<p>See chapter 18 here <a href="http://goo.gl/pLiEO" rel="nofollow">http://goo.gl/pLiEO</a>. If the dimension is really high then bounding box is the wrong creature to work with. A better choice is the ellipsoid. See chapter 16 about John's ellipsoid - it can be computed efficiently using quadratic programming in some cases.</p>

CC BY-SA 3.0
2011-11-04T15:06:46.127Z
A minor point: I first viewed your answer on my phone, and I try not to download pdf's, etc., on my phone, so I didn't click your link because I wasn't sure what it would do.  (Nothing malicious, I know, just my own quirk here.)  Anyway, if you would consider adding a few words of explanation about your links, especially if they are short links, I'd appreciate it.
Aaron Sterling
CC BY-SA 3.0
2011-11-04T05:10:37.970Z
2011-11-04T05:10:37.970Z
Sariel Har-Peled
<p>I need to develop an algorithm to define the minimum bounding box on an N-dimensional space.</p>

<p><a href="http://en.wikipedia.org/wiki/Minimum_bounding_box" rel="nofollow">http://en.wikipedia.org/wiki/Minimum_bounding_box</a></p>

<p>Every reference to this problem that I'm able to find is related to computer graphics (so, only 2 or 3 dimensions). Where can I find some references on the generalised version of this problem?</p>

CC BY-SA 3.0
2011-11-03T16:44:02.643Z
If the bounds of the "box" are axis aligned, just use min and max values for each dimension. Or are you looking for arbitrarily aligned minimum bounding boxes?
Ants
CC BY-SA 3.0
2011-11-04T02:36:34.853Z
Also, do you want an exact or approximate answer ?
Suresh Venkat
<cg.comp-geom>
Minimum BoundingBox on n-dimensional case
Thiago Moraes
# Minimum BoundingBox on n-dimensional case

(Asked by: username_0 on 2011-11-03)

I need to develop an algorithm to define the minimum bounding box on an N-dimensional space.

<http://en.wikipedia.org/wiki/Minimum_bounding_box>

Every reference to this problem that I'm able to find is related to computer graphics (so, only 2 or 3 dimensions). Where can I find some references on the generalised version of this problem?

**Tags:** cg.comp-geom
> **Comments:**
> **username_1**: If the bounds of the "box" are axis aligned, just use min and max values for each dimension. Or are you looking for arbitrarily aligned minimum bounding boxes?  
> **username_2**: Also, do you want an exact or approximate answer ?  

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## 1 answers

### Answer by username_3 on 2011-11-04. Score: 8

See chapter 18 here <http://goo.gl/pLiEO>. If the dimension is really high then bounding box is the wrong creature to work with. A better choice is the ellipsoid. See chapter 16 about John's ellipsoid - it can be computed efficiently using quadratic programming in some cases.

> **Comments:**
> **username_4**: A minor point: I first viewed your answer on my phone, and I try not to download pdf's, etc., on my phone, so I didn't click your link because I wasn't sure what it would do.  (Nothing malicious, I know, just my own quirk here.)  Anyway, if you would consider adding a few words of explanation about your links, especially if they are short links, I'd appreciate it.  

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