Finding Components of Rotated Ellipsoid using Euler Angles

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SUMMARY

The discussion focuses on calculating the components of a rotated ellipsoid in 3D space using Euler angles. The ellipsoid is defined by its three radii (Rx, Ry, Rz) and three Euler angles (Ix, Iy, Iz). To find the components in an arbitrary direction, the inverse rotation is applied using the angles -Ix, -Iy, -Iz, followed by the application of spherical coordinates equations: x = Rx sin(theta) cos(phi), y = Ry sin(theta) sin(phi), and z = Rz cos(theta). The Pythagorean theorem is then utilized to determine the distance from the center to the surface of the ellipsoid.

PREREQUISITES
  • Understanding of 3D geometry and ellipsoids
  • Familiarity with Euler angles and their application in rotations
  • Knowledge of spherical coordinates and their equations
  • Basic grasp of the Pythagorean theorem in three dimensions
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  • Research the mathematical principles of 3D transformations using Euler angles
  • Explore algorithms for calculating intersections of polyhedra in 3D space
  • Learn about the application of spherical coordinates in 3D modeling
  • Investigate numerical methods for solving geometric problems involving ellipsoids
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Mathematicians, computer graphics developers, and engineers working on 3D modeling, simulation, and collision detection involving ellipsoids and polyhedra.

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

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