Spherical Patch in 3D

Hello,

I am trying to make a 3d spherical segment. I am having problems with the atan2 function. in 2D my code is

clear all; close all;
p = linspace(-1/2,1/2,200);
[X,Y] = meshgrid(p,p); % box mesh
R = p(size(p,2))/2;
r = R/1.5;
alpha = deg2rad(45);

theta = atan2(Y,X);
f = figure('visible','on');
active = (X.^2 + Y.^2  <= R^2) & (X.^2 + Y.^2 >= r^2);
plot(X(active),Y(active),'o','MarkerFaceColor','blue');

active = (X.^2 + Y.^2  <= R^2) & (X.^2 + Y.^2 >= r^2) & (abs(theta)< alpha); 
hold on
plot(X(active),Y(active),'o','MarkerFaceColor','red');

here every thing is as I want(the red patch) ,but when I try to make the same patch in 3D, I am getting getting the wrong shape.

here is my code:

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;
alpha = deg2rad(45);
f = figure('visible','on');

theta = atan2(Z,X);

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')

Can anyone tell me what is wrong? I figured it out to be theta...

Does any one knows how to take correct angle

Answer 1

[Chris Dan]

I found out the answer

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;
alpha = deg2rad(45);
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')

Answer 2

[KSSV]

The shape is spherical and looks fine. You need to set the axis. Try

axis equal 

at the end.

[Chris Dan]

i found out the answer

theta = atan2(sqrt(X.^2+Y.^2),Z);