# How to calculate an area with obtained nodes?

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shahin sharafi on 4 Aug 2021
Commented: shahin sharafi on 9 Aug 2021
Hi Everyone,
I am going to calculate the area covered by nodes in the plot, but I do not know how! Could someone help me?
Thank you,
The code is copied as bellow:
clear all;clc;close all
%%
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);
%%
counter=[];
KP=0:0.1:3;
KD=0:0.1:3;
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)
hold on
end
end
end
hold on
%% 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
shahin sharafi on 4 Aug 2021
Thank you for your response. Could you please use boundary function for my code for an example? I copied the code in the question part. I really need it. Thank you!

darova on 5 Aug 2021
An example of boundary function. polyarea is used to calculate area
r = 1;
x = linspace(-1,1,20);
y = sqrt(r^2 - x.^2);
x = [x; x];
y = [y; -y];
x = x(:);
y = y(:);
k = boundary(x(:),y(:));
plot(x,y,'.-r')
line(x(k),y(k))
legend('original order of points', 'boundary order') polyarea(x(k),y(k))
ans = 3.1016
pi*r^2
ans = 3.1416
shahin sharafi on 9 Aug 2021
Thank you so much

R2019a

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