Reporting all intersection points, generalized segments: Difference between revisions
Jump to navigation
Jump to search
(Created page with "{{DISPLAYTITLE:Reporting all intersection points, generalized segments (Line segment intersection)}} == 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...") |
No edit summary |
||
| (5 intermediate revisions by the same user not shown) | |||
| Line 12: | Line 12: | ||
== Parameters == | == Parameters == | ||
$n$: number of line segments | |||
k: number of points of intersection | |||
$k$: number of points of intersection | |||
== Table of Algorithms == | == Table of Algorithms == | ||
| Line 23: | Line 24: | ||
|- | |- | ||
| [[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/doi/abs/10.1137/S0097539797329373 Time] & [https://epubs.siam.org/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/doi/abs/10.1137/S0097539797329373 Time] & [https://epubs.siam.org/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/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/citation.cfm?id=304991 Time & Space] | ||
|- | |- | ||
|} | |} | ||
== 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]] | ||
== 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
