How to find coordinates of intersecting line?

Hi, I have plot which is shown below and there is black (dashed) vertical line in x axis at 3. I need to find the coordinates of intersection between black line and red curve.

clear all; close all;

fs= 8192*2;        % sampling frequency                                              
dt = 1/fs;       % sample time                                             
T=5;             % duration of the signal                                       
Nt = T*fs;       % total number of samples
t = 0:dt:T-dt;   % time vector

% Source definition
f0 = 1;         % frequency at time t = 0s
f1 = 5;       % freqeuncy at time t = T 

%-------------------------------------------------------
beta = (f1-f0)/T;             % beta
finst = f0+beta*t.';         % instantaneous frequency
phi = 2*pi*cumsum(finst)*dt;

figure()
plot(wrapTo2Pi(phi),t,'r');
hold on
xline(3,'--k')
xlabel('phase')
ylabel('s')

Answer 1

[Matt J]

fs= 8192*2;        % sampling frequency                                              
dt = 1/fs;       % sample time                                             
T=5;             % duration of the signal                                       
Nt = T*fs;       % total number of samples
t = 0:dt:T-dt;   % time vector

% Source definition
f0 = 1;         % frequency at time t = 0s
f1 = 5;       % freqeuncy at time t = T 

%-------------------------------------------------------
beta = (f1-f0)/T;             % beta
finst = f0+beta*t.';         % instantaneous frequency
phi = 2*pi*cumsum(finst)*dt;

figure()
plot(wrapTo2Pi(phi),t,'r');
hold on
xline(3,'--k')
xlabel('phase')
ylabel('s')
hold off

z=wrapTo2Pi(phi(:)).';
n=nnz(diff(z)<-pi);
tc=interp1(phi,t,3+2*pi*(0:n) );
pc=0*tc+3;

 hold on; plot(pc,tc,'xb'); hold off

Answer 2

[Torsten]

fs= 8192*2;        % sampling frequency                                              
dt = 1/fs;       % sample time                                             
T=5;             % duration of the signal                                       
Nt = T*fs;       % total number of samples
t = 0:dt:T-dt;   % time vector
% Source definition
f0 = 1;         % frequency at time t = 0s
f1 = 5;       % freqeuncy at time t = T 
%-------------------------------------------------------
beta = (f1-f0)/T;             % beta
finst = f0+beta*t.';         % instantaneous frequency
phi = 2*pi*cumsum(finst)*dt;
phase = wrapTo2Pi(phi);
n = numel(phase);
v = (phase(1:n-1)-3).*(phase(2:n)-3);
idx = v <= 0;
coordinates = t(idx);
figure()
plot(phase,t,'r');
hold on
xline(3,'--k')
xlabel('phase')
ylabel('s')
plot(3*ones(size(coordinates)),coordinates,'o')
hold off

[Matt J]

I wonder if the jump discontinuity lines are to be considered part of the curve.

[Torsten]

Most probably not. But then take every second value from the "coordinates" array :-)