dhandapani
  • Richard Pollack
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)

Abstract

We prove that the number of distinct weaving patterns produced by n semi-algebraic curves in ℝ3 defined coordinate-wise by polynomials of degrees bounded by some constant d, is bounded by 2O(nlogn), where the implied constant in the exponent depends on d. This generalizes a similar bound obtained by Pach, Pollack and Welzl [3] for the case when d=1.

References

  1. 1.
    Alon, N., Pach, J., Pinchasi, R., Radoicic, R., Sharir, M.: Crossing Patterns of Semi-algebraic Sets; PreprintGoogle Scholar
  2. 2.
    Basu, S., Pollack, R., Roy, M.-F.: Algorithms in Real Algebraic Geometry. Springer, Heidelberg (2003)MATHGoogle Scholar
  3. 3.
    Pach, J., Pollack, R., Welzl, E.: Weaving Patterns of Lines and Line Segments in Space. Algorithmica, 9, 561–571 (1993)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Saugata Basu
    • 1
  • Raghavan Dhandapani
    • 2
  • Richard Pollack
    • 2
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Courant Institute of Mathematical SciencesNYUNew YorkUSA

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