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

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Cola
Cola 2021-10-11
评论： Cola 2021-10-16
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.

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Image Analyst
Image Analyst 2021-10-11
Someone just posted code from the Mathworks that does the local angle computation. See
https://www.mathworks.com/matlabcentral/answers/1469611-recalculate-binary-line-local-orientation?s_tid=srchtitle
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Cola
Cola 2021-10-16
@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
Cola 2021-10-16
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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