Re: determining boundary of a region in n-dimensional euclidean space
- To: mathgroup at smc.vnet.net
- Subject: [mg117183] Re: determining boundary of a region in n-dimensional euclidean space
- From: Nabeel Butt <nabeel.butt at gmail.com>
- Date: Thu, 10 Mar 2011 16:03:39 -0500 (EST)
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
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.
>> Thanks in advance !
>> I have uploaded the file on web and the link is :
>> http://www.megaupload.com/?d=EYOAPU9Q
>> 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
>
>
--
"We have not succeeded in answering all our problems.The answers we have
found only serve to raise a whole set of new questions.In some ways we feel
that we are as confused as ever,but we believe we are confused on a higher
level and about more important things."
"Maybe one day we get to see all the beauty present in this world"
Nabeel Butt
UWO,London
Ontario, Canada
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