Reporting all intersection points, convex polygons: 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 == | ||
| Line 24: | Line 24: | ||
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| [[NIEVERGELT. J.. AND PREPARATA (Section 3) (Reporting all intersection points, convex polygons Line segment intersection)|NIEVERGELT. J.. AND PREPARATA (Section 3)]] || 1982 || $O( | | [[NIEVERGELT. J.. AND PREPARATA (Section 3) (Reporting all intersection points, convex polygons Line segment intersection)|NIEVERGELT. J.. AND PREPARATA (Section 3)]] || 1982 || $O( n \log n + k )$ || $O(n)$ || Exact || Deterministic || [https://pdfs.semanticscholar.org/a571/cc92218132a1b0e65c2adbf663c79d015737.pdf Time] & [https://courses.cs.duke.edu/cps234/spring04/papers/NP82.pdf Space] | ||
|- | |- | ||
|} | |} | ||
== Time Complexity | == Time Complexity Graph == | ||
[[File:Line segment intersection - Reporting all intersection points, convex polygons - Time.png|1000px]] | [[File:Line segment intersection - Reporting all intersection points, convex polygons - Time.png|1000px]] | ||
== References/Citation == | == References/Citation == | ||
https://pdfs.semanticscholar.org/a571/cc92218132a1b0e65c2adbf663c79d015737.pdf | https://pdfs.semanticscholar.org/a571/cc92218132a1b0e65c2adbf663c79d015737.pdf | ||
Latest revision as of 09:05, 28 April 2023
Description
In this case, we are supplied with a list of convex polygons, and we wish to report all regions of intersection.
Related Problems
Generalizations: Reporting all intersection points, general polygons
Related: Reporting all intersection points, line segments, Reporting all intersection points, generalized segments, 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 |
|---|---|---|---|---|---|---|
| NIEVERGELT. J.. AND PREPARATA (Section 3) | 1982 | $O( n \log n + k )$ | $O(n)$ | Exact | Deterministic | Time & Space |
Time Complexity Graph
References/Citation
https://pdfs.semanticscholar.org/a571/cc92218132a1b0e65c2adbf663c79d015737.pdf