<p>Excellent question. I recommend you read the following book carefully. They describe how to solve this and a lot of other problems of this kind. In any case, this question is not appropriate for this forum.</p>

<p>Computational Geometry: Algorithms and Applications,
Mark de Berg, Otfried Cheong, Marc van Kreveld, Mark Overmars.</p>

CC BY-SA 3.0
2012-04-08T20:30:30.803Z
2012-04-08T20:30:30.803Z
Sariel Har-Peled
<p>I am looking for a algorithm or an idea for a algorithm for triangulation a polygon with holes (one outer polygon P containing several polygonal holes) via plane sweep. </p>

<p>The diagonals should partition the interior of P outside each hole. Express the complexity as a function of the total number of vertices n.</p>

<p>I will appreciate any ideas.
Thanks!</p>

CC BY-SA 3.0
2012-04-08T21:22:44.117Z
Welcome to cstheory, a Q&A site for *research-level* questions in *theoretical computer science* (TCS). Your question does not appear to be a research-level question in TCS. Please see the [FAQ] for more information on what is meant by this and suggestions for sites that might welcome your question. Finally, if your question is closed for being out of scope, and you believe you can edit the question to make it a research-level question, please feel free to do so. Closing is not permanent and questions can be reopened, check the [FAQ] for more information.
Kaveh
CC BY-SA 3.0
2012-04-08T21:23:04.850Z
You may want to check [cs.se].
Kaveh
CC BY-SA 3.0
2012-04-08T22:58:57.580Z
Given that comp-geom is usually a grad-level topic, I'm not sure this is totally out of scope for this site. It's definitely more advanced than cs.SE
Suresh Venkat
CC BY-SA 3.0
2012-04-09T07:49:30.807Z
I know very little about computational geometry, so this question is interesting to me. On the other hand, the line "express the complexity as a function of the total number of vertices n" makes it sound like a homework question.
Huck Bennett
<ds.algorithms><polygon>
Sweeping a Polygon With Holes
com
# Sweeping a Polygon With Holes

(Asked by: username_0 on 2012-04-08)

I am looking for a algorithm or an idea for a algorithm for triangulation a polygon with holes (one outer polygon P containing several polygonal holes) via plane sweep.

The diagonals should partition the interior of P outside each hole. Express the username_0plexity as a function of the total number of vertices n.

I will appreciate any ideas.
Thanks!

**Tags:** ds.algorithms, polygon

> **Comments:**
> **username_1**: Welusername_0e to cstheory, a Q&A site for *research-level* questions in *theoretical username_0puter science* (TCS). Your question does not appear to be a research-level question in TCS. Please see the [FAQ] for more information on what is meant by this and suggestions for sites that might welusername_0e your question. Finally, if your question is closed for being out of scope, and you believe you can edit the question to make it a research-level question, please feel free to do so. Closing is not permanent and questions can be reopened, check the [FAQ] for more information.  
> **username_1**: You may want to check [cs.se].  
> **username_2**: Given that username_0p-geom is usually a grad-level topic, I'm not sure this is totally out of scope for this site. It's definitely more advanced than cs.SE  
> **username_3**: I know very little about username_0putational geometry, so this question is interesting to me. On the other hand, the line "express the username_0plexity as a function of the total number of vertices n" makes it sound like a homework question.  

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## 1 answers

### Answer by username_4 on 2012-04-08. Score: 6

Excellent question. I reusername_0mend you read the following book carefully. They describe how to solve this and a lot of other problems of this kind. In any case, this question is not appropriate for this forum.

Computational Geometry: Algorithms and Applications,
Mark de Berg, Otfried Cheong, Marc van Kreveld, Mark Overmars.


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