## Ellipsoid/Triangle intersection

Practical and theoretical implementation discussion.
TheSFReader
Posts: 12
Joined: Tue Dec 06, 2011 8:18 am

### Ellipsoid/Triangle intersection

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

spectral
Posts: 382
Joined: Wed Nov 30, 2011 2:27 pm
Contact:

### Re: Ellipsoid/Triangle intersection

Maybe ask on a "math" forum...

TheSFReader
Posts: 12
Joined: Tue Dec 06, 2011 8:18 am

### Re: Ellipsoid/Triangle intersection

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...

hobold
Posts: 56
Joined: Wed Dec 21, 2011 6:08 pm

### Re: Ellipsoid/Triangle intersection

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

TheSFReader
Posts: 12
Joined: Tue Dec 06, 2011 8:18 am

### Re: Ellipsoid/Triangle intersection

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