Fit ellipse in 3D space
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I have xy coordinates of the ellipse in 2D space and its coordinate center (0.1427, -0.4418).
I would like to fit this ellipse xy coordinates in to the 3D space to replace the one which is not correct/perfect. The coordinate center in 3D space should be (0.1427, -0.4418, -0.0564) and the plane is defined in attachment.
How can I calculate the missing z axis data to draw the ellipse in 3D space on the desired plane?
Matt J on 28 Sep 2022
Edited: Matt J on 28 Sep 2022
Another possibility is to use this FEX download,
to fit the 3D data directly.
fobj=planarFit(xyz); %Fit a plane to xyz data
Rxyz=R*xyz; %Rotate xyz coordinates to be parallel to xy plane
fobj=ellipticalFit(Rxyz(1:2,:)); %ellipse fit to the rotated data (ignoring z-coordinate)
Rxyz=cell2mat(fobj.sample(0:2:360)); %Generate 'evenly' spaced samples around the ellipse
Rxyz(3,:)=z0; %re-insert z-coordinate
xyzFit=R'*Rxyz; %rotate back to 3D
scatter3(xyz(1,:),xyz(2,:),xyz(3,:),'filled'); hold on
scatter3(xyzFit(1,:),xyzFit(2,:),xyzFit(3,:)); hold off
xlabel X; ylabel Y; zlabel Z
More Answers (1)
Matt J on 27 Sep 2022
Edited: Matt J on 27 Sep 2022
I am searching for intersection of plane and ellipsoid
If that is the ultimate goal, you should just rewrite the ellipsoid equation in a rotated coordinate system where the intersection plane is the xy plane. That will result in a 2D equation for the intersection ellipse directly.
The appropriate basis vectors xaxis, yaxis, and zaxis can be obtained as,
and the 4x4 coordinate transform matrix needed to apply and invert the transformation is,
T=T*makehgtform('translate',-[0.1427, -0.4418, -0.0564]);