Separation of datum and decision of their mistake

[Karamel]

Choose any four group data from this data set. You will see. They will create a polygon and there is no any other data inside of these polygons, okay?

I marked red, green and yellow them for you. Even yellow, can you see, they can create any polygon and no folding from any other data.

I can't understand what you expect from me. This is my problem and I don't try to find any help, just try to find any idea to love this problem. You don't need to write code or any other things. Just think and imagine for solution.

[ataradov]

Your pictures are not showing, just attach them here.

Choose any four group data from this data set. You will see.

"You will see" is not a rigorous definition.

They will create a polygon and there is no any other data inside of these polygons, okay?

So you need to check that given 4 points form a polygon  that contains no other points from this data set? Then this is trivial, unless you have some speed optimization criteria.

[Karamel]

Can you see?

Do you say you can't see images now? 

[xrunner]

Choose any four group data from this data set. You will see. They will create a polygon and there is no any other data inside of these polygons, okay?

No not OK.

That is not true, as you can see in my attachment. You cannot choose "any four" and have no other data inside of the polygon.

[hamster_nz]

Choose any four group data from this data set. You will see. They will create a polygon and there is no any other data inside of these polygons, okay?

So is this black polygon also OK? If not, why not?

[Karamel]

You can choose only n, n+1, n+10, n+11 numbered data set.

Why don't you try to understand. This data set is okay. Please plot it and give numbers for each data. You can't choose like yours. 

[hamster_nz]

You can choose only n, n+1, n+10, n+11 numbered data set.

Why don't you try to understand. This data set is okay. Please plot it and give numbers for each data. You can't choose like yours. 

Let me restart your problem for you:

- I have a set of 100 (x,y) points, points[0] ... points[99].

- I want to take four points and form a quadrilateral
  (points[n] points[n+10], points[n+11], points[n+1])
  this gives 97 possible quadrilaterals, as we do not 'wrap around' from point(99) to point(0).

- If any two points neighboring points in a quadrilateral have the same pair of x,y values (i.e. are on top of each other), I want to discard that quadrilateral as it will be a triangle.

- I want to then test that if draw the quadrilateral, the points would be visited in a clockwise order,  and discard the quadrilateral where that is not true. 

This is close to to back-face culling. To do this I propose splitting the quadrilateral into two triangles, and testing them (points[n] points[n+10], points[n+11]) and (points[n+11],points[n+1],points[n]). If either of them are drawn counter-clockwise then the quadrilateral should be discarded.

- Then, I want to test that no other point falls inside (or on the edge?) of this quadrilateral.

Once again splitting into two triangles could help here. testing if a point is in a triangle is relatively easy

Does that describe what you are trying to do?

[ataradov]

Do you say you can't see images now? 

Your original message contained links to some image sharing site or something like this.  And they were not working. Don't blame this on me.

So the way  I understand this thing, you want to test that for any 4 points with coordinates (n, n+1, n+10, n+11) forming a quadrilateral, there are no other points in the quadrilateral? Then it is done by a simple test. Here is one description of the algorithm http://demonstrations.wolfram.com/AnEfficientTestForAPointToBeInAConvexPolygon/ . you can simplify that, since you always know the number of points.

But I don't see how this is anything like the original question. In the original question you yourself have selected a set of points that are not in the format (n, n+1, n+10, n+11) and said that it is not OK. Well, now it is not OK by definition. So what's the problem?

[DJohn]

Why don't you try to understand.

People are trying to understand, but you are describing the problem very badly.  Looking at your country, I am guessing that English isn't your first language, so I do sympathise.  But it's very difficult to understand what you're asking for.

This is my best guess of what you are asking:

You have the coordinates of 100 points.  You want to assign numbers 1 - 100 to them, in such a way that for each n from 1 to 9, 11 to 19, 21 to 29, and so on, the points labelled n, n+1, n+10, n+11 form a convex quadrilateral that contains no other point.

If the points had integer coordinates from (0,0) up to (9,9), then this numbering would be easy: from left to right and bottom to top.  But you need to solve this problem for any set of points, or be able to say that there is no solution.

Is that right?  By "no folding", do you mean that the quadrilaterals must be convex?

[metrologist]

I think he simply means that, taking his first grid example to understand which 4 points would normally be neighbors on that grid, yet in some other arrangement, verify that there are no other points infringing on the boundary of every possible 4-neighboring-point shape (already explained well as the n, n+1, n+10, n+11 set). I do not think the shapes need to be convex.

For example, take points:

1,2,11,12 and verify that none of the remaining 96 points fall on the area defined by those 4 points.

2,3,12,13 and verify that none of the remaining 96 points fall on the area defined by those 4 points.

3,4,13,14 and verify that none of the remaining 96 points fall on the area defined by those 4 points.

etc...


Exclusions:

Points 10,11 are not neighbors.

Points 20,21 are not neighbors.

Points 30,31 are not neighbors.

etc...

 

[metrologist]

there is a problem.

The problem is you are missing one of the neighboring points, so I do not understand your problem example...

If my interpretation is correct,  I might just take an approach of an if statement on all other non-neighboring points to see if their x value and y value is within the points of the neighboring data set.