Deriving rotation angle from the eigenvectors

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Sophie Wuerger
Sophie Wuerger 2019-10-15
编辑： Matt J 2022-3-15
For an ellipsoid, how can I get the rotation angle from the eigenvectors?
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Sophie Wuerger
Sophie Wuerger 2019-10-15
编辑：Matt J 2022-3-15
I think I just found the solution for the 3d rotation.
[center,radii,ecvecs,v,chi2]=ellipsoid_fit(dat,'');
[x, y, z] = ellipsoid(center(1), center(2),center(3), radii(1),radii(2),radii(3),30);
S=surf(x, y, z,'FaceAlpha', 0.3, 'EdgeColor', 'none', 'FaceLighting', 'gouraud')
.....
theta1 = -asind(R(3,1)); % y-axis
psi1 = atan2d(R(3,2)/cos(theta1),R(3,3)/cos(theta1)); % x-axis
phi1 = atan2d(R(2,1)/cos(theta1),R(1,1)/cos(theta1)); % z-axis
direction = [1 0 0]; %
rotate(S,direction,psi1,center)
direction = [0 1 0];
rotate(S,direction,theta1,center)
direction = [0 0 1];
rotate(S,direction,phi1,center)
Does that look allright?
Is there an easy way to obtain the projection onto the axes?
best
sophie
Qingda Hu
Qingda Hu 2022-3-15
Probably too late but I was trying to use the same ellipsoid_fit function
If you linearize x,y,z and just multiple it by the evecs you get what you want
[center, radii, evecs, pars ] = ellipsoid_fit_new(... );
[X,Y,Z] = ellipsoid(0,0,0,radii(1),radii(2),radii(3));
Xlin = X(:);
Ylin = Y(:);
Zlin = Z(:);
rotatedXYZ = [Xlin,Ylin,Zlin]*evecs';
X = reshape( rotatedXYZ(:,1),size(X));
Y = reshape( rotatedXYZ(:,2),size(X));
Z = reshape( rotatedXYZ(:,3),size(X));
surf(X,Y,Z);
(you can translate it as well)
Hopefully this is useful for someone.

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回答（1 个）

Matt J
Matt J 2022-3-15
编辑：Matt J 2022-3-15
If you download ellipsoidalFit() to do the fitting, the yaw-pitch-roll angles are avaialble directly from the object,
https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics
>> load data
>> fitobj=ellipsoidalFit(xyz)
fitobj =
ellipsoidalFit with properties:
center: [5.0483 2.0378 7.0195]
a: 20.0700
b: 10.0469
c: 4.9622
yaw: 39.6951
pitch: -29.7995
roll: 50.4333

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