On the realizable weaving patterns of polynomial curves in R3

Authors:
Saugata Basu;Raghavan Dhandapani;Richard Pollack
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA;Courant Institute of Mathematical Sciences, NYU, New York, NY;Courant Institute of Mathematical Sciences, NYU, New York, NY
Venue:
GD'04 Proceedings of the 12th international conference on Graph Drawing
Year:
2004

Citing 1
Cited 1

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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.