Point-in-Polygon: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Point-in-Polygon (Point-in-Polygon)}} == Description == With a given polygon $P$ and an arbitrary point $q$, determine whether point $q$ is enclosed by the edges of the polygon. == Parameters == No parameters found. == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference |- | Ray casting algorithm Shimrat; M (Point-in-Polygon...") |
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Point-in-Polygon - Time.png|1000px]] | [[File:Point-in-Polygon - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Point-in-Polygon - Space.png|1000px]] | [[File:Point-in-Polygon - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Point-in-Polygon - Pareto Frontier.png|1000px]] | [[File:Point-in-Polygon - Pareto Frontier.png|1000px]] | ||
Revision as of 14:05, 15 February 2023
Description
With a given polygon $P$ and an arbitrary point $q$, determine whether point $q$ is enclosed by the edges of the polygon.
Parameters
No parameters found.
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Ray casting algorithm Shimrat; M | 1962 | $O(n)$ | $O({1})$ | Exact | Deterministic | Time |
| Nordbeck and Rystedt (Grid Method) | 1967 | $O(a)$ | $O({1})$ | Exact | Deterministic | Time |
| Salomon (Swath Method) | 1978 | $O(nlogn)$ | $O(n^{2})$ | Exact | Deterministic | Time & Space |
| Nordbeck and Rystedt (Sum of area) | 1967 | $O(n)$ | $O({1})$ | Exact | Deterministic | Time |
| Preparata and Shamos (Wedge) | 1985 | $O(n)$ | $O(n)$ | Exact | Deterministic | Time & Space |
| Saalfeld (Sign of offset) | 1987 | $O(n)$ | $O({1})$ | Exact | Deterministic | Time |
| Preparata and Shamos (Intersection sum of angle) | 1985 | $O(n)$ | $O({1})$ | Exact | Deterministic | Time |
| Nordbeck and Rystedt (Orientation) | 1967 | $O(n)$ | $O({1})$ | Exact | Deterministic | Time |
Time Complexity Graph
Space Complexity Graph
Pareto Frontier Improvements Graph
