Making a spherical cap using equations of sphere

Question

Chris Dan 2022-3-24

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1679549-making-a-spherical-cap-using-equations-of-sphere

回答： Chris Dan 2022-3-29

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?

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Bruno Luong 2022-3-24

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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Answer 1

Bruno Luong 2022-3-24

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1679549-making-a-spherical-cap-using-equations-of-sphere#answer_925864

在 MATLAB Online 中打开

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;

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Chris Dan 2022-3-24

在 MATLAB Online 中打开

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 
radius_1 = p(size(p,2))/2; 
radius_2 = radius_1/2;
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 2022-3-24

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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Answer 2

Chris Dan 2022-3-29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1679549-making-a-spherical-cap-using-equations-of-sphere#answer_929559

在 MATLAB Online 中打开

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);
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')