Finding Components of Rotated Ellipsoid using Euler Angles

[TheDestroyer]

Hello guys,

I'm trying to find an algorithm to solve an overlap problem between many polyhedra in space, so here this question appears.

Imagine an Ellipsoid rotated by Euler angles in 3D space. This Ellipsoid could be characterised by its 3 radii Rx,Ry and Rz, and by 3 Euler angles in space Ix,Iy and Iz.

The question is, how do I get the components of those radii in an arbitrary direction in space after it being rotated by Euler angles? is this problem easy to solve? I don't know where to start.

Thank you

 

[TheDestroyer]

I think I got it.

One has to do the inverse rotation for the arbitrary direction by the angles -Ix,-Iy,-Iz. Then use the spherical coordinates equations to get the distances from the center.

x = Rx sin(theta) cos(phi)
y = Ry sin(theta) sin(phi)
z = Rz cos(theta)

then one could take use the Pythagorean to the distance from the center to the surface of that ellipsoid.

Is this approach correct?

Thanks

 

[TheDestroyer]

Oh my god! not a single comment? am I in the wrong place?