I'm teaching a workshop on digital fabrication and we need to figure out a way to sweep a profile along a path in 3 dimensions. To do this it is necessary to be able to rotate points around an arbitrary axis, given by a 3D vector.

Does anyone have any code that demonstrates a way to do this that even math illiterates could utilize I know this is a classic question in 3D graphics, but sadly my math skills are easily defeated.

Some references:
http://answers.google.com/answers/threadview?id=361441
http://gandalf-library.sourceforge.net/tutorial/report/node126.html

I've got some code that does that. It's part of my Vector library but hopefully should enable you to knock up a version that works.
Code:

// rotate v around _axis by ang radians.
Vector rotate(Vector v, Vector _axis,float ang)
{
 //use normalised values
  Vector axis=new Vector(_axis.nx(),_axis.ny(),_axis.nz());
  Vector vnorm=new Vector(v.nx(),v.ny(),v.nz());
  float _parallel=mDot(axis,v); //dot product
  Vector parallel=mul(axis,_parallel); //multiply all elements by a value
  Vector perp=sub(parallel,v); //subtract one vector from another
  Vector Cross=cross(v,axis); //cross product
  Vector result=add(parallel,add(mul(Cross,sin(-ang)),mul(perp,cos(-ang))));
  return result;
} 

I've just checked the code for one potential pitfall, in my code sub subtracts the first vector from the second, e.g. sub(a,b) = b-a

here's an alternative technique that might be of use:
http://www.davebollinger.com/works/p5/curvelathe/
(has potentially wide application once you get it)

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welcome, though most of the thanks should go to fry for making all the right tools available to us

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you could also create your own instances of a PMatrix and approach the hack in that manner, swapping them in/out for the camera matrix (and inverse) as needed: store the camera, set camera to your matrix, perform model transforms, call modelXYZ for your vertices, update your model transform from the camera, set back the original camera transform.  sounds tedious, but it works.  (use a class to own the matrices and do the swaps - makes it cleaner)

the advantage is that you could maintain your model transform independent of the camera, so that you could more easily "grow" an animated lathe/extrude/whatever during subsequent frames, instead of building the entire thing static as that demo does.