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

Abstract

Abstract. We prove that the number of distinct weaving patterns produced by n semi-algebraic curves in R 3 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 [3] for the case when d = 1.

Developing a labelled object-relational constraint database architecture for the projection operator

“…In this work, cylindrical decomposition is used to eliminate variables of a group of polynomial inequality constraints. More details can be found in [1,6,2].…”