Re: determining boundary of a region in n-dimensional

• To: mathgroup at smc.vnet.net
• Subject: [mg117218] Re: determining boundary of a region in n-dimensional
• From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
• Date: Fri, 11 Mar 2011 04:41:48 -0500 (EST)
• References: <201103102103.QAA11345@smc.vnet.net>

```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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