How to Calculate an area in MATLAB

Hi

I am going to to calculate the area covered by nodes using boundary and polyarea functions. However, calculated area is not correct. For comparison, I did sketched a triangle in code and compared its area with area covered by nodes. Even though the nodes area is larger than triangle one, Calculated area of triangle is bigger than nodes area. Why does not ployarea work in this situation?

Thank you in advance for your help.

Regards,

clear all;clc;close all
%%
x=[1.5;1.5;2.7];
y=[0.4;1.2;0.85];
plot(x,y,'o')
k = boundary(x,y,0.1);% generate boundary of data points
hold on;
plot(x(k),y(k));
Triangle_A = polyarea(x,y)
hold on
%%
Mass=60;Lenght=1;g=10;Ja=60;alpha=(Mass*Lenght*g)/Ja;Zeta3=411.67/Ja;
Time_Delay=0.2;
N=7;
%% 
s1=0;
s2=-Time_Delay;
[Phi_0_s,Phi_TD_s,Diff_Phi_TD_s]=Shape_Function(N,Time_Delay,s1,s2);
%%  
 [M,K]=M_K(N,Time_Delay);
%% 

count=1;
KP=0:0.1:3;
KD=0:0.1:3; 
x=zeros(1,count);
y=zeros(1,count);
 for ii=1:length(KP)
 KP(ii);
 for i=1:length(KD)
     
     
       
         KP1=Zeta3*KP(ii);
         KD1=Zeta3*KD(i);
        L=Evaluation(KP1,KD1,alpha,Phi_0_s,Phi_TD_s,M,K);

Max_Real_EignValues=max(real(eig(L)));

if Max_Real_EignValues<0
    plot(KP(ii),KD((i)),'r*','MarkerSize',5)
    
    x(1,count)=KP(ii);
    y(1,count)=KD(i);
    count=count+1;
    hold on
end

end
 end 
 hold on
 k = boundary(x',y');% generate boundary of data points
 plot(x(k),y(k))
 Curve_Area= polyarea(x,y)
%%  Below Lines are the functions related to top calculations



function [Phi_0_s,Phi_TD_s,Diff_Phi_TD_s]=Shape_Function(N,Time_Delay,s1,s2)

Phi_0_s(1)=1;
Phi_0_s(2)=1+2*s1/Time_Delay;  
for k=3:N
Phi_0_s(k)=((2*k-3)*Phi_0_s(2)*Phi_0_s(k-1)-(k-2)*Phi_0_s(k-2))/(k-1);
end 
Phi_0_s=Phi_0_s';
%% 
Phi_TD_s(1)=1;
Phi_TD_s(2)=1+2*s2/Time_Delay;  
for k=3:N
Phi_TD_s(k)=((2*k-3)*Phi_TD_s(2)*Phi_TD_s(k-1)-(k-2)*Phi_TD_s(k-2))/(k-1);
end 
Phi_TD_s=Phi_TD_s';
%% 
syms s
Phi_TTD_s=sym(zeros(1,N));
Phi_TTD_s(1)=1;
Phi_TTD_s(2)=1+2*s/Time_Delay;  
for k=3:N
Phi_TTD_s(k)=((2*k-3)*Phi_TTD_s(2)*Phi_TTD_s(k-1)-(k-2)*Phi_TTD_s(k-2))/(k-1);
end 
Diff_Phi_TD_s=diff(Phi_TTD_s,s);
Diff_Phi_TD_s=eval(subs(Diff_Phi_TD_s,s,-Time_Delay));
Diff_Phi_TD_s=double(Diff_Phi_TD_s);
Diff_Phi_TD_s=Diff_Phi_TD_s';

end 
%%
function  [A,B]=M_K(N,Time_Delay)

Delta=zeros(N,N);
A=zeros(N,N);
B=zeros(N,N);
for i=1:N
    for j=1:N
       if i==j
        Delta(i,j)=1;
       else 
         Delta(i,j)=0;  
       end
    end
    end 
for i=1:N
    for j=1:N
A(i,j)=(Time_Delay*Delta(i,j))/(2*i-1);  
      if i<j
       if rem(i+j, 2) == 1 
           B(i,j)=2; 
       else 
          B(i,j)=0;     
    end 
   end 
  end 
end

end
%%
function [L]=Evaluation(KP1,KD1,alpha,Phi_0_s,Phi_TD_s,M,K)
kp=KP1;
kd=KD1;

%% G1&G2
G1=alpha*Phi_0_s'-kp*Phi_TD_s';
G2=-kd*Phi_TD_s';
%% C3
C3=Phi_0_s'*inv(M)*Phi_0_s;
%% X Matrix
X1=(Phi_0_s*Phi_0_s')/C3;
X2=-((Phi_0_s*Phi_0_s'/M)*K)/C3;
X3=(Phi_0_s*G1)/C3;
X4=(Phi_0_s*G2-(Phi_0_s*Phi_0_s'/M)*K)/C3;
%% L Matrix
L1=K/M+X2/M;
L2=X1/M;
L3=X3/M;
L4=K/M+X4/M;

L=[L1 L2;L3 L4];

end

Answer 1

[KSSV]

This line:

Curve_Area= polyarea(x,y)

Should be

Curve_Area= polyarea(x(k),y(k))

Then you shall get:

Triangle_A =

    0.4800


Curve_Area =

    0.6450

[N/A]

Thank you so much.