Changing Vector Plot to Curve - Please HELP!

I am looking to calculate the area swept by h{13}. How do I change h{14} and h{15} to be able to find the area between two curves? Once they are changed, how can I calculate both the area and fill the area between the two curves?

hold on
axis ([-20 20 -20 20])
axis off
P1=[-11,0];
P2=[-1,0];
h{1}=plot([P1(1) P2(1)],[P1(2) P2(2)],'LineWidth',5,'Color','black');    
x=5*pi/8;
b=0:pi/40:x;
P7vct=nan(numel(b),2);
for k=1:numel(b)
    Z=[4,0];
    h{2}=viscircles(Z,5,'LineWidth',2,'LineStyle','--','Color','black');
    A=[0,0];
    h{3} = viscircles(A,1,'LineWidth',2,'Color','black'); 
    PA=A+[cos(b(k)-(pi)),sin(b(k)-(pi))];
    h{4}=viscircles(PA,.1,'Color','black');
    
    B = [4-4*cos(2*asin(.25)),-4*sin(2*asin(.25))];
    h{5} = viscircles(B,1,'LineWidth',2,'Color','green');
    PB=B+[cos(-b(k)-(pi/2)),sin(-b(k)-(pi/2))];
    h{6}=viscircles(PB,.1,'Color','green');
    
    C = [4-4*cos(4*asin(.25)),-4*sin(4*asin(.25))];
    h{7} = viscircles(C,1,'LineWidth',2,'Color','blue');
    PC=C+[cos(b(k)-(pi/2)),sin(b(k)-(pi/2))];
    h{8}=viscircles(PC,.1,'Color','blue');
    
    D = [4-4*cos(6*asin(.25)),-4*sin(6*asin(.25))];
    h{9} = viscircles(D,1,'LineWidth',2,'Color','red');
    PD=D+[cos(-b(k)-(pi/2)),sin(-b(k)-(pi/2))];
    h{10}=viscircles(PD,.1,'Color','red');
    
    E = [4-4*cos(8*asin(.25)),-4*sin(8*asin(.25))];
    h{11} = viscircles(E,1,'LineWidth',2,'Color','yellow');
    PE=E+[cos(b(k)-(pi/2)),sin(b(k)-(pi/2))];
    h{12}=viscircles(PE,.1,'Color','yellow');
    
    P3=B+[cos(b(k)),sin(b(k))];
    P4=C+[cos(b(k)),sin(b(k))];
    P5=D+[cos(b(k)),sin(b(k))];
    P6=E+[cos(b(k)-x),sin(b(k)-x)];
    P7=E+[11*cos(b(k)-x),11*sin(b(k)-x)];
    
    P6vct(k,:)=P6;
    P7vct(k,:)=P7;
    
    h{13} = plot([P6(1) P7(1)],[P6(2) P7(2)],'LineWidth',5,'Color','black');
    h{14}=plot(P6vct(:,1),P6vct(:,2),'LineWidth',3,'Color','black');
    h{15}=plot(P7vct(:,1),P7vct(:,2),'LineWidth',3,'Color','black');
    
    drawnow();
    pause(0.001);
    if k<numel(b)
    delete(vertcat(h{2:13}));
    end
end
hold off
axis ([-20 20 -20 20])
axis off

Answer 1

[Dev]

Hi @Allison Bushman,

By calculating the area swept by h{13}, I am assuming that we aim to calculate the area covered by the h{13} arm when it moves around the circumference of the h{14} arc.

To achieve the same, we can use the ‘polyarea’ function in MATLAB along with the ‘flipud’ function. For a detailed usage of these functions, please refer the documentation links below-

https://www.mathworks.com/help/releases/R2024b/matlab/ref/polyarea.html

https://www.mathworks.com/help/releases/R2024b/matlab/ref/flipud.html

I have also attached a reference code snippet which uses both these functions below.

% Calculate the area between the two curves
area = polyarea([P6vct(:,1); flipud(P7vct(:,1))], [P6vct(:,2); flipud(P7vct(:,2))]);

Next, to fill the area swept, we can use the ‘fill’ function in MATLAB. Below is a reference code snippet which fills in the area swept with a ‘cyan’ colour.

% Fill the area between the two curves
fill([P6vct(:,1); flipud(P7vct(:,1))], [P6vct(:,2); flipud(P7vct(:,2))], 'cyan', 'FaceAlpha', 0.5);

More information on the same can be found below-

https://www.mathworks.com/help/releases/R2024b/matlab/ref/fill.html

I have also attached the output plot received after using the above function for your reference below-

Here, the area swept by the arc h{13} (green) on the curve h{14} (black) is filled with ‘cyan’ colour.

I hope the above approach solves the purpose.