I need to determine the no. of loops and area under each loop from the xy plot.

I have the x and y data. I need to calclulate total no. loops formed and area under each loop. For the refference I am attaching the figure and x.mat and y.mat files

:

[Dyuman Joshi]

How do you define a loop in the given figure?

[Sahil Wani]

Area enclosed as shown in fig:

Answer 1

[Mathieu NOE]

hello

with the help of this FEX submission, it was quite simple :

Fast and Robust Self-Intersections - File Exchange - MATLAB Central (mathworks.com)

the loops are shown in color on top of your data plot

the self intersect points are shown as red diamonds markers

result is :

area = 71.3220 125.0467 132.8896

units are unknown

code :

load('x.mat')
load('y.mat')

% remove repetitive first x = 0 data at beginning
i0 = find(x<eps);
x = x(i0(end):end);
y = y(i0(end):end);

[x0,y0,segments]=selfintersect(x,y); % fex : https://fr.mathworks.com/matlabcentral/fileexchange/13351-fast-and-robust-self-intersections
figure(1)
plot(x,y,'b',x0,y0,'dr','markersize',15);
axis square
hold on

% compute area for each loop 
for k = 1:numel(x0)
    ind = (segments(k,1):segments(k,2));
    x_tmp = x(ind);
    y_tmp = y(ind);
    % compute area 
    area(k) = trapz(x_tmp,y_tmp);
    plot(x_tmp,y_tmp)
end

area

[Mathieu NOE]

hello @Sahil Wani

problem solved ?

[Dyuman Joshi]

@Mathieu NOE, wouldn't polyarea be a better fit here compared to trapz?

[Mathieu NOE]

hello @Dyuman Joshi

yes this is another alternative ; NB that results are quite the same , I am not sure where the small difference comes from.

I opted for trapz to get a better result (vs an Euler integral), but I don't know the method used in polyarea

Results :

area = 71.3220 125.0467 132.8896 (trapz)

area2 = 72.5056 125.3691 132.8896 (polyarea)

load('x.mat')
load('y.mat')
% remove repetitive first x = 0 data at beginning
i0 = find(x<eps);
x = x(i0(end):end);
y = y(i0(end):end);
[x0,y0,segments]=selfintersect(x,y); % fex : https://fr.mathworks.com/matlabcentral/fileexchange/13351-fast-and-robust-self-intersections
figure(1)
plot(x,y,'b',x0,y0,'dr','markersize',15);
axis square
hold on
% compute area for each loop 
for k = 1:numel(x0)
    ind = (segments(k,1):segments(k,2));
    x_tmp = x(ind);
    y_tmp = y(ind);
    % compute area 
    area(k) = trapz(x_tmp,y_tmp);
    area2(k) = polyarea(x_tmp,y_tmp);
    plot(x_tmp,y_tmp)
end

area
area2

[Mathieu NOE]

hello again @Sahil Wani

do you mind accepting my answer (if it has fullfiled your expectations ) ? tx