MATLAB: Finding the closest point on a line to another point

lineMATLABpoints

Hello all,
I am looking find the closest point on the line in the below image to each of the points shown by a circle.
I have 2 tables, one I will call line, and one I will call point:
line.x = [1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5]
line.y = [1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5]
point.x = [4.5, 2.1, 3.6]
point.y = [3.9, 2.7, 3.1]
scatter(point.x, point.y)
hold on
plot(line.x, line.y)
I want to find the closest defined point on the line (it has to be one of the points listed above, it can't be a point on the line between the defined points) that is closest to each of the circles.
Any tips on how to do this? I have found several similar threads but nothing that gets at what I'm after. Thanks all!!

Best Answer

Solving for the discrete points is actually a lot easier. Using your data as follows:
line.x = [1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5];
line.y = [1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5];
point.x = [4.5, 2.1, 3.6];
point.y = [3.9, 2.7, 3.1];
h = figure(); plot(line.x,line.y,'ok','MarkerFaceColor','k');
hold on, plot(point.x,point.y,'or')
h.Position(3) = h.Position(4); % sets the figure aspect ratio to 1.
I just find the distance to each point in your line. The first row of dist is the distance of every point in line to the [point.x(1) point.y(1)], row two is all the distances to the second point and so on:
dist = sqrt((line.y - point.y.').^2 + (line.x - point.x.').^2)
[~,idx] = min(dist,[],2); % index for the closest points, i.e. those with min distance.
Plot resulting points on the line that are closest.
hold on; plot(line.x(idx),line.y(idx),'.cyan','MarkerSize',18)
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