I was reviewing my view frustum culling code for a new OpenGL project I am working on, and was noticing a bit too many corner cases with large bounding volumes (e.g. spheres) and smaller frustums. Corner cases where the bounding volume is in no way intersecting will my frustum volume, yet getting accepted as visible. I am using the Lighthouse3d (http://www.lighthouse3d.com/tutorials/view-frustum-culling/) method (geometric frustum plane method not radar) for extracting planes and testing against bounding volumes.
Here is an example (all frustum plane normals face inward (blue lines) )
The above image is top down, but neither the top or bottom frustum planes reject the sphere either.
This family of intersect methods rely on having at least one of the frustum planes reject the volume as outside. But there are corner cases where the volumes do not intersect, yet none of the frustum planes reject the volume, for example in the image I posted.
How does one deal typically deal with such cases (while still using world space frustum plane culling techniques, if possible)?