Convex Polygonal Window: Difference between revisions

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== Parameters ==  
== Parameters ==  


n: number of lines
$n$: number of lines


p: number of edges on polygon
$p$: number of edges on polygon


== Table of Algorithms ==  
== Table of Algorithms ==  
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| [[Cyrus–Beck (Convex Polygonal Window; Convex Polyhedral window Line Clipping)|Cyrus–Beck]] || 1978 || $O(np)$ || $O({1})$ auxiliary? || Exact || Deterministic || [https://www.sciencedirect.com/science/article/pii/0097849378900213 Time]
| [[Cyrus–Beck (Convex Polygonal Window; Convex Polyhedral window Line Clipping)|Cyrus–Beck]] || 1978 || $O(np)$ || $O({1})$ || Exact || Deterministic || [https://www.sciencedirect.com/science/article/pii/0097849378900213 Time]
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Revision as of 08:52, 10 April 2023

Description

Line clipping is the process of removing lines or portions of lines outside an area of interest. Typically; any line or part thereof which is outside of the viewing area is removed. Here, the viewing area is a convex polygon.

Related Problems

Generalizations: Convex Polyhedral Window

Subproblem: Rectangular Window

Parameters

$n$: number of lines

$p$: number of edges on polygon

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Cyrus–Beck 1978 $O(np)$ $O({1})$ Exact Deterministic Time

Time Complexity Graph

Line Clipping - Convex Polygonal Window - Time.png

Space Complexity Graph

Line Clipping - Convex Polygonal Window - Space.png

Time-Space Tradeoff

Line Clipping - Convex Polygonal Window - Pareto Frontier.png

References/Citation

https://www.sciencedirect.com/science/article/pii/0097849394900647/pdf?md5=06bd1f11031af17d1fd34626c4e2f49b&pid=1-s2.0-0097849394900647-main.pdf