# How to do a 3D circle in matlab

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john pag on 17 Jun 2013
Hello,
I need a code for a 3D circle. I have the code but i can not to do 3D.
Thank you
Kye Taylor on 17 Jun 2013
Do you know the parametric equation for the circle in 3D?

Sean de Wolski on 17 Jun 2013

Kye Taylor on 17 Jun 2013
Edited: Kye Taylor on 17 Jun 2013
I assume you do not have a parametric form for the circle in 3D, but you do have the equation for the plane where the circle lives in 3D. In that case, i would solve this problem by creating the data in the xy-plane
% Original points, original plane
t = linspace(0,2*pi);
x = cos(t);
y = sin(t);
z = 0*t;
pnts = [x;y;z];
% unit normal for original plane
n0 = [0;0;1];
n0 = n0/norm(n0);
Then, I would rotate the circle data into a new plane
% unit normal for plane to rotate into
% plane is orthogonal to n1... given by equation
% n1(1)*x + n1(2)*y + n1(3)*z = 0
n1 = [1;1;1];
n1 = n1/norm(n1);
% theta is the angle between normals
c = dot(n0,n1) / ( norm(n0)*norm(n1) ); % cos(theta)
s = sqrt(1-c*c); % sin(theta)
u = cross(n0,n1) / ( norm(n0)*norm(n1) ); % rotation axis...
u = u/norm(u); % ... as unit vector
C = 1-c;
% the rotation matrix
R = [u(1)^2*C+c, u(1)*u(2)*C-u(3)*s, u(1)*u(3)*C+u(2)*s
u(2)*u(1)*C+u(3)*s, u(2)^2*C+c, u(2)*u(3)*C-u(1)*s
u(3)*u(1)*C-u(2)*s, u(3)*u(2)*C+u(1)*s, u(3)^2*C+c];
% Rotated points
newPnts = R*pnts;
Visualize:
plot3(newPnts(1,:),newPnts(2,:),newPnts(3,:),'ko')
Rudranarayan Kandi on 12 Sep 2018
very nice approach for plotting in a different plane with normal specified.!!!! Cheers!!!