Plot only the surfaces within a bounding surface?

I have a large cylinder with base in the x-y plane intersected by smaller cylinders with base in the x-z plane. I'd like to plot only the surfaces belonging to the larger cylinder, however my smaller cylinder sticks out of the larger volume. How can I make the surface of the small cylinder bounded by the large cylinder?

Below is the code.

rs = 9.0;
Cxt = -6.0;
Czt = 3.0;
dia_tube = 1.0;

% for the larger cylinder plotting
[xs1 ys1] = GetCircle(rs, 0, 0, 0, 2*pi);
Ns = length(xs1);
zmins = zeros(1,Ns);
zmaxs = zeros(1,Ns) + 6;
xs = [xs1;xs1];
ys = [ys1;ys1];
zs = [zmins;zmaxs];
surf(xs,ys,zs);
alpha 0.5;
hold on

% for smaller cylinder(s)
[xt zt] = GetCircle(dia_tube*0.5, Cxt, Czt, 0, 2*pi);
    for i = 1:Ns
    ymin = -(rs^2 - xt(i)^2)^(1/2);
    ymax = (rs^2 - xt(i)^2)^(1/2);
    end
xt = [xt;xt];
yt = [ymin;ymax];
zt = [zt;zt];
surf(xt,yt,zt);
axis equal

% with the circle generator 
function [x y] = GetCircle(r, h, k, a, b)
    t = linspace(a, b, 40);
    x = r*cos(t) + h;
    y = r*sin(t) + k;
end

I was hoping ymin and ymax would allow me to do this, but we just find the min and max of the x data such that the edge of the tubes are aligned.

I also tried changing

yt = [ys1;ys1];

to match the cylinder case, but this left me with a weird 2D shape. Thanks for your help.

Answer 1

[iontrap]

I was able to figure out the solution:

[xt zt] = GetCircle(dia_tube*0.5, Cxt, Czt, 0, 2*pi); %% make a circle for the small cylinder
for i = 1:Ns
    y_temp(i) = sqrt(rs^2 - (xt(i))^2); %% the y value belonging to the large cylinder corresponding to a given x value of small cylinder.
end
xt3 = [xt;xt]; %% change this to a different variable for clarity.
yt3 = [y_temp;-y_temp];
zt3 = [zt;zt];
surf(xt3,yt3,zt3);

gives the result -

[Mathieu NOE]

yeah, I was about to send you my code

it's the same but no need for the for loop

rs = 9.0;
Cxt = -6.0;
Czt = 3.0;
dia_tube = 1.0;
% for the larger cylinder plotting
[xs1, ys1] = GetCircle(rs, 0, 0, 0, 2*pi);
Ns = length(xs1);
zmins = zeros(1,Ns);
zmaxs = zeros(1,Ns) + 6;
xs = [xs1;xs1];
ys = [ys1;ys1];
zs = [zmins;zmaxs];
surf(xs,ys,zs);
alpha 0.5;
hold on

% for smaller cylinder(s)
[xt, zt] = GetCircle(dia_tube*0.5, Cxt, Czt, 0, 2*pi);
y_temp = sqrt(rs^2 - xt.^2);
xt = [xt;xt];
yt = [y_temp;-y_temp];
zt = [zt;zt];
surf(xt,yt,zt);
axis equal

% with the circle generator 
function [x, y] = GetCircle(r, h, k, a, b)
    t = linspace(a, b, 40);
    x = r*cos(t) + h;
    y = r*sin(t) + k;
end

[iontrap]

Great! Thanks for your help.

[Mathieu NOE]

my pleasure !

Answer 2

[Mathieu NOE]

hello

seems to me there is no need for a for loop to compute ymin & ymax

also ymin = - ymax , so we can avoid creating yet another variable in the workspace

and ymax can be directly computed as

ymax = (rs^2 - (abs(Cxt)+0.5*dia_tube)^2)^(1/2);

final result :

rs = 9.0;
Cxt = -6.0;
Czt = 3.0;
dia_tube = 1.0;
% for the larger cylinder plotting
[xs1, ys1] = GetCircle(rs, 0, 0, 0, 2*pi);
Ns = length(xs1);
zmins = zeros(1,Ns);
zmaxs = zeros(1,Ns) + 6;
xs = [xs1;xs1];
ys = [ys1;ys1];
zs = [zmins;zmaxs];
surf(xs,ys,zs);
alpha 0.5;
hold on
% for smaller cylinder(s)
[xt, zt] = GetCircle(dia_tube*0.5, Cxt, Czt, 0, 2*pi);
ymax = (rs^2 - (abs(Cxt)+0.5*dia_tube)^2)^(1/2);
xt = [xt;xt];
yt = [ymax;-ymax];
zt = [zt;zt];
surf(xt,yt,zt);
axis equal

% with the circle generator 
function [x, y] = GetCircle(r, h, k, a, b)
    t = linspace(a, b, 40);
    x = r*cos(t) + h;
    y = r*sin(t) + k;
end

[iontrap]

Thanks for your response. The reason I tried to use a loop was to create a curved bounding surface rather than a planar bounding surface. There is still the problem shown in the attached picture.