How to find the closest point to a line

Question

Blue 2022-11-2

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https://ww2.mathworks.cn/matlabcentral/answers/1842123-how-to-find-the-closest-point-to-a-line

评论： 012786534 2022-11-3

Hello,

I am having a bit of a hard time finding which point (i.e centroid) is closest to a line formed by the start and end coordinates. The lines are always in a straight line.

points = array2table([1,48,-55,48.1,-55.1; 2, 50,-55,50.1,-55.1], 'VariableNames', {'name', 'start_lat','start_long','end_lat','end_long'})
centroids = cell2table({'A', 47, -56; 'B', 51,-54}, 'VariableNames', {'name', 'centroid_lat','centroid_long'})
desired_output = cell2table({1,48,-55,48.1,-55.1, 'A'; 2, 50,-55,50.1,-55.1, 'B'}, 'VariableNames', {'name', 'start_lat','start_long','end_lat','end_long', 'closet_centroid'})

Thank you,

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Blue 2022-11-2

I have edited the question to change the centroids positions. I simply want to associate each centroid to the closest line formed by the start and end positions of each point

Davide Masiello 2022-11-2

How do you determine the distance between a line and a point?

Is the distance between the point and the line centroid ok?

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Answer 1

Walter Roberson 2022-11-2

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https://ww2.mathworks.cn/matlabcentral/answers/1842123-how-to-find-the-closest-point-to-a-line#answer_1090013

See https://www.mathworks.com/matlabcentral/answers/95608-is-there-a-function-in-matlab-that-calculates-the-shortest-distance-from-a-point-to-a-line#answer_281258 -- and it looks like @Rik created https://www.mathworks.com/matlabcentral/fileexchange/64396-point-to-line-distance based on that.

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Blue 2022-11-3

在 MATLAB Online 中打开

Based on the posts suggested by Walter I would do this to solve my question:

points = array2table([1,48,-55,48.1,-55.1; 2, 50,-55,50.1,-55.1], 'VariableNames', {'name', 'start_lat','start_long','end_lat','end_long'});
centroids = cell2table({'A', 47, -56; 'B', 51,-54}, 'VariableNames', {'name', 'centroid_lat','centroid_long'});
for i = 1:height(points)
    v1 = [points.start_lat(i), points.start_long(i)];
    v2 = [points.end_lat(i), points.end_long(i)];
    if length(v1) == 2, v1(3) = 0; end    %extend 1x2 to 1x3 if needed
    if length(v2) == 2, v2(3) = 0; end    %extend 1x2 to 1x3 if needed
    for  j = 1:height(centroids)
        pt = [centroids.centroid_lat(j), centroids.centroid_long(j)];
        if size(pt, 2) == 2, pt(1, 3) = 0; end  %extend nx2 to nx3 if needed
        v1_ = repmat(v1, size(pt, 1), 1);
        v2_ = repmat(v2, size(pt, 1), 1);
        a = v1_ - v2_;
        b = pt - v2_;
        distance(j) = sqrt(sum(cross(a,b,2).^2,2)) ./ sqrt(sum(a.^2,2));
    end
    [~, idx] = min(distance);
    points.associated_centroid(i) = centroids.name(idx)
end

Rik 2022-11-3

在 MATLAB Online 中打开

Since you know you only put in 2 points, why not create the vector including the 0? That way you also get to skip the test with length (which I wouldn't use anymore.

I also removed the repmat call, as you only provide a single point.

points = array2table([1,48,-55,48.1,-55.1; 2, 50,-55,50.1,-55.1],...
    'VariableNames', {'name', 'start_lat','start_long','end_lat','end_long'});
centroids = cell2table({'A', 47, -56; 'B', 51,-54},...
    'VariableNames', {'name', 'centroid_lat','centroid_long'});
for i = 1:height(points)
    v1 = [points.start_lat(i), points.start_long(i), 0];
    v2 = [points.end_lat(i)  , points.end_long(i)  , 0];
    for  j = 1:height(centroids)
        pt = [centroids.centroid_lat(j), centroids.centroid_long(j), 0];
        a = v1 - v2;
        b = pt - v2;
        distance(j) = sqrt(sum(cross(a,b,2).^2,2)) ./ sqrt(sum(a.^2,2));
    end
    [~, idx] = min(distance);
    points.associated_centroid(i) = centroids.name(idx);
end
points
points = 2×6 table
    name    start_lat    start_long    end_lat    end_long    associated_centroid
    ____    _________    __________    _______    ________    ___________________

     1         48           -55         48.1       -55.1             {'A'}       
     2         50           -55         50.1       -55.1             {'B'}       