Asked by Kelly McGuire
on 15 Jan 2019

I have two overlapping spheres, and I am using the Monte Carlo method to calculate the volume of the combined spheres. Everything is working except for one part. I need to find a way to NOT double count points placed in the overlapping region so that I can correctly calculate the ratio of points inside the spheres to the points outside in the cube. Can someone help me with how not to double count points in the overlapping region? Here is my code so far:

clc

clear all

S=input('Number of Simulations: ');

N=input('Number of Points: ');

fileID = fopen('Volume.txt','w');

for k = 1:S

[X, Y, Z]=sphere;

a = [1 1 1 1.2; 2.293,1,1,1.8];

%Draw sphere #1

figure('color','white');

s1=surf(X*a(1,4)+a(1,1), Y*a(1,4)+a(1,2), Z*a(1,4)+a(1,3),'FaceColor', [1 1 1],'edgecolor','none','FaceAlpha',0.6);

light

axis equal

set(gca,'Color','k')

hold on

%Draw sphere #2

s2=surf(X*a(2,4)+a(2,1), Y*a(2,4)+a(2,2), Z*a(2,4)+a(2,3),'FaceColor', [0 1 0],'edgecolor','none','FaceAlpha',0.5);

daspect([1 1 1])

view(30,10)

xlabel('x')

ylabel('y')

zlabel('z')

x1range1 = -0.2;

x1range2 = 4.2;

y1range1 = -0.9;

y1range2 = 2.9;

z1range1 = -0.9;

z1range2 = 2.9;

hit1 = 0; %Points inside spheres

hit2 = 0;

for i = 1:N

%Define Box Range and Randomize Points

x = (x1range2-x1range1).*rand(N,1)+x1range1;

y = (y1range2-y1range1).*rand(N,1)+y1range1;

z = (z1range2-z1range1).*rand(N,1)+z1range1;

x1=x-1;

y1=y-1;

z1=z-1;

r1=sqrt(x1.^2+y1.^2+z1.^2);

x2=x-2.293;

y2=y-1;

z2=z-1;

r2=sqrt(x2.^2+y2.^2+z2.^2);

ii = r1<=1.2;

jj = r2<=1.8;

hit1 = sum(ii);

hit2 = sum(jj);

plot3(x(ii), y(ii), z(ii), 'w+');

%plot3(x(~ii), y(~ii), z(~ii), 'r+');

plot3(x(jj), y(jj), z(jj), 'g+');

drawnow

end

SpherePercentVolume = (hit1+hit2)/N;

Volume = ((x1range2-x1range1)*(y1range2-y1range1)*(z1range2-z1range1))*SpherePercentVolume

fprintf(fileID,'%6.3f\r\n',Volume);

end

fclose(fileID);

load Volume.txt

average = mean(Volume);

stdev = std(Volume);

fileID = fopen('AvgVolume.txt','w');

fprintf(fileID,'%6s','Average Volume: ');

fprintf(fileID,'%6.3f\r\n',average);

fprintf(fileID,'%6s','Standard Deviation: ');

fprintf(fileID,'%6.3f',stdev);

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## 2 Comments

## David Goodmanson (view profile)

Direct link to this comment:https://nl.mathworks.com/matlabcentral/answers/439801-duplicate-points-in-overlapping-section-of-two-overlapping-spheres#comment_660865

## Kelly McGuire (view profile)

Direct link to this comment:https://nl.mathworks.com/matlabcentral/answers/439801-duplicate-points-in-overlapping-section-of-two-overlapping-spheres#comment_660896

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