Octrees are typically clipped to the frustum just like polygons are, but there
are many ways. One approach is to project the eight vertices at the corners of
an octree node, and perform vertex coding/clipping on them (see the document
http://www.flipcode.com/documents/wwh6.txt for a brief look into 3D clipping).
This, of course, can be done hierarchically, only traversing when a node is
partially within the frustum. But be careful... if the node is large enough, all
eight points may lie outside the frustum (surrounding it) forcing you to clip
The only online documentation on beam-trees that I've seen is from Harmless
Algorithms, right here on flipCode.
Beam trees are one of those things I would like to write a document on, but
there's a long list of documents to write, and beam-trees are somewhere near the
Response provided by Paul Nettle