How to plot circular phase in planar axis without lines going from ymin to ymax when data goes from -pi to pi?

I am try to plot a phase response curve on a planar axis. This means when the response is near it may shift directly to π because they are mathematically equivalent in this case. When I plot this on a typical axis, it can lead to a lot of big vertical lines crossing from ymin to ymax which make the appearance of a big shift in the data where none exists. I would like to get rid of this while still plotting using a line as the data is sampled highly enough that continuity should be reasonably inferred. See an image of the problem below.

Instead what I am looking for is to remove the abrupt cross graph lines that occur when values around pi and -pi cross over. Something like this figure which I've drawn over a scatter plot of the same figure.

Is there anyway to have a continuous line that stops during abrupt transitions?

Edited: Edit to add the goal plot to the main text, in answer to star strider's response!

Answer 1

[Star Strider]

I am not certain what result you want. The phase plots appear to be radian measure and otherwise relatively continuous, so see if the unwrap function will do what you want.

[Keith Doelling]

Sorry I wasn't clear, before! I'm looking to make this figure without hand drawing it in Inkscape!

Basically the exact same as the first plot I showed but without the abrupt lines which cross the whole figure and mean nothing!

[Star Strider]

It would help to have the code.

Detect the abrupt transition and set that value to NaN to avoid plotting that particular line segment (actually line point, if all goes according to plan).

Try something like this —

x = linspace(0, 2*pi, 250);
y = rem(2*sin(x) - x/2, pi);

figure
plot(x, y)

Lv = diff([0 y]) > 0.5;                             % Detect Abrupt Transition
y(Lv) = NaN;                                        % Set It To 'NaN'

figure
plot(x, y)

% hold on
% plot(x, gradient(y))                            % Logic Behind This Approach
% hold off

Another option would be to detect the individual line segments and plot them separately in a loop.

EDIT — (25 Sep 2023 at 15:10)

Still no actual data to work with.

You can prevent the ‘wrapping’ in the blue line by sorting it and its independent variable vector by the independent variable vector. Use the sortrows function.

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[Keith Doelling]

Thank you! Solution 1 has the unfortunate side effect of deleting the first data point either before or after the jump, but it's probably the most straightforward answer. Otherwise, I would have to insert nans between the two points for both x and y, and if y has multiple columns (it does), then it gets weirder and weirder. Thanks for your input!

[Star Strider]

As always, my pleasure!

The alternative approach that involves plotting the segments still requires NaN entries to avoid plotting the connecting llines, although if I remember correctly, it previously didn’t require them —

x = linspace(0, 2*pi, 250);
y = rem(5*sin(x) - x/2, pi);

figure
plot(x, y)

idx = find(diff(sign(abs(y) - pi*0.955)));
idx = [1 idx numel(x)];                                 % This Requires 'idx' To Have An Even Number Of Elements.   
idxm = reshape(idx, 2, [])

idxm = 2×6

1 32 87 136 165 220 30 85 135 163 218 250

figure
hold on
for k = 1:size(idxm,2)
    idxrng = idxm(1,k) : idxm(2,k);
    plot([NaN x(idxrng(2:end))], [NaN y(idxrng(2:end))])
end
hold off

.