How to draw the tangent line on a curve

I would like to plot the tangent of the curve I (V) and find the slope and then the intersection of the tangent with the x axis (V0).

I am attaching the curve data (I, U) and a summary image of what I am looking for. Thank you in advance for your help

Answer 1

[Star Strider]

Try this —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/668953/Tan.xlsx')

T1 = 42×2 table
      I          V    
    ______    ________

         0           0
         0    0.064516
         0     0.14337
         0     0.20072
         0     0.36559
         0     0.45878
    4.6681     0.55197
    19.593     0.63799
    40.963     0.73118
     58.96      0.7957
    79.604     0.86022
    114.14      0.9534
    138.19      1.0108
    164.38      1.0681
    181.86      1.1039
    207.75      1.1541

I = T1.I;
V = T1.V;
dI = gradient(I);
dV = gradient(V);

Vi = 1.3;                                               % Choose Voltage Value To Calculate Slope
Ii = interp1(V, I, Vi);
dVi = interp1(V, dV, Vi)

dVi = 0.0299

dIi = interp1(V, dI, Vi)

dIi = 18.8851

Slope = dIi/dVi

Slope = 631.9586

YIntercept = Ii - Slope * Vi

YIntercept = -528.9232

XIntercept = -YIntercept / Slope

XIntercept = 0.8370

figure
plot(V,I)
hold on
plot(Vi, Ii, 'p')
plot(xlim, xlim*Slope+YIntercept, '-r')
plot(XIntercept, 0, 'sr')
hold off
grid
xlabel('V')
ylabel('I')
text(Vi, Ii, sprintf('$I = %.3f \\times V %+.3f \\rightarrow \\ $', Slope, YIntercept), 'Horiz','right', 'Vert','middle', 'Interpreter','latex')
text(XIntercept, 0, sprintf('$%.4f V \\downarrow $', XIntercept), 'Horiz','right', 'Vert','bottom', 'Interpreter','latex')
ylim([0 max(ylim)])

.

[Inou]

Thank you very much, it works.

I have a question please: How do I do it if I don't know the shape of the curve at the beginning and I don't know the inflection point.

Because this part will be included in a loop that will calculate the slope and V0 of each model (the different sheets of the Tan2.xls file). I attach the file Tan2.xlsx (I(U) of models 1-3) and your code in the loop

I think I need to find the inflection point of each model to draw their tangent. But I don't know exactly how to find it...

[Star Strider]

As always, my pleasure!

The inflection point problem was not part of the original request, so

I define ‘inflection point’ as the point where the slope changes sign, for example:

x = linspace(-2, 2, 250);
y = tanh(x);
dx = gradient(x);
dy = gradient(y);
slope = dy./dx;
d2yd2x = gradient(slope);

figure
yyaxis left
plot(x, y,    x, slope)
yyaxis right
plot(x, d2yd2x)
grid
legend('$y(x)$','$\frac{dy}{dx}$','$\frac{d^2y}{dx^2}$', 'Location','best', 'Interpreter','latex')

So the inflection point here is at ‘x=0’.

The slope appeared to me to be essentially constant (with respect to ‘V’), so I chose ‘Vi’ arbitrarily on the basis of the supplied plot image. There is one large change in the slope (however not an ‘inflection point’ as I define it) at abouit ‘V=0.5’:

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/668953/Tan.xlsx');
I = T1.I;
V = T1.V;
dI = gradient(I);
dV = gradient(V);
d2Id2V = gradient(dI./dV);                                      % Second Derivative
[~,idx1] = max(abs(d2Id2V))

idx1 = 7

Vi = V(idx1)

Vi = 0.5520

figure
yyaxis left
plot(V, dI./dV)
ylabel('$\frac{dI}{dV}$', 'Interpreter','latex')
yyaxis right
plot(V, d2Id2V)
ylabel('$\frac{d^2I}{dV^2}$', 'Interpreter','latex')
grid
xlabel('$V$', 'Interpreter','latex')

Using this with my earlier code:

Ii = interp1(V, I, Vi);
dVi = interp1(V, dV, Vi)

dVi = 0.0896

dIi = interp1(V, dI, Vi)

dIi = 9.7964

Slope = dIi/dVi

Slope = 109.3283

YIntercept = Ii - Slope * Vi

YIntercept = -55.6780

XIntercept = -YIntercept / Slope

XIntercept = 0.5093

figure
plot(V,I)
hold on
plot(Vi, Ii, 'p')
plot(xlim, xlim*Slope+YIntercept, '-r')
plot(XIntercept, 0, 'sr')
hold off
grid
xlabel('V')
ylabel('I')
text(Vi, Ii, sprintf('$I = %.3f \\times V %+.3f \\rightarrow \\ $', Slope, YIntercept), 'Horiz','right', 'Vert','middle', 'Interpreter','latex')
text(XIntercept, 0, sprintf('$%.4f V \\downarrow $', XIntercept), 'Horiz','right', 'Vert','bottom', 'Interpreter','latex')
ylim([0 max(ylim)])

This is the best I can do with these data.

I have no idea how you want to define the voltage at which to draw the tangent. With more information, I will do my best to help with that.

(I verified that the ‘Tan2.xlsx’ file is a duplicate of the original file, so I am not using it here.)

C3 = readcell('https://www.mathworks.com/matlabcentral/answers/uploaded_files/669983/Tan_Mat.txt');

.

[Inou]

Thank you for your explanations.

My mistake on the understanding of the inflection point, because precisely the slope is constant.

The point of intersection of the tangent with the x-axis must be within [0.7 ; 0.9], the first derivative gives a better estimate of this point.

[Star Strider]

As always, my pleasure!

I am slightly lost, however. If the objective is to find values of ‘I’ and ‘V’ to produice an x-axis intercept within those limits, a simple search using a for loop would likely work. If the intent is different, a somewhat more sophisticated approach would be necessary.

[Sharatkumar Kondikoppa]

In your code you have taken Vi =1.3 , did you choose randomly or took a mean value ? Can you explain me.

Or can I choose any value ?

[Star Strider]

I chose that value for ‘Vi’ since although the exact point was not stated, it was certainly implied in the ‘image001.png’ plot.

So ‘Vi’ can be any point in the curve.

Answer 2

[Asmit Singh]

This answer might be useful.