Making a spherical cap using equations of sphere

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hamzah khan
hamzah khan on 24 Mar 2022
Answered: hamzah khan 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(0, 'DefaultFigureRenderer','painters');
set(0, 'DefaultFigureRenderer', 'OpenGL');
% 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)) ;
hold on
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
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.

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Accepted Answer

Bruno Luong
Bruno Luong on 24 Mar 2022
phi=linspace(pi/2,pi/6,30); % the cap end is determined by pi/6 change accordinglt
axis equal;
Bruno Luong
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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More Answers (1)

hamzah khan
hamzah khan on 29 Mar 2022
alternate 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);
active = (X.^2 + Y.^2 + Z.^2 <= R^2) & (X.^2 + Y.^2 +Z.^2 >= r^2) & (abs(theta) <= alpha);
hold on

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