calculate area of boundary of set of 2d-data point

Example: I wanna calculate the area of the boundary of set 2d-data as below illustration: I use the code(polyarea) as follows:

clear;clc;
x=[1;5;5;1;2];
y=[5;5;1;1;3];
plot(x,y,'.')
k = boundary(x,y);% generate boundary of data points
hold on;
plot(x(k),y(k));
A = polyarea(x,y);%calculate the area of boundary

But the result is: 12 <--- wrong???

How can I fix it?

Answer 1

[Roger Stafford]

I would advise you to "close" the polygon so that the first point is the same as the last point. Otherwise, Matlab may be a bit confused as to how the polygon is defined.

x=[1;5;5;1;2;1];
y=[5;5;1;1;3;5];

[ha ha]

Thanks so much. You're right.

May I ask you a favor? If i have set of data (x,y), and i wanna calculate the area of boundary as below illustration. How can I do that?

[ha ha]

This is the sample code for calculating the area of boundary of set of 2d-data point:

clear;clc;
x=[x1;x2;x3;x4;x5;.....;xn];
y=[y1;y2;y3;y4;y5;.....;yn];
plot(x,y,'.')
k = boundary(x,y);% generate boundary of data points. %this is index of all point located in the boundary
hold on;
plot(x(k),y(k));
X=x(k);Y=y(k);%return the original x,y coordinate corresponding to each index k
A = polyarea(X,Y);%calculate the area of boundary

[Niklas Kurz]

I like you! You allowed me a second, highly valuable perspective on this issue. Even posted on my date of birth. So it was just destined to be.

Answer 2

[Mehdi Mosafer]

There is a simpler way; just get the 2nd output of the function "boundary:"

[k,A] = boundary(x,y)

Here, "A" is the area.