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Constructing frustum split from projection matrix

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hi there, I have been trying to split a view frustum in half along its z-axis (view direction) by un-projecting corner points from normalized device space into world space.

i.e. the set of points { (-1,-1,0), (1,-1,0), (1,1,0), (-1,1,0) }

But have just realized that the relationship between the z values is non-linear so you can't un-project them in this way. Is there any other way to do this just using the projection matrix rather than having to store fov angles etc. for the frustum?

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