# Making a spherical cap using equations of sphere

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Chris Dan on 24 Mar 2022
Answered: Chris Dan on 29 Mar 2022
Hello everyone,
I am trying to make a spherical cap using points or nodes and mesh grid . I dont want to use built in functions. I am having some problems. Here is my code
% plotting script
% select : which plot you want
set(groot,'defaultLegendInterpreter','latex');
set(0, 'DefaultFigureRenderer','painters');
set(0, 'DefaultFigureRenderer', 'OpenGL');
set(groot,'defaultAxesTickLabelInterpreter','latex');
set(groot,'defaulttextInterpreter','latex');
%%
% Plot the sphere or spherical patch
p = linspace(-1/2,1/2,10);
[X,Y,Z] = meshgrid(p,p,p);
theta= atan(Y./X);
active = (X.^2+Y.^2 +Z.^2 <= radius_1);
active_2 = (X.^2+Y.^2 +Z.^2 <= (radius_1 -radius_2)) ;
figure()
plot3(X(active),Y(active),Z(active),'o','MarkerFaceColor','red');
hold on
plot3(X(active_2),Y(active_2),Z(active_2),'o','MarkerFaceColor','cyan');
I cannot draw the spherical cap. I have the thetha but how do i use it to cut the sphere to make spherical cap and i want to know which nodes are inside the cap and which are outside the cap using mesh grid.
Does anyone knows how to do it?
Bruno Luong on 24 Mar 2022
X.^2+Y.^2 +Z.^2 is the square of the distance to origin, then you compare with radius and diffderence of radius, it does noot make any interpretable sense to me.

Bruno Luong on 24 Mar 2022
phi=linspace(pi/2,pi/6,30); % the cap end is determined by pi/6 change accordinglt
theta=linspace(0,2*pi,120);
r=3;
[PHI,THETA]=meshgrid(phi,theta);
X=r*cos(THETA).*cos(PHI);
Y=r*sin(THETA).*cos(PHI);
Z=r*sin(PHI);
surf(X,Y,Z)
axis equal;
Chris Dan on 24 Mar 2022
hii,
thanks . this is my code now
clear all; close all;
p = linspace(-1/2,1/2,50);
[X,Y,Z] = meshgrid(p,p,p); % box mesh
active = (X.^2+Y.^2 +Z.^2 <= radius_1 & Z >= radius_2); % plot sphere
figure()
plot3(X(active),Y(active),Z(active),'o','MarkerFaceColor','red');
hold on
and it is making the spherical cap, thanks
one last question, if i want to fit in the angle thetha, how can i use it?
theta is the angle between y and x if we look at the sphere is 2D
Bruno Luong on 24 Mar 2022
Sorry I don't understand what you ask for.
And in your last code you are still compare distance squared with radius without squared.

### More Answers (1)

Chris Dan on 29 Mar 2022
clear all; close all;
p = linspace(-1/2,1/2,100);
[X,Y,Z] = meshgrid(p,p,p); % box mesh
R = p(size(p,2))/2;
r = R/1.5;
f = figure('visible','on');
theta = atan2(sqrt(X.^2+Y.^2),Z);
active = (X.^2 + Y.^2 + Z.^2 <= R^2) & (X.^2 + Y.^2 +Z.^2 >= r^2);
plot3(X(active),Y(active),Z(active),'o','MarkerFaceColor','blue');
active = (X.^2 + Y.^2 + Z.^2 <= R^2) & (X.^2 + Y.^2 +Z.^2 >= r^2) & (abs(theta) <= alpha);
hold on
plot3(X(active),Y(active),Z(active),'o','MarkerFaceColor','red');
saveas(f,'3d_patch','fig')

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