Algorithm to partition an area - find points close to each other

Question

Is there an algorithm to find all points with a set distance from each other ? Or all rectangles that are touching ?

I divide the plane (in lat/lon coordinate system, of certain limits) in sample rectangles of n x n, and each rectangle gets a value from 0 to 7. I need to be able to show islands for each value. n > 100 - could be 15000.

I have written some very brute-force code, but I only managed to get some very rough rectangles...

Example of my input:

111111111111111122222111
111221122222111122211111
111222222222111112211111
111222222111111112211111
111221111113311112111111
111111111113311111111111

The above, defined using points in a rectangle (each 1 and 2 and others being rectangles that I acquire through some sampling...) - I end up having a few thousands - possibly a hundred thousands little rectangles, and I would like to get the regions of each kind.

I have discovered that I can get the regions, using a convex hull algorithm - if I can properly separate the rectangles (or their center points) into regions.

At the input to my function, I would get only rectangles with the same metric.

Example:

1111111111111111     111
111  11     1111   11111
111         11111  11111
111      11111111  11111
111  111111  1111 111111
11111111111  11111111111


                22222
   22  22222    222
   222222222     22
   222222        22
   22            2

I would like to find some algorithm so I can get the rectangles that are touching, or the points that are at a certain distance from each other, in separate sets (they have absolute coordinates), so I can run the convex hull algorithm on the resultant sets.

Since the rectangles are created from sampling, they are identical in width/height.

Is there such a thing ?

My code is in VB.NET, but C#, or any language or pseudocode would help.

Thank you very much.

Edit:

I have all kinds of tests, like

Public Function AreTwoRectanglesNearEachOther(ByRef one As RectangleF, ByRef two As RectangleF) As Integer
        If Math.Abs(one.Right - two.Left) <= distance_lat Then
            Return 1    ' one is before two
        ElseIf Math.Abs(two.Right - one.Left) <= distance_lat Then
            Return -1   ' one is after two
        ElseIf Math.Abs(two.Top - one.Bottom) <= distance_lon AndAlso one.Right - two.Left > 0 Then
            Return 2    ' one is above two
        ElseIf Math.Abs(one.Top - two.Bottom) <= distance_lon AndAlso one.Right - two.Left > 0 Then
            Return -2   ' one is below two
        Else
            Return 0    ' they are not next to each other
        End If
    End Function

where distance_lat and distance_lon is dim_lat/10, respectively dim_lon/10

http://stackoverflow.com/questions/3895204/find-edge-that-a-rectangle-is-touching-on-another-rectangle maybe this will help? or maybe this http://stackoverflow.com/questions/13670167/how-to-find-intersection-rectanglepoints-of-instersecting-rectangles?rq=1 — Gilad, Jan 26 '13 at 02:41
Step back for a moment and educate me on how this is not simply a connected component labeling, please ? — mmgp, Jan 26 '13 at 02:43
I need to find groups of rectangles or points, out of a hundred thousands or a few hundred thousands. Every idea I came with had 5 layers of loops within loops, and it seemed to be and least O(n factorial squared) or more — Thalia, Jan 26 '13 at 02:53
@Mihaela but the example output you give is just the result of a connected component labeling. So you don't want that, but something else ? (Nice running time you got there :)) — mmgp, Jan 26 '13 at 02:59
@mngp this is exactly what I need, the word "labeling" confused me. Thanks to you, I found some links now, that I can experiment with tomorrow - compared to my approach, the example I was looking at has the idea of setting children of labels already found, so that he will not have to go back repeatedly to check every group that has been already allocated. So smart ! — Thalia, Jan 26 '13 at 07:17

score 0 · Accepted Answer · answered Mar 28 '13 at 16:35

0

Thank you mmgp - I did implement the connected component labeling algorithm - it was a wonderful idea.

answered Mar 28 '13 at 16:35

Thalia

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Algorithm to partition an area - find points close to each other

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