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.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Alon, N., Pach, J., Pinchasi, R., Radoicic, R., Sharir, M.: Crossing Patterns of Semi-algebraic Sets; Preprint
Basu, S., Pollack, R., Roy, M.-F.: Algorithms in Real Algebraic Geometry. Springer, Heidelberg (2003)
Pach, J., Pollack, R., Welzl, E.: Weaving Patterns of Lines and Line Segments in Space. Algorithmica, 9, 561–571 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Basu, S., Dhandapani, R., Pollack, R. (2005). On the Realizable Weaving Patterns of Polynomial Curves in \(\mathbb R^3\) . In: Pach, J. (eds) Graph Drawing. GD 2004. Lecture Notes in Computer Science, vol 3383. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31843-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-31843-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24528-5
Online ISBN: 978-3-540-31843-9
eBook Packages: Computer ScienceComputer Science (R0)