[Algorithms] Re: line trace against parametric surface

[<gd...@er...>]

>> Do there exist any algorithms or papers relating to finding the first 
>> point of intersection between a ray/line segment and a curved surface 
>> that don't involve any tesselation of the surface?

You might want to google for "Bezier Clipping method". Here are a few papers 
on intersecting a ray against various implicit representations: 

ray intersection bezier patch:
http://www.tricity.wsu.edu/~bobl/personal/mypubs/2002_raybez.pdf 

ray intersection implicit convex objects:
http://www.dtecta.com/papers/jgt04raycast.pdf 

ray intersection on implicit csg surface:
http://www.win.tue.nl/vis/papers/2001/lipschitz.pdf 

graphics gem:
http://www1.acm.org/pubs/tog/GraphicsGems/gemsiv/curve_isect/ 

Erwin Coumans
http://www.continuousphysics.com