Intersection of three cylinders

I am trying to graph the intersection of three perpendicular cylinders each centered along one of the axes. I’m using a provided program to graph over a polar region. I started by finding the intersection of two cylinders and then trying to intersect with the third but I’m not sure how to do this. Any hints are appreciated.

Answer 1

[KSSV]

Have a look here:

https://in.mathworks.com/matlabcentral/answers/93623-how-do-i-plot-the-line-of-intersection-between-two-surfaces

[Kat]

Thank you, that helps!

Answer 2

[Joffre Veloz Pazmiño]

This is the volume of the 3-cylinder intercession

clc,clear
r0 = 2;
t = linspace(0,2*pi,9);        
r = repmat([0 r0/sqrt(2)],[1 4]);   
r = [r 0];
t1 = linspace(0,6*pi,90);
r1 = interp1(t,r,t1);               

T = [t1;t1];
Z = [r1;-r1];
[X,Y] = pol2cart(T,r0);             

h(1) = surf(X,Y,Z);
h(2) = surface(X,Z,Y);
h(3) = surface(Z,Y,X);
[x1,y1] = pol2cart(t1,r0);

line(x1,y1,r1,'linewidth',3)
line(x1,y1,-r1,'linewidth',3)

axis equal