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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