Making a spherical cap using equations of sphere

16 次查看（过去 30 天）
Chris Dan
Chris Dan 2022-3-24
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?
  1 个评论
Bruno Luong
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.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Bruno Luong
Bruno Luong 2022-3-24
Ran in:
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 个评论
显示 6更早的评论
Chris Dan
Chris Dan 2022-3-24
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
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.

请先登录，再进行评论。

更多回答（1 个）

Chris Dan
Chris Dan 2022-3-29
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')

类别

在 Help Center 和 File Exchange 中查找有关 Surface and Mesh Plots 的更多信息

标签

产品


版本

R2020a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by