Re: determining boundary of a region in n-dimensional euclidean space

• To: mathgroup at smc.vnet.net
• Subject: [mg117231] Re: determining boundary of a region in n-dimensional euclidean space
• From: Nabeel Butt <nabeel.butt at gmail.com>
• Date: Sat, 12 Mar 2011 05:08:51 -0500 (EST)

```Thanks Oliver ! Ill look in to it for sure...Nabeel

On Fri, Mar 11, 2011 at 4:21 AM, Oliver Ruebenkoenig
<ruebenko at wolfram.com>wrote:

> On Thu, 10 Mar 2011, Nabeel Butt wrote:
>
> Hi Daniel
>>     Thanks for your response.Actually the problem is two-fold here.The
>> first step is to actually extract the boundary points from a set of points
>> in a list.I have found that built-in ConvexHull function in mathematica
>> can
>> do for 2-dimensions this extraction process.There exists a program also
>> for
>> 3-dimensions written in mathworld.To my best of my knowledge it hasnt been
>> implemented in higher dimensions that well in mathematica(was just a
>> random
>> google search though !!) . Anyways after we get the list for boundary
>> points , like you said I can use Interpolation on list to represent it
>> numerically.What I am more interested in is actually extracting the
>> boundary
>> points from a set of points -Does there exist more robust convexhull like
>> functions for higher dimensions ? Or after having a list of points I can
>> send them to another software which helps me get the convex hull in high
>> dimensions.Possibly if I can call another software inside mathematica that
>> would be great.
>>      Thanks once again.
>>                                 Nabeel
>>
>
> Nabeel,
>
> in 3D you could use TetGenConvecHull.
>
> For higher dimensions you could use the QHull (up to 9 dimensions if I
> recall correctly) interface I wrote for the IMTEK Mathematica supplement.
> You can find that here
>
>
> Hth,
>
> Oliver
>
>
>
>>
>> On Thu, Mar 10, 2011 at 12:33 PM, Daniel Lichtblau <danl at wolfram.com>
>> wrote:
>>
>> Nabeel Butt wrote:
>>>
>>> Dear Mathematica lovers ,
>>>>               A simple but interesting question which would help me in
>>>> my
>>>> research.I have written mathematica programs which help me define a
>>>> region
>>>> in terms of numerical points in that space.Visualising the boundary if
>>>> the
>>>> region is not difficult since it is just a simple plotting task.I am
>>>> however
>>>> interested in determining a smooth functional equation for the boundary
>>>> of
>>>> the region or even the set of points on boundary.Does there exist
>>>> Mathematica programs or built-in functions that could effectively deal
>>>> with
>>>> this kind of problem.
>>>>       I have uploaded the file on web and the link is :
>>>>                 Nabeel
>>>>
>>>>
>>> Is there some reason not to define it based on interpolation of the
>>> actual
>>> boundary points? This could be done with ListInterpolation.
>>>
>>> Daniel Lichtblau
>>> Wolfram Research
>>>
>>>
>>>
>>
>>
>>

--
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Nabeel Butt
UWO,London