Since I can make those spheres, planes, and now triangles, I suppose I'm almost done with the raytracer. Cubes- well, pretty much any 3D shape- can be made from triangles, so all the shapes I wanted have been implemented. Reflection, here I come!
Here's my test scene again; you can still see the blue spheres. The plane (green thing) is a hexagon because I have set its boundaries to a cube 400 units (3D pixels? Voxels?) on a side. That's another benefit of my new parser...