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

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.

Answer 1

[Image Analyst]

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

[Cola]

@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]

Eliminating iteration by code:

c1=Data(1:2000,:);

c2=Data(2:2001,:);

c=sqrt((c1(:, 1)-c2(:, 1)).^2+(c1(:, 2)-c2(:, 2)).^2)