Simple sphere and polygon tests such as are documented in PolyColly? For sphere the calculation should be something such as:

Collided = S1r-S2r>S1v-S2v

Where S1 and S2 are the two spheres, r is the radius of the sphere, v is the spheres vector (normalized).

As for polygon collision, search the forums, there is a port of PolyColly that I posted up (in http://www.pascalgamedevelopment.com...ght=poly+colly) that should be easy to migrate to 3D instead of 2D.