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Draw a circle for arbitrary orientation on spherical surface

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P Maity
P Maity on 6 Feb 2020
Commented: Adam Danz on 7 Feb 2020
I would like to draw a circular loop on spherical surface for a fixed orientation of theta(i.e. polar angle on sphere) and variying the azimuthal angle. The following code only generates the circle which are parallel to the equiatorial plane, but I need arbitrary orientation of ploar angle on the sphere. Pl somebody help me.
clear; clc;
N=10;
[X,Y,Z]=sphere(N);
C=zeros(N+1,N+1);
x=7;
y=1;
r=10;
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

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Accepted Answer

Jim Riggs
Jim Riggs on 7 Feb 2020
Edited: Jim Riggs on 7 Feb 2020
My approach is to define the circle around the X-axis, then rotate it into the desired position through a Yaw-Pitch rotation.
% Specify the user inputs
Rmag= 10; % Sphere radius
radius = 1; % circle radius
psi = 30*pi/180; % yaw rotation angle
theta = -45*pi/180; % pitch rotation angle (negative rotation is up)
% Define vectors and Calculate the YAW-PITCH transformation matrix
alpha = asin(radius/Rmag);
YAW = [cos(psi), -sin(psi), 0; sin(psi), cos(psi), 0; 0, 0, 1]; % Planar YAW rotation
PITCH = [cos(theta), 0, sin(theta); 0,1,0; -sin(theta), 0, cos(theta)]; % Planar PITCH rotation
YP = YAW*PITCH; % YAW-PITCH rotation matrix
% Rc = Column Vector pointing to circle on X-Axis (start point)
Rc = [Rmag*cos(alpha); 0; radius];
R = YP*[Rmag; 0; 0]; % Vector pointing to Circle center
% Now sweep the Rc vector around the X-axis to generate the circle
% This is done by adding a planar ROLL rotation to YP
clear C
C = []; % C is the vector containing the circle X-Y-Z cordinates
for phi = 0:pi/50:2*pi
ROLL = [1, 0, 0; 0, cos(phi), -sin(phi); 0, sin(phi), cos(phi) ];
YPR = YP*ROLL; % 3-dimentional transform
Rnew = YPR*Rc;
C = [C, Rnew];
end
% plot the result
[Sx,Sy,Sz]=sphere(50);
figure;
mesh(Rmag.*Sx, Rmag.*Sy, Rmag.*Sz); % draw the sphere
hold on;
plot3([0, R(1)], [0, R(2)], [0,R(3)], 'r'); % Vector to Circle center
plot3(C(1,:), C(2,:),C(3,:), 'b'); % Circle
axis equal

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Show 3 older comments
Jim Riggs
Jim Riggs on 7 Feb 2020
1) Make sure that your circle is calculated corectly.
2) If you still can't see the circle, that means that it is inside the mesh.
Try making the size of the sphere slightly smaller, (or slightly increase Rmag when calculating the circle)
Then the circle should be visible.
[EDIT] Also, you can make the mesh transparent with the following;
h = mesh(Rmag.*Sx, Rmag.*Sy, Rmag.*Sz); % draw the sphere
h.FaceColor = 'none';
or, you can make the face transparent by changing the "Alpha" value (1 = opaque (default) , <1 = transparent)
h.FaceAlpha = '0.85';
P Maity
P Maity on 7 Feb 2020
@Jim: Thanks a lot for your reply. It is appearing. It's really great.
Adam Danz
Adam Danz on 7 Feb 2020
Also, make sure the circle isn't appearing on the other side of the sphere that is not visible from the view point.
There are two solutions to that
1) use view(az,el) to rotate the plot.
2) make the sphere partially transparent.

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