# How to calculate the area of the curve around a point?

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Cola on 11 Oct 2021
Commented: Cola on 16 Oct 2021
There is a curve, and the coordinates of each point of the curve is known. Is there a way to calculate the area of the curve around a point? Thanks!
For example, I plot a curve by Data.mat as shown below, and (0,20) is a point of attraction.
Now I want to calculate the area as shown below by Data.mat.
The whole area can be divided to these parts.

Image Analyst on 11 Oct 2021
Someone just posted code from the Mathworks that does the local angle computation. See
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Cola on 16 Oct 2021
@Image Analyst Thank you very much. And there is a code for reference.
Code:
delta_x=Data(:, 1)-0;
delta_y=Data(:, 2)-20;
L=sqrt(delta_x.^2+delta_y.^2)
a=L(1:2000,1);
b=L(2:2001,1);
for i=1:1:2000
c(i,:)=sqrt((Data(i, 1)-Data(i+1, 1)).^2+(Data(i, 2)-Data(i+1, 2)).^2)
end
p=(a+b+c)./2; %% Heron's formula
S=sqrt((p-a).*(p-b).*(p-c).*p)
Total_S=sum(S)
Cola on 16 Oct 2021
Eliminating iteration by code:
c1=Data(1:2000,:);
c2=Data(2:2001,:);
c=sqrt((c1(:, 1)-c2(:, 1)).^2+(c1(:, 2)-c2(:, 2)).^2)

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