Rotate an Ellipsoid towards a point

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

Answer 1

[Bruno Luong]

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))

[trailer ranger]

Nice! This code appears to work like a charm!

[Matt J]

@trailer ranger then you should Accept-click this, or one of the other answers, whichever works best for you.

Answer 2

[DGM]

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)

[trailer ranger]

Hi, Thanks for the answer.

I have updated the question to account for an arbitrary point in space.

Would you please be so kind as to adapt the answer? What is the rotate function doing?

[DGM]

I edited it so that you can enter the destination point.

[trailer ranger]

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

Answer 3

[Matt J]

Very simple with this FEX package,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

gtEllip=ellipsoidalFit.groundtruth([],[0,0,0],[10,1,1],[45,-45,0]);

plot(gtEllip)

[trailer ranger]

Hi,

Thanks for the reply! But I was hopping to get a solution without 3rd party packages.