Plotting Points On A Nyquist Curve

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Hi folks,
MATLAB newbie here but unfortunately I've been presented with a rather complex MATLAB question that I need some help with.
I need to create a MATLAB GUI with an axes object that will display the Nyquist plot of a transfer function (the TF will ultimately be specified by the user but for the moment I'm using a hard-coded value).
I can create a Nyquist plot easily enough and I have managed to ensure that it doesn't appear as a Figure but instead appears on the axes object of the form. But the next requirement is far more difficult to me.
The program needs to select 50 points at random along the curve and display them as coloured dots or pixels. I know that the NYQUIST function returns the real and imaginary numbers of a Nyquist plot as a matrix of values - is there a way to use that information to choose points along the curve?
Thanks

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Craig
Craig 2016-3-15
This would allow you to plot points on the nyquist plot for different frequencies.
sys = tf(1,[1,1,1]);
nyquist(sys);
hold on;
w = logspace(-2,2,100); % these points could be picked randomly
nyquist(sys,'*',w)

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