How to draw the tangent line on a curve

Question

Inou 2021-6-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/868168-how-to-draw-the-tangent-line-on-a-curve

评论： Star Strider 2022-1-23

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

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Answer 1

Star Strider 2021-6-29

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/868168-how-to-draw-the-tangent-line-on-a-curve#answer_736063

在 MATLAB Online 中打开

Try this —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/668953/Tan.xlsx')
T1 = 42×2 table
IV______________

         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)])

.

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Star Strider 2021-6-30

在 MATLAB Online 中打开

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');

.

Sharatkumar Kondikoppa 2022-1-23

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 2022-1-23

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.

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Answer 2

Asmit Singh 2021-6-29

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https://ww2.mathworks.cn/matlabcentral/answers/868168-how-to-draw-the-tangent-line-on-a-curve#answer_736068

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