Calculate minimum distance between points in a mesh

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mitja jancic
mitja jancic 2019-4-24
评论： KSSV 2019-12-28
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.
  1 个评论
David Wilson
David Wilson 2019-4-24
编辑：David Wilson 2019-4-24
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:
tmp.png

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采纳的回答

KSSV
KSSV 2019-4-24
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')
  2 个评论
asasdasdasdadsadasd
asasdasdasdadsadasd 2019-12-28
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

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更多回答（1 个）

Guillaume
Guillaume 2019-4-24
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)

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