How to Calculate Area Between a Curve and Two Lines?

Hi Everyone,

I am trying to calculate area (yellow area in attached figure) between curve and vertical and horizental axies lines. the code is provided as below. Could anyone help me?

Thank you in advance for you help.

Thank you,

clear all

clc

close all

%%

m=60;L=1;J=60;g=9.81;beta2=411.67;

KPb=2.15;KDb=0.75;

Time_Delay_Brain=0.19;

Time_Delay_Exo=0.05;

%%

for j=1:length(Time_Delay_Brain)

for jj=1:length(Time_Delay_Exo)

if Time_Delay_Exo(jj) ==0.05

n=11;

else

n=8;

end

%%

tau1=Time_Delay_Brain(j);tau2=Time_Delay_Exo(jj);

W = linspace(0, n*pi, 1000);omega=W;

Kpe=@(omega)J.*cos(omega.*tau2).*omega.^2 - KDb.*beta2.*omega.*sin(omega.*tau1 - omega.*tau2) + L.*cos(omega.*tau2).*g.*m - KPb.*beta2.*cos(omega.*tau1 - omega.*tau2);

Kde=@(omega)(omega.^2.*J.*sin(omega.*tau2) - KDb.*beta2.*omega.*cos(omega.*tau1 - omega.*tau2) + m.*g.*L.*sin(omega.*tau2) + KPb.*beta2.*sin(omega.*tau1 - omega.*tau2))./omega;

%%

D_Curve_PD_KPe=Kpe(omega);

D_Curve_PD_KDe=Kde(omega);

%%

plot(D_Curve_PD_KPe,D_Curve_PD_KDe,'color',[2*Time_Delay_Exo(jj) 2*Time_Delay_Brain(j) Time_Delay_Exo(jj) *Time_Delay_Brain(j)],'LineWidth', 0.2)

axis([0,18000,0,2500]);

hold on

end

hold on

end

plot([0 18000],[0 0],'color',[1 0 0],'LineWidth', 3)

plot([0 0],[0 2500],'color',[1 0 0],'LineWidth', 3)

Answer 1

[Scott MacKenzie]

At the end of your code, add...

x = D_Curve_PD_KPe;
y = D_Curve_PD_KDe;

cropLogical = x > 0;
x = x(cropLogical);
y = y(cropLogical);

% define vertices of polyshape and plot 
x = [0 0    x  x(end) 0];
y = [0 y(1) y  0      0];
ps = polyshape(x,y);
plot(ps, 'facecolor', 'y');

% compute and output area
a1 = polyarea(x,y);
fprintf('area = %.2f\n', a1);

Output:

area = 16482962.65

[N/A]

Thank you for your respone, I appreciate it. However, as I change the Time_Delay_Exo from 0.05 to 0.25, I will get the wrong answer. Actually, I need two conditions for cropLogical = x > 0; (for example cropLogical = x > 0 && cropLogical = y > 0; simultaneously) I will copy past the code again. Basicly, I need the area of curve that mentioned in following attached figures.

Thank you!

clear all

clc

close all

%%

m=60;L=1;J=60;g=9.81;beta2=411.67;

KPb=2.15;KDb=0.75;

% Time_Delay_Brain=0.19:0.001:0.2;

% Time_Delay_Exo=0.05:0.02:0.25;

Time_Delay_Brain=0.19;

Time_Delay_Exo=0.25;

%%

figure('DefaultAxesFontSize',15,'DefaultAxesFontName','Times')

for j=1:length(Time_Delay_Brain)

for jj=1:length(Time_Delay_Exo)

if Time_Delay_Exo(jj) ==0.05

n=11;

else

n=8;

end

%%

tau1=Time_Delay_Brain(j);tau2=Time_Delay_Exo(jj);

W = linspace(0, n*pi, 1000);omega=W;

Kpe=@(omega)J.*cos(omega.*tau2).*omega.^2 - KDb.*beta2.*omega.*sin(omega.*tau1 - omega.*tau2) + L.*cos(omega.*tau2).*g.*m - KPb.*beta2.*cos(omega.*tau1 - omega.*tau2);

Kde=@(omega)(omega.^2.*J.*sin(omega.*tau2) - KDb.*beta2.*omega.*cos(omega.*tau1 - omega.*tau2) + m.*g.*L.*sin(omega.*tau2) + KPb.*beta2.*sin(omega.*tau1 - omega.*tau2))./omega;

%%

D_Curve_PD_KPe=Kpe(omega);

D_Curve_PD_KDe=Kde(omega);

%%

plot(D_Curve_PD_KPe,D_Curve_PD_KDe,'color',[2*Time_Delay_Exo(jj) 2*Time_Delay_Brain(j) Time_Delay_Exo(jj) *Time_Delay_Brain(j)],'LineWidth', 0.2)

xlabel ('Exo Kp','FontSize',18, 'FontName', 'Times')

ylabel ('Exo Kd','FontSize',18, 'FontName', 'Times')

title('Kd vs Kp for Analytical Solution', 'FontName', 'Times','FontSize',14)

% axis([0,18000,0,2500]);

hold on

end

hold on

end

x = D_Curve_PD_KPe;

y = D_Curve_PD_KDe;

cropLogical = x > 0 ; %(I need "cropLogical = y > 0" Condition as well)

x = x(cropLogical);

y = y(cropLogical);

% define vertices of polyshape and plot

x = [0 0 x x(end) 0];

y = [0 y(1) y 0 0];

ps = polyshape(x,y);

plot(ps, 'facecolor', 'y');

% compute and output area

a1 = polyarea(x,y);

fprintf('area = %.2f\n', a1);

[Scott MacKenzie]

It sounds like you want the area in region I -- with 0,0 at the bottom-left. In this case, modify my code by changing

cropLogical = x > 0 ;

to

cropLogical = x > 0 & y > 0 ;

[N/A]

Thank you so much. It does work! You saved me