How to Calculate an area in MATLAB

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N/A
N/A 2021-8-6
评论： N/A 2021-8-6
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

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采纳的回答

KSSV
KSSV 2021-8-6
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

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