Separation of datum and decision of their mistake

[Karamel]

Hi,

I have a general problem(not exactly with electronics, computers etc.)

Think like this. I have dots which I know their positions in x-y coordinates. They have numbers. 1-2-3-4.....98-99-100

1-2-11-12 are neighbor
2-3-12-13 are neighbor
11-12-21-22 are neighbor

but 2-3-12-14 there is a problem. 14 isn't neighbor with 2-3 and 12


As I said, I have only X-Y axis and their coordinates. Matlab is very convenient platform to work. Firstly, I will deal with diagonal data like below.



On image, everything is okay. I am trying to find a way and check they are okay or not.

[ataradov]

So what is the problem? To check if given 4 numbers are close on a 10x10 grid? Are they always be sqares?

If so, it appears to be pretty easy in abstract. Pick the lowest number (N). One other number must be N+1. You have established lower base of your square.

The other numbers must be N+10 and N+11.

[Karamel]

You are right but when complexity increases, there are some problems with working only distances.

My datum are never locating like exactly diagonal but if you check them with eyes, they preserve their diagonal shape. For example,

there is no problem.


there is a problem.


or there is a problem.


Now, my program works with calculating their distances and some cases it gives wrong result so, working with distance is not true approach for that problem.

[ataradov]

I don't understand any of your pictures. What I'm supposed to be seeing there?

The problem is someting you formulate. Do so.

If they are not located on the grid, then how are they numbered? Is it always groups of 4? What do you actually want to know?

[xrunner]

You are right but when complexity increases, there are some problems with working only distances. ...

Now, my program works with calculating their distances and some cases it gives wrong result so, working with distance is not true approach for that problem.

I don't understand either. Any given placement of random points on an X-Y grid will yield values you can calculate for each point to any other existing point. Then you have a list of distances for comparison. That's all the information there is to get - XY of each point, the number of points, and distances to other points. I don't know how it can give a "wrong" result.

You seem to be leaving us with a gap in understanding of what you are trying to achieve.

[cncjerry]

if neighbor implies distance, then just compute a circle around each of the points and see if the target points lie within the circle radius (neighbor distance).  Or just compute the vector distance from each point and see if it is less than the neighbor distance.  both solutions imply an x,y grid. 

this sounds like the traveling salesman problem and if I remember correctly, the solution in terms of minimum distance has been found.

Another way to do it is to take the x,y points and load them into just about any drilling optmization program and let it figure it out.

[Karamel]

I don't understand any of your pictures. What I'm supposed to be seeing there?

The problem is someting you formulate. Do so.

If they are not located on the grid, then how are they numbered? Is it always groups of 4? What do you actually want to know?

This is my trap. Every data must be located square, otherwise, I have a problem but, you don't understand that it doesn't must be exact square.

You are right but when complexity increases, there are some problems with working only distances. ...

Now, my program works with calculating their distances and some cases it gives wrong result so, working with distance is not true approach for that problem.

I don't understand either. Any given placement of random points on an X-Y grid will yield values you can calculate for each point to any other existing point. Then you have a list of distances for comparison. That's all the information there is to get - XY of each point, the number of points, and distances to other points. I don't know how it can give a "wrong" result.

You seem to be leaving us with a gap in understanding of what you are trying to achieve.

Distance calculation doesn't give me any folding information. Therefore, it gives wrong result.

[ataradov]

This is my trap. Every data must be located square, otherwise, I have a problem but, you don't understand that it doesn't must be exact square.

How do you number things. You need to mathematically define what "exact square" means in your case.

If you  it is still good enough that you can obviously align things, then it does not matter. If it is not good enough, then it is a totally different task. Any you need to give way more information.

What is the source data that you have.  Can you post actual list of points, and identify a few places you want to pass/fail. Pictures in task like this don't help at all.

[Karamel]

Okay guys,

I have an idea, maybe, I can use voronoi diagram for this problem. Every neighbor must share neighbor area otherwise, there is a problem but how can I implement it?

(This is such a image which shows what voronoi is)

[ataradov]

We don't understand what the problem is. How would we know if this will solve it?

[xrunner]

Okay guys,

I have an idea, maybe, I can use voronoi diagram for this problem.

OK a voronoi diagram ... I didn't study it in my field but OK -

https://en.wikipedia.org/wiki/Voronoi_diagram

It exists and can be generated - but for what reason?

As has been stated - What is the problem you want to solve?

[ataradov]

- Check that you have a group of four to test.
- Sort the group of four in order. (Three compare and swap tests).
- Check that your group of four is X, X+1, X+10 and X+11 (where X is the value of the lowest point?

I already proposed that. But this does not work for non-exact squares, whatever that is.

[Karamel]

Third time, I am writing.

Problem:
- I have 100 sample data. They must be located 10x10 in XY plane but not exactly square.
- Neighborhood must be preserved with every data. Meaning that there shouldn't be any folding.
- Any data shouldn't inside of any other data region.

What do I have:
- Only data coordinates.

What did I try:
- Calculate their distance and decide are they neighbor or not. It doesn't work.

Which idea do I have:
Voronoi.

At below. There are ten datum. They can split with voronoi but, I am not sure, voronoi is good way for me. Maybe it is stupid idea.

[ataradov]

- I have 100 sample data. They must be located 10x10 in XY plane but not exactly square.

What does "not exactly square" mean mathematically? Are they still aligned enough that you can assign them to a 10x10 grid locations?

If the picture is representative of the actual data, then map it to the 10x10 grid and proceed with advice from reply #1.

You are asking us to solve mathematical problem and refuse to supply mathematical definitions for source data.

Can you actually provide one full data set?

[xrunner]

Third time, I am writing.

Problem:
- I have 100 sample data. They must be located 10x10 in XY plane but not exactly square.
- Neighborhood must be preserved with every data. Meaning that there shouldn't be any folding.
- Any data shouldn't inside of any other data region.

So is it the case, that you want to draw a line around each data point, such that each point has an area around it that is the maximum it can have, with respect to every other neighbor at the same time also having it's maximum area, and so on? Is that the problem you want to solve?

[Karamel]

Okay, let's talk mathematically.

Plot these values with Matlab or any other program, you will see any four neighbor is not square, but there is no any folding.
I don't know how can I represent it mathematically? Just imagine.

-

Code: [Select]

2,32694515300473 3,19594853070491
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-1,49697278629696 3,61227250912198
-0,812252816983230 3,82792629280857
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0,390461004711642 3,99667043104063
0,884635482977476 3,89297309863322
1,41862585593114 3,70047870224348
1,94486026951645 3,50023255289683
2,12802722655400 3,46714450605330
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0,463479763231325 3,76685862271947
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1,34596147203459 3,20013782630764
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3,86215834352058 0,831019367099838
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3,50448492247770 -0,316371793207998
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2,63660425944077 -2,60922485106903
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3,70563437043324 -1,55718114930929
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-1,04661509519607 -4,06115243199433
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-0,473749811791085 -3,73474467970858
0,334443810077910 -3,74919758503128
1,09949897620091 -3,67366096540719
1,85682170564657 -3,41166696348707
2,57626860496710 -2,97429585155003
3,15288140241824 -2,48699543909825
3,55848249402213 -2,00876817060237
3,68518627149908 -1,72471305201884

[ataradov]

Is this how your data supposed to look like?

[hamster_nz]

I did plot those points, but could not understand.

I think our issue is we have no clear understanding of the concept of "neighbor".

To me it is "share a common boundary", which works with shapes, but not a list of points.

[Karamel]

Is this how your data supposed to look like?

Yes. Exactly it is.

I did plot those points, but could not understand.

I think our issue is we have no clear understanding of the concept of "neighbor".

To me it is "share a common boundary", which works with shapes, but not a list of points.

Try to give numbers to them on graph. Like this 1-2-3.....98-99-100.

You will see that

1-2-11-12 are neighbor like rectangular. 2-3-12-13 as well.

another example, 78-79-88-89.

Now, I need to prove it with mathematically and finally I need to write its code. This is my job. I am just searching a way to solve this problem.

[ataradov]

Yes. Exactly it is.

Cool, can you now paint some clusters on the picture that would show some examples of good and bad neighbors?

The way I understand the goal right now, there is no single solution.

[hamster_nz]

Are you wanting to select four points, point

• , point[x+10], point[x+11], point[x+1] and testing to see if they form a four-sided polygon, with the points run clockwise around the boundary, with no angles > 180 degrees?

This is much like back-face culling in computer graphics : https://en.wikipedia.org/wiki/Back-face_culling

[Karamel]

Yes. Exactly it is.

Cool, can you now paint some clusters on the picture that would show some examples of good and bad neighbors?

The way I understand the goal right now, there is no single solution.

I think, we don't talk same language. I have given datum. Please give them numbers with starting first one. 1-2-3-4.....100 and show them with numbers on graph. You will see what I am talking about. In this data set, there is no any problem and this is the problem. I need to prove it with mathematically. This is my fourth time that I am writing my problem.

Are you wanting to select four points, point

• , point[x+10], point[x+11], point[x+1] and testing to see if they form a four-sided polygon, with the points run clockwise around the boundary, with no angles > 180 degrees?

This is much like back-face culling in computer graphics : https://en.wikipedia.org/wiki/Back-face_culling

They must be create any polygon but shouldn't be any other point inside any each polygon. (folding)

[ataradov]

I think, we don't talk same language. I have given datum.

You have not given enough information. If you think you have, that's great, but don't expect an answer from us.

Please give them numbers with starting first one. 1-2-3-4.....100 and show them with numbers on graph.

So all points in the array are exactly numbered already, and number corresponds to the index, correct? But now what's the goal?

There are two situations here. One - calculations are done purely on the indexes, for which we have provided a solution. Second one - calculation involve coordinates, but then it is not clear how to mix indexes. You need to fix one or the other. We can ether check that correctly selected square in the index space corresponds to some geometric configuration in the coordinate space, or check something purely based on the coordinates.


Also, can you give some information on the source of the data. It may help with the solution. This looks like a very damaged QAM constellation, but I can't see how your math would be useful for this.

[Karamel]

So all points in the array are exactly numbered already, and number corresponds to the index, correct? But now what's the goal?

There are two situations here. One - calculations are done purely on the indexes, for which we have provided a solution. Second one - calculation involve coordinates, but then it is not clear how to mix indexes. You need to fix one or the other. We can ether check that correctly selected square in the index space corresponds to some geometric configuration in the coordinate space, or check something purely based on the coordinates.


Also, can you give some information on the source of the data. It may help with the solution. This looks like a very damaged QAM constellation, but I can't see how your math would be useful for this.

Fifth time, I am telling you. Please prove that 1-2-11-12 are neighbor, they represent four cornered polygon and there is no any folding with any other data.

And do it for all any other four group data.

This is my problem. How can I give you more information than this? What should I say more?

[ataradov]

Fifth time, I am telling you. Please prove that 1-2-11-12 are neighbor, they represent four cornered polygon and there is no any folding with any other data.

You keep using terms that you have not defined. What is the definition of "neighbor" and "folding"?

This is my problem. How can I give you more information than this? What should I say more?

You can provide actual examples on your actual data sets.

But I think I will sit this one out, I spent enough time on this, and you are not providing enough information.