Reporting all intersection points, generalized segments: Difference between revisions
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Line segment intersection - Reporting all intersection points, generalized segments - Time.png|1000px]] | [[File:Line segment intersection - Reporting all intersection points, generalized segments - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Line segment intersection - Reporting all intersection points, generalized segments - Space.png|1000px]] | [[File:Line segment intersection - Reporting all intersection points, generalized segments - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Line segment intersection - Reporting all intersection points, generalized segments - Pareto Frontier.png|1000px]] | [[File:Line segment intersection - Reporting all intersection points, generalized segments - Pareto Frontier.png|1000px]] | ||
Revision as of 14:04, 15 February 2023
Description
In this case, the segments are generalized (i.e. have algebraic degree ≥1); we still wish to report all points of intersection.
Related Problems
Subproblem: Reporting all intersection points, line segments
Related: Reporting all intersection points, convex polygons, Reporting all intersection points, general polygons, Counting number of intersection points, line segments
Parameters
n: number of line segments
k: number of points of intersection
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Jean-Daniel Boissonnat and Franco P. Preparata. | 1997 | $O( n log n + k log n)$ | $O(n)$ | Exact | Deterministic | Time & Space |
| Balaban. | 1995 | $O( nlog n + k )$ | $O(n)$ | Exact | Deterministic | Time & Space |
| Boissonnat; Snoeyink | 1999 | $O( nlog n + k )$ | $O(n)$ | Exact | Deterministic | Time & Space |
Time Complexity Graph
Space Complexity Graph
Pareto Frontier Improvements Graph
References/Citation
https://dl-acm-org.ezproxy.canberra.edu.au/citation.cfm?id=304991
https://dl-acm-org.ezproxy.canberra.edu.au/doi/10.1145/304893.304991)