Reporting all intersection points, generalized segments: Difference between revisions
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== Parameters == | == Parameters == | ||
n: number of line segments | $n$: number of line segments | ||
k: number of points of intersection | $k$: number of points of intersection | ||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Jean-Daniel Boissonnat and Franco P. Preparata. (Reporting all intersection points, generalized segments Line segment intersection)|Jean-Daniel Boissonnat and Franco P. Preparata. ]] || 1997 || $O( n log n + k log n)$ || $O(n)$ || Exact || Deterministic || [https://epubs-siam-org.ezproxy.canberra.edu.au/doi/abs/10.1137/S0097539797329373 Time] & [https://epubs-siam-org.ezproxy.canberra.edu.au/doi/epdf/10.1137/S0097539797329373 Space] | | [[Jean-Daniel Boissonnat and Franco P. Preparata. (Reporting all intersection points, generalized segments Line segment intersection)|Jean-Daniel Boissonnat and Franco P. Preparata. ]] || 1997 || $O(n \log n + k \log n)$ || $O(n)$ || Exact || Deterministic || [https://epubs-siam-org.ezproxy.canberra.edu.au/doi/abs/10.1137/S0097539797329373 Time] & [https://epubs-siam-org.ezproxy.canberra.edu.au/doi/epdf/10.1137/S0097539797329373 Space] | ||
|- | |- | ||
| [[Balaban. (Reporting all intersection points, generalized segments Line segment intersection)|Balaban.]] || 1995 || $O( | | [[Balaban. (Reporting all intersection points, generalized segments Line segment intersection)|Balaban.]] || 1995 || $O(n \log n + k )$ || $O(n)$ || Exact || Deterministic || [https://dl-acm-org.ezproxy.canberra.edu.au/doi/pdf/10.1145/220279.220302 Time & Space] | ||
|- | |- | ||
| [[Boissonnat; Snoeyink (Reporting all intersection points, generalized segments Line segment intersection)|Boissonnat; Snoeyink]] || 1999 || $O( | | [[Boissonnat; Snoeyink (Reporting all intersection points, generalized segments Line segment intersection)|Boissonnat; Snoeyink]] || 1999 || $O(n \log n + k )$ || $O(n)$ || Exact || Deterministic || [https://dl-acm-org.ezproxy.canberra.edu.au/citation.cfm?id=304991 Time & Space] | ||
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[[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]] | ||
== References/Citation == | == References/Citation == | ||
Latest revision as of 09:05, 28 April 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 | $O(n \log n + k )$ | $O(n)$ | Exact | Deterministic | Time & Space |
| Boissonnat; Snoeyink | 1999 | $O(n \log n + k )$ | $O(n)$ | Exact | Deterministic | Time & Space |
Time Complexity Graph
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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)