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 > > http://portal.uni-freiburg.de/imteksimulation/downloads/ims > > 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. >>>> 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