Select a point on the graph

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luca
luca on 9 Oct 2019
Commented: luca on 9 Oct 2019
Hi given the following code,
figure(1);
scatter(x(:,1),x(:,2));
hold on;
scatter(member_value(:,1),member_value(:,2),'r');
legend({'Data','Pareto Frontier'})
I obtain a graph like this
untitled.jpg
And I want to select the red point that is closest to the origin.
May someone help me with the code?
  2 Comments
Adam
Adam on 9 Oct 2019
What do you mean by 'select' it? You can click on it and select it if you wish, but that depends what you want to do having 'selected' it.
If you mean programmatically find it then isn't it just a simple case of pythagoras, having subtracted your origin from all points? (Or some built-in distance function that does the maths for you anyway)
luca
luca on 9 Oct 2019
Yes the idea is to use something like pythagoras, that able me to find the point with the minimum distance from the origin. But do you know how can I implement it?

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Accepted Answer

Adam Danz
Adam Danz on 9 Oct 2019
Edited: Adam Danz on 9 Oct 2019
To find the coordinate closest to the origin (0,0),
d = hypot(member_value(:,1),member_value(:,2));
[~, minIdx] = min(d);
plot(member_value(minIdx,1),member_value(minIdx,2),'ks','MarkerSize',12);
hypot() method avoids potential under/overflow: https://www.mathworks.com/help/matlab/ref/hypot.html
  8 Comments
Adam Danz
Adam Danz on 9 Oct 2019
Edited: Adam Danz on 9 Oct 2019
Let's say you have 4 coordinates (black dots, below).
Each of those coordinates forms a right-triangle where 1 side of the triangle is the 'x-coordinate and the other side of the triangle is the y-coordinate. The hypotenuse of the triangle is the line that extends from (0,0) to the dot.
hypot() inputs are the x and y coordinates which are the sides of each triangle. It outputs the length of the hypotenuse which is the distance of the dot from (0,0). The hypotenuse are the diagonal lines in the image below.
Hypotenuse demo code for the image above:
clf()
x = rand(4,2).*8+1;
scatter(x(:,1),x(:,2));
hold on;
axis equal
xlim([0,9])
ylim([0,9])
grid on
leg = plot(x(:,[1,1])', [x(:,2),zeros(size(x,1),1)]', '-','LineWidth',2);
hyp = plot([x(:,1),zeros(size(x,1),1)]', [x(:,2),zeros(size(x,1),1)]', '-','LineWidth',2);
set(hyp,{'Color'},{leg.Color}')
d = hypot(x(:,1),x(:,2));
labels = strsplit(sprintf('h=%.1f\n',d'));
t = text(x(:,1)-.2,x(:,2),labels(1:end-1),'HorizontalAlignment','right');
luca
luca on 9 Oct 2019
Thanks Adam ! now its clear how it works

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More Answers (1)

Turlough Hughes
Turlough Hughes on 9 Oct 2019
You can do the following:
[~,ind]=min(sqrt(member_value(:,1).^2+member_value(:,2).^2)); %find index for point closest to origin
hold on; plot(member_value(ind,1),member_value(ind,2),'.k');
Note, that if x was arranged as a row vector this will not work, but this is not the case for you.

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