In principle this is possible with spread sheet software (Excel, Calc, ...) but this will be cumbersome, especially for larger data sets.

There are a number of freely available programming languages that allow you to calculated the distance matrices and search for the smallest distance. Examples are Turbo Delphi, Turbo Pascal, C++, Visual Basic, Fortran, COBOL, ... (to my opinion, C languages are slightly more difficult to learn; Pascal & Basic will allow a very easy introduction and solution for a non-programmer).

Another option for a free software is R (http://www.r-project.org). In contrast to the above mentioned programming languages, in R you can state your problem in a more mathematica/statistical way and it's quite easy to visualize the data and the results. There are ready functions available for the calculation of distance matrices.

You are giving to few information on your data set. Can you publish a small part of it?

Do you need to extract data point values or do you already have them?

Then we can suggest soft, or even code.

Best

Thanks for the answers so far - here a selection of 10 values from 2 groups.

Basically, I'll have to calculate the distance between the closest points (once they are in the correct order). So far I sorted them by the first value, which influences those calculations the most. However, those might not be the closest pair of points in 3D...

Group 1:

99.16 -0.44 0.34

95.32 -0.63 0.87

92.55 -0.47 0.42

90.21 0.01 1.17

89.01 -1.97 -1.72

87.43 0.17 1.83

86.17 -1.99 -1.70

84.58 0.16 1.87

82.88 -2.36 -1.79

81.45 0.67 1.54

78.92 0.66 1.58

Group 2:

89.48 -0.34 3.27

82.82 0.33 1.40

78.79 0.14 0.83

74.68 1.19 2.41

73.26 -1.08 -5.30

69.64 0.72 -2.92

66.70 3.76 2.31

64.84 -0.09 -7.93

61.49 3.07 -2.65

58.28 0.13 -12.20

58.20 6.53 3.48

Do you want to have (a) the minimum distance between any of these points or (b) between points within each group or (c) between points of different groups?

In General, a (Eukledian) distance between two points P1=(x[1]|y[1]|z[1]) and P2 = (x[2]|y[2]|z[2]) is calculated as

d = sqrt( (x[1]-x[2])² + (y[1]-y[2])² + (z[1]-z[2])² )

(a three-dimensional extension of Pythagoras' theorem)

For (a) you need to calculate all pair-wise distances between all points and find the smallest number. For (b) you do this on the data for each group separately. For (c) the simplest (brut-force) solution is to do the same as for a (all pair-wise), then ignore all distances between points of the same group and select the smallest of the remaining values.

I wanted to add something...

The results can be visualized for instance in a dendrogram, see attachment for the data you provided. "a" means "Group 1" and "b" means "Group 2". The minimum distance is between the points #11 in Group 1 ("a 11") and Point #3 in Group 2 ("b 3"). The minimum distance between points within Group 1 is #2/#3, within Group 2 it is #5/#6.

I told you Michael it will be easier ;)

Jochen made a nice explanation! Well done the three-dimensional extension of Pythagoras' theorem :)

Great stuff. Thanks a lot!

What I want is option (C) between points of different groups - and sort the results by distance. I did calculate the Eukledian distance using Excel (I know it's not a math/stats program, but that's where the data is currently stored) - and it takes a long time, especially with a bigger amount of data (24 points for each group, ~20groups to be compared with each other).

That's why I wondered if there is any software that does it more automated - so you import the data sets & it compares/sorts it automatically. R or Matlab would be an option I'd have available in my office, but I haven't really worked too much with it.

On my i5-760 with 2.8GHz and 8GB RAM the calculation of a distance matrix of 24x20 points with R takes about 2.4 ms.

Given you have the data in a plain text file with 4 columns, separated by spaces, like

A.1 3.45 17.13 12.36

A.2 34.92 6.32 0.66

...

A.24 19.45 23.22 4.86

B.1 34.65 17.78 3.24

...

T.24 45.12 15.43 7.32

The first column is the group label (A, B, C...) connected vie a dot (or underscore or anything else except a space) to the point number within the group (1, 2, 3 ...). The other three columns are the x, y, and z coordinates.

The following R code will give you all minimum point distances between the groups:

Pts = read.delim("Volume:\\path to the file\\filename", header=FALSE, row.names=1, sep=" ")

d = as.matrix(dist(Pts))

for (g1 in 1:19) {

grp1 = grep(LETTERS[g1],colnames(d))

for (g2 in (g1+1):20) {

grp2 = grep(LETTERS[g2],colnames(d))

sub.d = d[grp1, grp2]

idx = which.min(sub.d)

mod = idx %/% nrow(sub.d)

ir = mod+1

ic = idx - (mod*nrow(sub.d))

print(sub.d[ic,ir,drop=FALSE])

}

}

The first line reads the data into a variable. The second line calculated the distance matrix. The for-loops defines a subset of the matrix with a given group in the rows and another group in the column. From this subset the minimum is determined and the position in terms of row and column in the subset matrix is calculated. Finally, the found item is printed along with its row name and column name.

Takes about 40ms to get all results on my computer...

The code is quick-and-dirty; it can be optimized and made more flexible but this is not required here (since it solves your problem). The code assumes than there are exactly 20 groups. If you have a different number of groups you need to change the values 20 and 19 in the loops accordingly.

Hope this helps.

Hi Michael,

You may also try Grapheur (grapheur.com) or LiONSolver (lionsolver.com) (if you need not to see/calculate distances but to examine your data structure more deeply). They are not very free, but you may download a fully functional demo which runs for 30 days.

Actually, why limit yourself into 3D space, if you can use nD space? That your look at the data might be very different...

Of course, if you only need the Eucledean distance only... But there are also other distances (Mahalonbis, etc., depending whether the data are projected on sphere, torus, or any other map).

Here is a short Mathematica program that finds the nearest neighbor to a specified point p for a 3-D data set (200 points) and a plot of the data

mat =Array[RandomReal[ {0, 4}] & , {200, 3}] ;

p={2,1,3};

data=Flatten[{Blue,PointSize[0.02],Map[Point,mat]}];

testPoint={Red,PointSize[0.02],Point[p]};

nearestneighbor=Extract[mat,Ordering[Total[(Transpose[mat]-p)^2],1]];

Show[Graphics3D[{testPoint,{Green,PointSize[0.02],Point[nearestneighbor]},data}]]

In[18]:= nearestneighbor

Out[18]= {1.50291,1.01451,2.75676}

The plot of the data showing p (red dot) is shown below

Here is the plot

HI,

If your reference point has coordinates (x0,y0,z0)

The next step is to calculate the distance from every point (x,y,z) to your reference point:

d=sqrt( (x-x0)**2 +(y-y0)**2 + (z-z0)**2) )

the minimum distance is the closest point to your reference point.

I suppose that you have knowledge of programming such as Fortran or C++. I use Fortran if you wish. On the other hand, I found this on the web related to array using language R, it's for 2D but easy to extrapolate in 3D:

http://stackoverflow.com/questions/3083841/how-do-i-perform-array-indexing-in-r-language

If my understanding of your question correct, you want sort your data. Unlike the R space, The relationship between point in the the R^3 space is not larger or smaller. You only can get the distance from a particular point (eg the origin of coordinates) as a measure of the size for sorting (regardless of sign).