If you're using DirectX 7, the utility library has these functions for creating simple 3D objects.

D3DXCreateBox
D3DXCreateCylinder
D3DXCreatePolygon
D3DXCreateSphere
D3DXCreateTeapot
D3DXCreateTorus

You can pull the vertices out of the created objects.

If you want to do it yourself, check out
http://www.magic-software.com/gr_dcmp.htm

and look in the Tesselation section. There are methods for making spheres, cylinders and bicubic patches.

Could anyone point me to some good discussions on how to use triangles to draw more complex 3D objects? I'm specifically looking for algorithms and/or code to perform surface approximations. Right now, I'm just interested in the basics (i.e. creating spheres, squares, disks, etc.).

how would you go about making a terrain collision detection thing with d3dim?

how would you store 3d levels or scenes? a 2d array and the value would equal the height?
like that thing you drew.
00000
01100
01110
00100

hrm.
how would you go about making sure another model is on a terrain with hills and slants and slopes? how would you move an object around a 3d level and check for collisions? would you do if the model is in a level object then? where can i find out about all the suff id like to know?