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MathGroup Archive 2005

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Re: Distance from point to set

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55324] Re: [mg55273] Distance from point to set
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sat, 19 Mar 2005 04:45:32 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Piotr,

pointset = Table[{Random[Real, {-1, 1}], Random[Real, {-1, 1}]}, {15}]

{{0.5305433510989825, -0.9835285661296697}, 
  {0.5149981888311421, 0.07030452237485907}, 
  {-0.5548609965862412, -0.6706534564593198}, 
  {0.4558425442584053, -0.12739148149428103}, 
  {-0.9655103281065733, -0.05179566007389713}, 
  {0.4904660178309532, 0.8356363263603159}, 
  {0.16628343930149758, -0.042530943920831454}, 
  {0.3659938304114865, 0.8630592267325137}, 
  {0.5645610817860498, 0.628260167352799}, 
  {0.8354119739988664, 0.47802415636698714}, 
  {0.3895290445491575, -0.6189409509144874}, 
  {0.6809555054832066, -0.4166538650333329}, 
  {0.858985693450175, -0.6354123847848178}, 
  {-0.8340426833479355, 0.513041612591808}, 
  {0.41384669003641616, -0.9647589283254978}}

distance[set_][point_] := 
  Min[(Sqrt[Plus @@ ((point - #1)^2)] & ) /@ set]

distance[pointset][{2, 2}]
1.90642

For a 3D case...

pointset3d = 
  Table[{Random[Real, {-1, 1}], Random[Real, {-1, 1}], 
      Random[Real, {-1, 1}]}, {5}]
{{-0.3514875029445578, -0.4986924916835682, 
   -0.981757049847647}, {0.46371338462627243, 
   0.25898345250628485, -0.8797515407690808}, 
  {-0.6627125553308537, -0.11963275034039467, 
   0.3999977590561097}, {0.7556608440157371, 
   -0.8286698719829182, 0.3673256370677973}, 
  {0.9861510690196937, 0.7204197723412349, 
   0.46121535562342286}}

distance[pointset3d][{2, 2, 1}]
1.71916

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 


From: Piotr Kowalski [mailto:pkowalsk at ibspan.waw.pl]
To: mathgroup at smc.vnet.net


Hello,

I would like to compute distance d(x,A) from a point 'x' to a set 'A',
(all in R^n, where n=2 or n=3) that is:

   d(x,A) = min ||x - a|| (forall a in A)
   where: n=2 or n=3,
          x is point in R^n, A is subset of R^n
          ||  || is norm (euclidean, max, etc).

Can I find Mathematica function or package for such problem ?

Thank you in advance,
P. Kowalski





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