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MathGroup Archive 2005

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Re: Problems with ExtendGraphics/Delaunay Triangulation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53578] Re: Problems with ExtendGraphics/Delaunay Triangulation
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 19 Jan 2005 01:59:27 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <csioin$nnr$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

a Delauny triangulation has to calculate the areas of the triangles
and if the points are colinear than the area is zero, but on a
computer zero is almost never zero, it is something like 0.1*10^-12
and that is the problem with all Delauny triangulations in machine 
precision.

Mathematica, with its high precision arithmentic should do the
Delauny triangulation in its kernel and all the problems with the
fixed machine precision will dissapear.

Regards
  Jens

<jrome at mail.com> schrieb im Newsbeitrag news:csioin$nnr$1 at smc.vnet.net...
> Hi,
>
> I've been having a problem with the Delaunay Triangulation command,
> "Delaunay" in a Mathematica notebook I am using. The problem is, the
> program seems to lock up for certain data sets. Specifically, I have a
> 2D array of about 3000 nodes that locks it up. I did some experiments,
> and found that it worked fine for the first 1550 nodes, but not the
> first 1575 nodes. Upon looking at the data set, I noticed that 4 nodes
> in that range (between 1500 & 1575) were consecutively numbered and in
> a straight line. When I altered this values by less than 1%, the
> Delaunay triangulation worked fine.
>
> So, I decided to go back to my code (as I was writing this question, as
> a matter of fact!), and added a small random number to every value in
> my matrix. This is not an ideal solution, but it seems to work for now.
> I'd still like to figure out what the problem with the Delaunay
> triangulation is, and find out if there are better solutions to my
> problem. Thank you very much. You've already been a big help!
> 



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