# 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
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Kye Taylor on 17 Jun 2013
Do you know the parametric equation for the circle in 3D?

Sean de Wolski on 17 Jun 2013

### More Answers (1)

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!!!