Finding tangent to a curve

I have some data in x and y form. The data gives a plot as shown in the figure,

I want to draw tangent line on this curve, I am new to Matlab and would like someone to answer here.

Thank you!

[Faisal]

The tangent line should be on the left (steepest) side of the curve.

[John D'Errico]

There would be infinitely many tangent lines on a curve that is not perfectly linear. What property would be satisfied by the tangent line that you desire to see? Remember that we cannot read your mind, as much as we try.

[Mathieu NOE]

@Faisal

are you looking for tangent line or the 1st order polynomial fit (straight line fit) of that portion of the signal ?

[Faisal]

I got my anwer,

I had to find the polynomial first to fit the data.

then take the derivetive. I have used this code, if there's anything missing, please do mention;

close all;

clear all;

clc;

file='C_1.xlsx';

[x] = xlsread(file,1,'C2:C5092');

[y] = xlsread(file,1,'A2:A5092');

plot(x,y,'.'); hold on

n = 10;

[p,~,mu] = polyfit(x,y,n); % degree 10 polynomial fit, centered and scaled

% Plot the fit with the data

xfit = linspace(min(x),max(x),5091);

yfit = polyval(p,xfit,[],mu);

plot(xfit,yfit,'r')

idx = input(['Enter index in the range ',num2str([1 length(x)]),':']);

x0 = x(idx);

f = @(x) polyval(p,x,[],mu);

df = derivest(f,x0); % Here is the derivative

% Calculate the end points of a tangent line

xt = [x0-5 x0+9];

yt = f(x0) + (xt-x0)*df;

plot(xt,yt,'g','LineWidth',1.5);

[Mathieu NOE]

if you want someone to double check your code ,please provide the data file

tx

[Faisal]

@Mathieu NOE

Sure thing, Here is the file.

[Mathieu NOE]

Ok

basocally no big deal , simply a few points I think the code could be improved :

• no need to fit a polynomial curve here , everything can be done directly on the experiimental data
• always make sure that you don't have too much rounding on excel data , this can create issue in diff / gradient computation
• I thought maybe the tangent must be computed automatically at certain x/y point but the user is requested to entre the x index (??)
• endpoints of the tangent are computed automatically

issue with x rounding : see what you get when you plot(diff(x))

my suggestion so far :

close all;
clear all;
clc;
file='C_2.xlsx';
% [x] = xlsread(file,1,'C2:C5092');
% [y] = xlsread(file,1,'A2:A5092');
data = xlsread(file);
y = data(:,1);
x = data(:,2);

% NB : x is not constant sampling (check with plot(diff(x)) you will see resolution issue)
xnew = linspace(min(x),max(x),300); % we really don't need much more than 300 points on this curve
ynew = interp1(x,y,xnew,'linear');
% overwritte data (my personnal choice)
x = xnew;
y = ynew;
clear xnew ynew

plot(x,y,'-*');
hold on

% slope (gradient)
dx = mean(diff(x));
slop = gradient(y,dx);

idx = input(['Enter index in the range ',num2str([1 length(x)]),':']);
x0 = x(idx);
y0 = y(idx);
df = slop(idx);
% Calculate the end points of a tangent line
xt = [max(0,x0-y0/df)  x0+(max(y)-y0)/df ];
yt = y0 + (xt-x0)*df;
plot(x0,y0,'dr',xt,yt,'r','LineWidth',2.5);

[Faisal]

great one.

This one is even more reasonable and esthetically good and most importantly code is more simpler. Thank you@Mathieu NOE for your help. It was great

[Mathieu NOE]

My pleasure !