Sort coordinates in two directions at the same time

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user20912 2023-5-1

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评论： user20912 2023-5-3

采纳的回答： Matt J

Hi,

I'm working with coordinates and I need to sort them increasing in both x- and y-directions a the same time.

I was thinking on something like

[~,order_x] = sort(lon,'ascend');

[~,order_y] = sort(lat,'ascend');

And then using these as index for lon and lat. The problem is that this process changes the real coordinates. On the attached image, the blue dots represents the original locations and the red number the locations that I got when I use both index at the same time. Which are in the wrong locations.

Any idea how can how sort the points?

Thanks

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Matt J 2023-5-1

移动：Matt J 2023-5-1

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Perhaps this is what you meant to write?

for i1 = 1:size(lon)
   text(lon(order_x(i1)),lat(order_y(i1)),num2str(i1),'color','r')
end

user20912 2023-5-1

移动：Matt J 2023-5-1

Oh yeah. It was a typo. Sorry for that. Any idea how can sort them together?

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Matt J 2023-5-1

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load data_coordinates

tf=~isnan(x)&~isnan(y);

[x,y]=deal(x(tf),y(tf));

[~,t]=sort( [lon-x(1),lat-y(1)]*[x(end)-x(1);y(end)-y(1)] );

[lon,lat]=deal(lon(t),lat(t));

H=plot(x,y,lon,lat,'x');

scatlabel(H(2))

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Matt J 2023-5-2

You just draw a ray from (x(1),y(1)) to (lon,lat) and project the ray onto the line. The projected length of that ray is the thing we are sorting.

user20912 2023-5-3

That makes sense. I ended up using your solution. Thanks!

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Matt J 2023-5-1

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编辑：Matt J 2023-5-1

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It's not possible to sort so that the Nx2 matrix [lat(:),lon(:)] increases monotonically in both columns simultaneously, but you can sort them lexicographically:

tmp=num2cell(sortrows([lat(:),lon(:)]) ,1);
[lat,lon]=deal(tmp{:});

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James Tursa 2023-5-1

编辑：James Tursa 2023-5-1

Would the desired ordering for the above image be 1,2,5,3,6,4,8,7,10,9,... etc.? I.e., pick off the points in order as you move a perpendicular along the line? You could just rotate all the points (e.g. into a vertical line) and then sort by latitude. But since this is all on the surface of a sphere (or spheriod), that begs the question what is really meant by the ordering you want. I.e., spherical trig conversions are probably involved to get what you want in a rigorous fashion. And what exactly is this line? Is it an arbitrary curve, a line on the Mercator projection, or is it really a great circle arc? E.g., if the line was really a great circle arc and passed near the north pole, you couldn't rely on any type of simple ordering or rotations to get the desired result. So, can you describe in more detail what is your actual desired outcome, what exactly is this line, and what range limitations (if any) your data have? Maybe if the data is always clustered in a small area sufficiently away from the poles a simple rotation followed by a sort (or the equivalent) would be good enough for you.

user20912 2023-5-2

编辑：user20912 2023-5-2

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Would the desired ordering for the above image be 1,2,5,3,6,4,8,7,10,9,... etc.?  
I.e., pick off the points in order as you move a perpendicular along the line?  
You could just rotate all the points (e.g. into a vertical line) and then sort by
latitude.

That is correct. I also think that is better to rotate all the points, but the method I was using, didn't work. About what is the meaning of the line, is just a straight line between two points that are close on Earth; the distance is lower than 1 km. So, all I need is to find a way to sort in the way you describe.

PS: I didn't find the option to cite.

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