Calculate minimum distance between points in a mesh

Assuming I have N points in a unit 2 or 3 dimensional box. How do I find the two points that are the closest and possible plot a circle around them?

So I am starting with randomly distributed points in 2D space:

A = rand(20, 2);

x = A(:, 1); % x coordinates

y = B(:, 2); % y coordinates

Now I want to find the minimum distance, print it and plot a circle around the two points to somehow mark them.

[David Wilson]

I assume you mean A(:,2) above. You could try pdist from the stats toolbox.

Something like:

A = rand(20, 2);
x = A(:, 1); % x coordinates
y = A(:, 2); % y coordinates

plot(x,y,'s')

D = pdist(A);
D = squareform(D); 
D = D + max(D(:))*eye(size(D)); % ignore zero distances on diagonals 
[minD,idx] = min(D(:)); 

[r,c]=find(D==minD);
hold on 
plot(x(c), y(c), 'r*')

% Now plot a circle around the two points 
c = [mean(x(c)), mean(y(c))]; % centerpoint 
r = minD/2; 
t = linspace(0,2*pi); 
xc = r*exp(1j*t);
plot(real(xc)+c(:,1), imag(xc)+c(:,2),'r-')

hold off 
axis equal

giving:

Answer 1

[KSSV]

A = rand(20, 2);
x = A(:, 1); % x coordinates
y = A(:, 2); % y coordinates

d = pdist2(A,A) ;
% Get minimum distance 
d(d==0) = NaN ; 
[val,idx] = min(d(:)) ;
[i,j] = ind2sub(size(d),idx) ;

% plot circle 
C = [mean(x([i j])) mean(y([i j]))] ;
R = val ; 
th = linspace(0,2*pi) ; 
xc = C(1)+R*cos(th) ; 
yc = C(2)+R*sin(th) ; 

plot(x,y,'.r')
hold on
plot(x(i),y(i),'+k')
plot(x(j),y(j),'+k')
plot(xc,yc,'b')

[asasdasdasdadsadasd]

Dear @ KSSV,

may I ask, how can we determine the minimum distance between two points in (one) each triangular element (3 nodes) in a very efficient way in Matlab?

Best

[KSSV]

YOu may get your required code from this toolbox, try out.

https://in.mathworks.com/matlabcentral/fileexchange/25555-mesh2d-delaunay-based-unstructured-mesh-generation

Answer 2

[Guillaume]

Here is one way:

points = rand(20, 2);   %demo data

distance = hypot(points(:, 1) - points(:, 1).', points(:, 2) - points(:, 2).');  %distance between all points
distance(logical(tril(ones(size(distance))))) = Inf;  %point below diagonal are symmetric of upper triangle. Also remove diagonal from minimum search
[mindistance, location] = min(distance(:));
[point1, point2] = ind2sub(size(distance), location);

fprintf('minimum distance of %g between point %d and %d\n', mindistance, point1, point2)