Umm... Quake, and Quake II (and so will Quake III) use BSP trees. Half-Life licensed Quake II engine, which means, Half-Life uses the same thing--BSP trees.
Quake II uses OpenGL mainly, or if there is a 3Dfx Voodoo card present, then it uses 3Dfx Mini-GL Driver to do the rendering (since there is no OpenGL ICD yet for 3Dfx Voodoo's... I think).
And, the reason why its so fast, is because it uses only a part of the OpenGL. On the other hand, Unreal is so slow because of its beatiful special fx. Not that Quake II is nothing, I could *never* do such a master-piece, but it is fast because its limited.
Hmm... what type of a computer and configuration do you have? You can't really expect much on a low-end system--any Pentium first generations really. I would say second generation CPU's are the bottom line these days.
Also, are the polygons texture mapped or gouraud shaded? Any special FX enabled? (Alpha Blending, Anti-Aliasing--this is a killer, Depth cueing)? Fog is good to have--especially in Landscape stuff, but it does have a good effect on the frame rates.
Also, are you enabling back-face culling? If not, that could really help--especially in landscape apps.
- prauppl