Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
Theoretical Computer Science
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
On the zone of a surface in a hyperplane arrangement
Discrete & Computational Geometry
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Fast Detection of Polyhedral Intersections
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Almost Tight Upper Bounds for Vertical Decompositions in Four Dimensions
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Counting and representing intersections among triangles in three dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Hi-index | 0.00 |
We introduce (1/r)-cuttings for collections of surfaces in 3-space that are sensitive to an additional collection of curves. Specifically, let S be a set of n surfaces in R 3 of constant description complexity, and let C be a set of m curves in R 3 of constant description complexity. Let 1= r = min{ m,n } be a given parameter. We show the existence of a (1/ r )-cutting ? of S of size O ( r 3+e ), for any e 0 , such that the number of crossings between the curves of C and the cells of ? is O ( m 1+e ). The latter bound improves, by roughly a factor of r , the bound that can be obtained for cuttings based on vertical decompositions.We view curve-sensitive cuttings as a powerful tool that is potentially useful in various scenarios that involve curves and surfaces in three dimensions. As a preliminary application, we use the construction to obtain a bound of O ( m 1/2+e n 2+e ), for any e 0 , on the complexity of the multiple zone of m curves in the arrangement of n surfaces in 3-space