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How to place text label near line, but avoiding other lines and labels?

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KAE on 10 Jun 2021
Commented: dpb on 10 Jun 2021
I would like to plot many lines and put a text label near each line. But often the text labels lie over other lines or labels, and so can't be read. How can I reduce visual clutter by smarter label placement? I don't want to move the labels manually due to the large number of plots. Nor should the label text have a white background because it would obscure the plotted data. A plot legend doesn't work due to the large number of lines; the label needs to be near the line instead.
Here's an example of how the labels are hard to read. How can I clean this up?
x = 1:10;
nLine = 15;
y = rand(size(x));
for iLine = 1:nLine
y = rand(size(x));
h = plot(x, y); % Plot a line
hold on;
% Put a text label at the max of the line
iMax = find(y == max(y)); % Find the highest point
% Label the line
t = text(x(iMax), y(iMax), ['Line ' num2str(iLine)], 'color', get(h, 'color'));
% Could also randomly pick a point on line to label; that will be
% cluttered too
% Instead, want to place label near line but where it won't overlap
% anything
box off;
% Looks so cluttered!
dpb on 10 Jun 2021
"I do hope smart placement is possible because clabel places text in a smart way..."
But not smart in the sense of your problem -- it has defined isolines in which it simply inserts a value every so often; it doesn't have to worry about another isoline intersecting or occluding the one it's currently working on (at least with smooth surfaces for which it was developed; I supposed one could dream up a counter-example).
If data are scattered all over as your example of random lines is; then KAE's suggestion of labeling at the ends of the lines or a vertical legend outside the axes is about the only choice there is.
It's not an easy problem in general, virtually all references to algorithms I found are for cartography applications that could be adapted I suppose, but in a fairly quick look I didn't find anything specific.

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