How to find area enclosed between two curves?

Question

Prakash Chettri 2022-2-21

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1654835-how-to-find-area-enclosed-between-two-curves

回答： Torsten 2022-2-22

Lx = 150;     
Ly = 150;     
T0 =0;      
T1 = pi/4;   
T=3.175;
N=8;
W=N*T;
X0=Lx/2;
Y0=0;
W_nominal=W/2;
for a=1:2
r=rem(a,2);
if r==0
xp=0; xn=0; i=1;
while (xp>=0 && xp<=Lx/2) 
 XPaxisl(i)=xp+(i-1)*Lx/1200;     xp=XPaxisl(i);
 XNaxisl(i)=xn+(i-1)*(-Lx)/1200;  xn=XNaxisl(i);
 Th(i)=T0+2*((T1-T0)*(XPaxisl(i)))/Lx;
 TH(i)= T0+2*((T0-T1)*(XNaxisl(i)))/Lx;
 Wp(i)=W_nominal/cos(Th(i));
 WP(i)=W_nominal/cos(TH(i));
 ypl(i)=Wp(i)+(Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxisl(i))/Lx)))));
 ynl(i)=WP(i)+(Lx/(2*(T1-T0))*((-log(cos(T0)))+log(cos(T0+((2*(T0-T1)*XNaxisl(i))/Lx)))));
 i=i+1;
end
 plot(XPaxisl,ypl, '-g')
 hold on
 plot(XNaxisl,ynl, '-g')
 hold on
end
 %% shifting 
    r=rem(a,2);
    if r==0
     xp=0; xn=0; i=1; y=0; yn=0;
    while (xp>=0 && xp<=Lx/2) && (y<=Ly/2)
     XPaxiss1(i)=xp+(i-1)*Lx/1200;     xp=XPaxiss1(i);
     yps1(i) =(a*W_nominal)+Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxiss1(i))/Lx))));
i=i+1;
    end
    else
     xp=0; xn=0; i=1; y=0; yn=0;
    while (xp>=0 && xp<=Lx/2) && (y<=Ly/2)
      XPaxiss1(i)=xp+(i-1)*Lx/1200;     xp=XPaxiss1(i);
      XNaxiss1(i)=xn+(i-1)*(-Lx)/1200;  xn=XNaxiss1(i);
      yps1(i) =(a*W_nominal)+Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxiss1(i))/Lx))));
      yns1(i)= (a*W_nominal)+Lx/(2*(T1-T0))*((-log(cos(T0)))+log(cos(T0+((2*(T0-T1)*XNaxiss1(i))/Lx))));
i=i+1;
    end
 plot(XPaxiss1,yps1, '-r')
 hold on
 plot(XNaxiss1,yns1, '-r') 
 xlim([-Lx/2 Lx/2])
 ylim([-Ly/2 Ly/2])
    end
 end

I want to claculate the area between red and green curves using trapz but im not getting the exact result and it is showing error while calculating.can anyone tell how can i calculate area? I attached code for reference.

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Answer 1

Torsten 2022-2-22

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https://ww2.mathworks.cn/matlabcentral/answers/1654835-how-to-find-area-enclosed-between-two-curves#answer_901935

在 MATLAB Online 中打开

Lx = 150;     
Ly = 150;     
T0 =0;      
T1 = pi/4;   
T=3.175;
N=8;
W=N*T;
X0=Lx/2;
Y0=0;
W_nominal=W/2;
for a=1:2
    r=rem(a,2);
    if r==0
        xp=0; xn=0; i=1;
        while (xp>=0 && xp<=Lx/2) 
            XPaxisl(i)=xp+(i-1)*Lx/1200;     xp=XPaxisl(i);
            XNaxisl(i)=xn+(i-1)*(-Lx)/1200;  xn=XNaxisl(i);
            Th(i)=T0+2*((T1-T0)*(XPaxisl(i)))/Lx;
            TH(i)= T0+2*((T0-T1)*(XNaxisl(i)))/Lx;
            Wp(i)=W_nominal/cos(Th(i));
            WP(i)=W_nominal/cos(TH(i));
            ypl(i)=Wp(i)+(Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxisl(i))/Lx)))));
            ynl(i)=WP(i)+(Lx/(2*(T1-T0))*((-log(cos(T0)))+log(cos(T0+((2*(T0-T1)*XNaxisl(i))/Lx)))));
            i=i+1;
        end
        %figure(1)
        plot(XPaxisl,ypl, '-g')
        hold on
        plot(XNaxisl,ynl, '-g')
        hold on
        x1 = XPaxisl;
        y1 = ypl;
        x2 = XNaxisl;
        y2 = ynl;
    end
    %% shifting 
    r=rem(a,2);
    if r==0
        xp=0; xn=0; i=1; y=0; yn=0;
        while (xp>=0 && xp<=Lx/2) && (y<=Ly/2)
            XPaxiss1(i)=xp+(i-1)*Lx/1200;     xp=XPaxiss1(i);
            yps1(i) =(a*W_nominal)+Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxiss1(i))/Lx))));
            i=i+1;
        end
    else
        xp=0; xn=0; i=1; y=0; yn=0;
        while (xp>=0 && xp<=Lx/2) && (y<=Ly/2)
            XPaxiss1(i)=xp+(i-1)*Lx/1200;     xp=XPaxiss1(i);
            XNaxiss1(i)=xn+(i-1)*(-Lx)/1200;  xn=XNaxiss1(i);
            yps1(i) =(a*W_nominal)+Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxiss1(i))/Lx))));
            yns1(i)= (a*W_nominal)+Lx/(2*(T1-T0))*((-log(cos(T0)))+log(cos(T0+((2*(T0-T1)*XNaxiss1(i))/Lx))));
            i=i+1;
        end
        plot(XPaxiss1,yps1, '-r')
        hold on
        plot(XNaxiss1,yns1, '-r') 
        xlim([-Lx/2 Lx/2])
        ylim([-Ly/2 Ly/2])
        x3 = XPaxiss1;
        y3 = yps1;
        x4 = XNaxiss1;
        y4 = yns1;
    end
end
x2=x2(end:-1:1);
y2=y2(end:-1:1);
x4=x4(end:-1:1);
y4=y4(end:-1:1);
X1 = horzcat(x2(1:end-1),x1)
Y1 = horzcat(y2(1:end-1),y1);
X2 = horzcat(x4(1:end-1),x3)
Y2 = horzcat(y4(1:end-1),y3);
%figure(2)
%plot(X1,Y1)
%hold on
%plot(X2,Y2)
%xlim([-Lx/2 Lx/2])
%ylim([-Ly/2 Ly/2])
Area = trapz(X1,abs(Y1-Y2)) 

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Answer 2

Abolfazl Chaman Motlagh 2022-2-21

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1654835-how-to-find-area-enclosed-between-two-curves#answer_901375

在 MATLAB Online 中打开

i don't think the code you include in your question content related to what you want.

you have to vector, which are values of your curves at your grid points x.

here's an example for doing this task:

x = 0:0.1:20;

y1 = exp(x/2);

y2 = (x).^3;

dY = abs(y1-y2);

plot(x,y1,'Color','r','LineWidth',2);

hold on; grid on;

plot(x,y2,'Color','g','LineWidth',2);

plot(x,dY,'Color','b','LineWidth',2);

legend('y1 = exp(x/2)','y2= x^3','|y1-y2|','Location','best');

Diff = trapz(x,dY);

disp(['Area between 2 Curves :' num2str(Diff)])

Area between 2 Curves :26164.3149

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Prakash Chettri 2022-2-22

Thank you for the help. But i want to calculate area between curve given by "ypl(i)" and "yps1(i)" over x domain as XPaxisl(i) as noted in a code attached by me.

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