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Draw a circle for arbitrary orientation on spherical surface

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AVM
AVM 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

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
  6 Comments
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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