# Finding 8 vertices of a frustum from the 6 planes defining it

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ob1    122
I'm trying to find the 8 vertices of an arbitrary frustum (ie. not necessarily a view frustum from a projection matrix) using just the 6 planes defining it. This is basically so that I can display the frustum in 3D space for debugging etc. My current plan is to do a 3-plane intersection point calculation for each corner (which I'm currently trying to read up on), however I was wondering if there was a simpler, more direct route to finding the vertices. Thanks for any info, ob1

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grhodes_at_work    1385
For an arbitrary frustum, I'm afraid you're stuck with your current approach, unless you know anything "special" about the planes or frustum shape.

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Charles B    863
Right, it's a 3x3 matrix inversion (3 plane equations) for each vertex in any general case.

Else check of you have any additional info to exploit in your context. Getting the vertices of a standard VF is straightforward when defined à la OpenGL (xmin, ...., zfar) and a rotation/translation matrix. Maybe you can also have obvious coordinates in other referentials (an oriented box for instance).

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jyk    2094
I also use the 3 planes method. There are probably other ways to do it, but I don't know that it would be an important thing to optimize.

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ob1    122
Yeah, I think I'll stick with the 3-plane method for now then, since at the moment I'm just using it for debugging.

Incidently, if anyone is interested I've found a nice formula for finding the intersection point of 3 planes:

http://astronomy.swin.edu.au/~pbourke/geometry/3planes/

This is less complex than some of the other methods I've come across via google, and seems to work perfectly as far as I've tested it.

ob1