Find points within a certain distance of a point

I have a 100 by 2 matrix of 100 x and y coordinates. For each x, y- coordinates I want to compute distance from every other x, y-coordinate within the matrix and create a 2-D array with the points that are within a distance of 100 from each point. Any help? Thank you in advance!! This is what I have so far, the result is the distance from just the first set of points. I want to loop through each of the points.

A= [40.8504  171.3564
  587.0150  277.7693
  534.6382  201.7993
  126.7681  271.1941
  568.2468  511.1568
  239.4433  273.8657
  356.6801  596.7002
  502.6793  249.0090
  417.0619  137.1853
   72.5468  584.0626
  213.3594  217.7381
  304.1814  500.0268
  343.7102  310.6837
  487.7260  131.2077
   31.6978  458.0418
  244.3493  346.3767
   70.9269  445.2531
  417.1997  341.9932
  146.6901  530.5202
   35.8071  190.4143
  592.4875  275.6106
  183.8519  296.2981
  267.6878  371.1306
  494.7850  153.3958
  439.6924   48.7718
  367.2361  189.6672
  286.4973  266.1874
  337.3543  100.3856
  369.7438  576.1130
  133.3710  248.8937
  427.1103  564.4894
  177.1575  367.4444
  413.4330  335.9265
  176.4288  331.0766
  170.1338  490.0941
  549.3505   30.8605
  510.4268   45.3470
  432.7743  499.5853
  415.8379  246.3115
   16.7261  441.5396
   52.1727    9.6495
  180.4457   92.3413
  205.7786  489.2302
  525.2715  477.1678
  153.2615  595.6637
   77.1528  218.9533
   89.2199  170.4176
  207.7396  255.6136
  510.8726  442.3980
   45.6925  169.6155
  425.2625  157.6051
  493.0561  385.6737
  288.9014  283.9012
  520.7237  308.7363
   82.5716   38.1560
  181.9178  364.0340
  147.4173  492.0537
   54.6747   60.4496
  131.1049  599.3833
  217.6165  202.4072
  422.8320   12.2127
  595.2158  425.1874
  434.7470  217.9533
  575.9956  317.3215
  363.2477  381.2383
  451.9813  549.5836
  211.6979  134.7063
  498.0325  258.4985
  215.7108  339.1568
  167.4092  542.0809
   39.9130  272.1907
  197.9183  436.0215
  571.8909  300.4348
  277.1690  571.4164
  294.3354  262.1698
  288.4176  450.6247
  328.1266  480.3169
   23.2771  514.6075
  323.5743  188.7017
  193.8247   61.1335
  290.8283  421.8025
   62.0086   86.4285
  582.8345   43.5660
  174.8900  539.8010
  237.2108  578.1350
  164.1080  549.2339
  449.9186  192.6590
  148.5850  343.0218
  135.7795  465.0395
  475.8121   16.6119
  502.5542  168.8421
  416.1112  267.7820
  533.3713  252.3326
  448.7790   77.0000
  319.4817  436.2359
  497.7837  307.7780
  170.1447  530.0457
  510.7536  432.1919
  369.4765  234.9124
  535.5857  338.3505]
B=A
i=1:100
A(i,1)
A(i,2)
B(1,:); 
B(2,:); 
distances = sqrt(( (A(i,1 )- B(1,:)).^2 + (A(i,2) - B(2,:)).^2 )) ;

Answer 1

[Image Analyst]

You can use pdist2() in the stats toolbox to compute the distance of every point to every other point.

distances = pdist2(A, A);

Find which points are within 100 of each other

closePoints = distances < 100;

closePoints is a 100 by 100 array saying whether each point is close to any other point. So, for example, considering points 3 and 5, if point 3 and point 5 are within 100 of each other, then the (3,5) location of closePoints will be true. If they are farther away, then it will be false. Same for any other location in the array. So you know just by looking at the closePoints array, which points are close or not close to each other.

[puttogether]

Thank you, This is what I was looking for

Answer 2

[Roger Stafford]

You can do this:

n = size(A,1);
[I,J] = meshgrid(1:n);
I = I(:); J = J(:);
D = reshape(sqrt((A(I,1)-A(J,1)).^2+(A(I,2)-A(J,2)).^2),n,n);

D will be an n-by-n matrix in which the i-th row and j-th column will be the distance between points A(i,:) and A(j,:).

I'm not sure just what you meant by "points that are within a distance of 100 from each point." It would either be

T1 = D<=100;

where T1 is an n-by-n matrix of true values for all i,j pairs of points that are no more distant than 100, or

T2 = all(D<=100,2);

where T2 is a column vector which is true for all points in A each of which is simultaneously no greater distance than 100 from all other points.

[puttogether]

Thank you all. Appreciate all the assist. Both approaches worked!

Answer 3

[Walter Roberson]

If you have the Statistics toolbox, use rangesearch()