# Making a spherical cap using equations of sphere

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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);

radius_1 = p(size(p,2))/2;

radius_2 = radius_1 /2;

[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?

##### 1 Comment

Bruno Luong
on 24 Mar 2022

### Accepted Answer

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;

##### 8 Comments

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.

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