Rotate an Ellipsoid towards a point

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Hello to all,
I would like to rotate an elipsoid such that the major axis points torwards a point.
Currenly I have:
theta = linspace(0, pi, 25);
phi = linspace(0, 2*pi, 25) ;
x = 10*sin(theta)'*cos(phi);
y = 1*sin(theta)'*sin(phi);
z = 1*cos(theta)'*ones(size(phi));
surf(x,y,z)
alpha 0.5
xlim([-10 10])
ylim([-10 10])
zlim([-10 10])
hold on
scatter3(5,5,5)
quiver3(0,0,0, 5,5,5)
And I would like the major axis to point towards an arbitrary point. e.g., the point (5,5,5) . Since only one of axis will have a different dimension, I am not concerned with the rotation over the ellipsoid axis. How can I achieve this?
Best regards

Accepted Answer

Bruno Luong
Bruno Luong on 24 Apr 2022
Edited: Bruno Luong on 24 Apr 2022
axlgt = [5,1,1];
P = [5;6;7];
[~,i] = max(abs(axlgt));
ei = accumarray(i,1,[3,1]);
a=cross(P,ei);
T=makehgtform('axisrotate', a, -atan2(norm(a),P(i)));
R=T(1:3,1:3);
theta = reshape(linspace(0, pi, 25), 1, [], 1);
phi = reshape(linspace(0, 2*pi, 25), 1, 1, [] );
xyz0 = axlgt(:).*[sin(theta).*cos(phi);
sin(theta).*sin(phi);
cos(theta).*ones(size(phi))];
xyz = pagemtimes(R,xyz0);
xyz = permute(xyz,[2 3 1]);
figure;
surf(xyz(:,:,1),xyz(:,:,2),xyz(:,:,3))
shading flat
alpha 0.5
xlim([-10 10])
ylim([-10 10])
zlim([-10 10])
hold on
scatter3(P(1),P(2),P(3))
quiver3(0,0,0, P(1),P(2),P(3))
  2 Comments
Matt J
Matt J on 24 Apr 2022
@trailer ranger then you should Accept-click this, or one of the other answers, whichever works best for you.

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More Answers (2)

DGM
DGM on 24 Apr 2022
Edited: DGM on 24 Apr 2022
Try this:
theta = linspace(0, pi, 25);
phi = linspace(0, 2*pi, 25) ;
x = 10*sin(theta)'*cos(phi);
y = 1*sin(theta)'*sin(phi);
z = 1*cos(theta)'*ones(size(phi));
hs = surf(x,y,z);
pt = [5 5 5]; % this is the vector to which the ellipse should be aligned
majax = [1 0 0]; % this is the vector on which the ellipse is aligned
rotaxis = cross(majax,pt);
rotate(hs,rotaxis,90-atand(1/sqrt(2)),[0 0 0])
alpha 0.5
shading flat
xlim([-10 10])
ylim([-10 10])
zlim([-10 10])
hold on
scatter3(5,5,5)
quiver3(0,0,0, 5,5,5)
  3 Comments
trailer ranger
trailer ranger on 24 Apr 2022
Edited: trailer ranger on 24 Apr 2022
If I choose the point [1, 1, 0], it will look weird.
In the x-y plane looks incorrect:
In the x-z and y-z plane it look Ok.
Edit: The point [1,2,3] doest not look Okl:
theta = linspace(0, pi, 25);
phi = linspace(0, 2*pi, 25) ;
x = 10*sin(theta)'*cos(phi);
y = 1*sin(theta)'*sin(phi);
z = 1*cos(theta)'*ones(size(phi));
hs = surf(x,y,z);
pt = [1 2 3]; % this is the vector to which the ellipse should be aligned
majax = [1 0 0]; % this is the vector on which the ellipse is aligned
rotaxis = cross(majax, pt);
rotate(hs,rotaxis,90-atand(1/sqrt(2)),[0 0 0])
alpha 0.5
shading flat
hold on
scatter3(pt(1), pt(2), pt(3))
quiver3(0,0,0,pt(1), pt(2), pt(3))
xlim([-10 10])
ylim([-10 10])
zlim([-10 10])
xlabel("x")
ylabel("y")
zlabel("z")
% view ([90 0 0]) % y-z
% view ([0 90 0]) % x-z
view ([0 0 90]) % x-y

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Matt J
Matt J on 24 Apr 2022
Edited: Matt J on 24 Apr 2022
Very simple with this FEX package,
gtEllip=ellipsoidalFit.groundtruth([],[0,0,0],[10,1,1],[45,-45,0]);
plot(gtEllip)
  1 Comment
trailer ranger
trailer ranger on 24 Apr 2022
Hi,
Thanks for the reply! But I was hopping to get a solution without 3rd party packages.

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