Can I use ismembertol to find x,y coordinates that are close to each other?

I want to compare coordinates from one array to coordinates from another. Can this work since I cannot directly put ordered pairs into a matrix in MATLAB?

Answer 1

[Jon]

If I am understanding what you are trying to do correctly I think this would do what you ask

% Define some example coordinates
A = [1.3 2.8
    2.5 3.9
    6.2 8.7
    5.4,4.3];
B = [2.49 3.88
    5.39,4.31];
% Define tolerance
tol = 0.02;

% Find points in A that match B
Amatch = A(ismembertol(A,B,tol,'ByRows',true),:)

Amatch = 2×2

2.5000 3.9000 5.4000 4.3000

[Jon]

Sorry, I don't understand your question at all. In my example above the first column is the x coordinate, the second column is the you coordinate. The coordinate values I give are not integers, as you can see they all have something to the right of the decimal point. Are we perhaps getting confused about whether to use commas or periods as the decimal separator? In MATLAB a period (".") is always used as the decimal separator not a comma (",")

[student]

Thanks!

[Jon]

As @Star Strider suggests, rather than putting tolerances separately on the x and y coordinates, the Euclidean distance from the points in B to the points in A is a good criteria for judging whether they approximately match.

If you have the Statistical and Machine Learning toolbox, then you can use pdist2 for this as described by @Star Strider.

If you don't have the Statistical and Machine Learning toolbox, you could compute the distances and use them as follows

% Define some example coordinate
A = [1.3 2.8
    2.5 3.9
    6.2 8.7
    5.4,4.3];
B = [2.49 3.88
    5.39,4.31];

% Define tolerance for matching points
tol = 0.05; % adjust for your needs

% Find distance from each point in B to each point in A
% in a distance matrix, D, with D(i,j) giving distance from ith point in A
% to jth point in B
% Represent 2d points as complex values for easy distance manipulation as
% vectors instead of m by 2 matrices
Ac = A*[1;1i];
Bc = B*[1;1i];

D = abs(Ac - Bc.'); % matrix whose i,j entry give d

% Find matching rows in A corresponding to each row in B based on distance
% tolerance
idx = find(D<=tol); % return linear indices into distance matrix
[r,~] = ind2sub(size(D),idx); % find row in A which matches 

% List the matching points
Amatch = A(r,:)

Amatch = 2×2

2.5000 3.9000 5.4000 4.3000

% Or, you could just find the matches based on the closest value without a
% specific tolerance
[~,r]  = min(D);
Amatch = A(r,:)

Amatch = 2×2

2.5000 3.9000 5.4000 4.3000

[Jon]

Did this answer your question?

Answer 2

[Star Strider]

The best approach to find (x,y) pairs that are close to each other is probably to use pdist2. You can then compare the distances. The ismember function can then be useful in finding the closest pairs.

Example —

A = randn(10,2)

A = 10×2

-0.9422 0.0717 2.3691 1.7775 -0.8306 -0.4153 -2.1050 0.2304 0.3308 1.3710 -0.7083 -1.1922 -0.3769 0.3738 -0.2065 -1.2760 1.6947 -0.2010 0.9019 -0.7153

B = randn(9,2)

B = 9×2

0.0959 2.3267 -0.3266 1.3585 -1.1101 -0.2051 1.8024 -0.4148 -0.9464 1.4494 -0.8747 2.5306 -0.8180 -1.0263 -2.6085 -0.1066 1.2114 -0.5300

[D,I] = pdist2(A,B, 'euclidean','smallest',size(A,1))

D = 10×9

0.9841 0.6575 0.3237 0.2394 1.2171 1.6726 0.1989 0.6059 0.3607 2.0093 0.9860 0.3497 0.9493 1.2796 2.2135 0.6111 1.6758 0.5847 2.3386 1.4265 0.9342 2.1858 1.3777 2.4598 0.6605 1.8045 1.6022 2.4825 1.8440 1.0657 2.2643 1.6817 2.6085 1.1050 2.1884 1.8274 2.8942 2.1060 1.0860 2.3140 1.8683 2.9462 1.4679 2.2827 2.0307 2.9908 2.4103 1.4012 2.3176 2.6523 3.3301 1.7478 2.6715 2.0452 3.0394 2.5529 2.0757 2.6283 2.8241 3.7002 1.7988 3.2898 2.0950 3.1469 2.5791 2.1355 2.6330 2.8464 3.7265 2.6447 3.5628 2.2360 3.6095 2.6373 2.8048 2.7874 3.1144 3.7501 2.6584 4.3042 2.5816 3.6153 2.7281 4.0045 3.9603 3.3317 3.8648 4.2449 5.3222 3.4024

I = 10×9

5 5 1 9 7 5 6 4 10 7 7 3 10 5 7 3 1 9 2 1 7 8 1 1 8 3 8 1 3 6 2 4 4 1 6 7 3 4 4 5 3 3 7 7 6 9 10 8 7 6 2 10 8 3 4 9 10 6 8 10 4 5 5 10 6 5 3 10 6 9 10 1 6 8 9 1 9 9 5 9 2 8 2 2 4 2 8 2 2 4

Ds = sort(D(:),'ascend');
[~,idx] = ismember(D,Ds(1:10));                                                         % Return Informaton For The Closest 10 Pairs
[r,c] = arrayfun(@(x)find(idx == x), 1:10);                                             % Return Row & Col Indices
DistIdx = table(Ds(1:10),r(:),c(:), 'VariableNames',{'Distance','A Row','B Row'})       % Results Table

DistIdx = 10×3 table
    Distance    A Row    B Row
    ________    _____    _____

    0.19885       1        7  
    0.23937       1        4  
    0.32372       1        3  
    0.34974       2        3  
    0.36068       1        9  
    0.58469       2        9  
    0.60585       1        8  
    0.61113       2        7  
    0.65747       1        2  
    0.66046       3        7  

Make appropriate changes to get the desired result.

.