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### Ellipsoid/Triangle intersection

Posted: **Tue Apr 16, 2013 12:20 pm**

by **TheSFReader**

Hi guys.

I'm looking for some pointers to compute ellipsoid/triangle intersection (and intersection distance). Is "normalizing" the ellipse into a sphere sufficient ?

### Re: Ellipsoid/Triangle intersection

Posted: **Tue Apr 16, 2013 12:56 pm**

by **spectral**

Maybe ask on a "math" forum...

### Re: Ellipsoid/Triangle intersection

Posted: **Tue Apr 16, 2013 1:21 pm**

by **TheSFReader**

Yes, probably. However, since it would be used in an Rartracing like use, with performance implications, I wondered if someone here had already found this case...

### Re: Ellipsoid/Triangle intersection

Posted: **Tue Apr 16, 2013 7:30 pm**

by **hobold**

What information exactly is your input?

- are the ellipsoid's main axes arbitrary? or parallel to some coordinate axis? in world coordinates or in local coordinates?

- is the triangle specified by its three vertices or some other way?

What information exactly do you want to compute?

- a boolean "does (not) intersect" can be computed analytically, as described here:

http://vectorizer.org/IntersectQuadricTetrahedron.html
- distance to an ellipsoid is surprisingly complex to compute:

http://www.geometrictools.com/Documenta ... ipsoid.pdf

### Re: Ellipsoid/Triangle intersection

Posted: **Thu Apr 18, 2013 9:04 am**

by **TheSFReader**

Thanks.

Actually, it would be used to compute intervisibility from one radio antenna to an area / set of points.