MATLAB: Fit a circle to 3d dots

fitting circle to data

Hi, I have dots spread like a tube in a 3d space. I want to fit a circle to this data (the data is attached). The plane that the circle should be in is:
   S1=[-15.8,8.6,1.3];
   S2=[-10.5,10.3,-3.3];
   S3=[-15.2,8.9,1.6];
   normal = cross(S1-S2, S1-S3);
   A = normal(1); B = normal(2); C = normal(3);
   D = dot(normal,S1);
This is what I was trying to do:
    plot3(n1,n2,n3,'*')   %The dots
    hold on
    a2=[mean(n1),mean(n2),mean(n3)]; %Center of the dots
    plot3(a2(1),a2(2),a2(3),'*','color','g')
    a3=dist(a2,[n1;n2;n3]); %calculate the radius
    t = linspace(0,2*pi,40);
    x=(mean(a3).*sin(t)+mean(n1));
    y=(mean(a3).*cos(t)+mean(n2));
    z = (A * x + B * y - D)/(-C);
    plot3(x,y,z,'*','color','r')
But I can't set the circle right in place (it is grater than what it should be). could you help?

Best Answer

There is probably something not working with the way you rotate the circle back into the plane. This works:
S1=[-15.8,8.6,1.3];
S2=[-10.5,10.3,-3.3];
S3=[-15.2,8.9,1.6];
normal  = cross(S1-S2, S1-S3);                % compute reference frame axes
nz      = normal'/norm(normal);
normal2 = cross(nz, [0; 1; 0]);
nx      = normal2/norm(normal2);
ny      = cross(nz, nx)/norm(cross(nz, nx));  % end compute reference frame axes
R       = [nx ny nz];                         % compute rotation matrix 
plot3(n1,n2,n3,'*')   %The dots
hold on; grid; box;
a2=[mean(n1),mean(n2),mean(n3)]; %Center of the dots
plot3(a2(1),a2(2),a2(3),'*','color','g')
a3=dist(a2,[n1;n2;n3]); %calculate the radius
t = linspace(0,2*pi,40);
x0=(mean(a3).*sin(t));                        % get circle coordinates in x-y plane...
y0=(mean(a3).*cos(t));
z0      = zeros(1,length(x0));
xyz     = bsxfun(@plus, R*[x0; y0; z0], a2'); % rotate circle plane and adjust center
plot3(xyz(1,:),xyz(2,:),xyz(3,:),'-','color','r')
Related Question