How to plot a circle on a spherical surface?

Question

Dhritiman Talukdar 2018-8-30

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/416808-how-to-plot-a-circle-on-a-spherical-surface

编辑： Walter Roberson 2024-8-25，19:06

I have written a code which plots a circle(with center (x,y) and radius r) on the surface of a sphere. But, it does not work properly in the boundary, that is near y=0. The code:

close all; clear all; clc
N=100;
[X,Y,Z]=sphere(N);
C=zeros(N+1,N+1);
x=75;
y=1;
r=15;
for i=1:N+1
    for j=1:N+1
        d=sqrt(((i-x)^2)+((j-y)^2));
        if (d<=r)
            C(i,j)=1;
        end
    end
end
figure
surf(X,Y,Z,C)
axis equal
% shading interp
% light

The code works properly for values of y>r like y=15,16,17... Can anybody please help to make it work for values of y less than r?

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KALYAN ACHARJYA 2018-8-30

编辑：KALYAN ACHARJYA 2018-8-30

在 MATLAB Online 中打开

Check it for y=100, not circle. Also, if condition always false, by varying y value.

d<=r

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Answer 1

KALASH 2024-8-25，18:57

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/416808-how-to-plot-a-circle-on-a-spherical-surface#answer_1504739

编辑：Walter Roberson 2024-8-25，19:06

在 MATLAB Online 中打开

Hi @Dhritiman Talukdar,

I understand that you want to plot a circle on the surface of the sphere. The issue you're encountering is related to how the circle is defined on the surface of the sphere. When y is close to zero, the circle might be partially or entirely outside the bounds of the sphere's surface parameterization due to the way you're calculating the distance d in a Cartesian coordinate system rather than on the sphere's surface.

Have a look at the below code for a possible solution:

close all; clear all; clc 
N = 100; 
[X, Y, Z] = sphere(N); 
% Parameters for the circle 
x = 75; % Longitude in degrees 
y = 1;  % Latitude in degrees 
r = 15; % Radius in degrees 
% Convert degrees to radians for computation 
x_rad = deg2rad(x); 
y_rad = deg2rad(y); 
r_rad = deg2rad(r); 
% Calculate the circle's center in Cartesian coordinates 
center_x = cos(y_rad) * cos(x_rad); 
center_y = cos(y_rad) * sin(x_rad); 
center_z = sin(y_rad); 
% Create a circle in spherical coordinates 
theta = linspace(0, 2*pi, 100); 
circle_x = cos(r_rad) * cos(theta); 
circle_y = cos(r_rad) * sin(theta); 
circle_z = sin(r_rad) * ones(size(theta)); 
% Rotate circle to the correct position on the sphere 
% Rotation matrix to align the circle with the sphere's surface 
R = [cos(x_rad), -sin(x_rad), 0; sin(x_rad), cos(x_rad), 0; 0, 0, 1] * ... 
    [cos(y_rad), 0, sin(y_rad); 0, 1, 0; -sin(y_rad), 0, cos(y_rad)]; 
circle_points = R * [circle_x; circle_y; circle_z]; 
% Plot the sphere 
figure 
surf(X, Y, Z, 'FaceAlpha', 0.5, 'EdgeColor', 'none'); 
hold on 
% Plot the circle on the sphere 
plot3(circle_points(1, :), circle_points(2, :), circle_points(3, :), 'r-', 'LineWidth', 2); 
% Set the view and other plot properties 
axis equal 
xlabel('X') 
ylabel('Y') 
zlabel('Z') 
title('Circle on Sphere') 
grid on 
hold off 