On the realizable weaving patterns of polynomial curves in ℝ3

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 2 O(n log n), where the implied constant in the exponent depends on d. This generalizes a similar bound obtained by Pach, Pollack and Welzl for the case when d = 1. © Springer-Verlag Berlin Heidelberg 2004.