Given two arbitrary surfaces, what is the accurate and quite fast algo to find collision within X distance?
A key search phrase is "collision detection." You may find some references at this MO posting, "Intersection of Polyhedra."
And here is a more recent reference:


  Jiménez, Juan J., and Rafael J. Segura. "Collision detection between complex polyhedra." Computers &amp; Graphics 32.4 (2008): 402-411. (Journal link.)


Google Scholar shows this has been cited by 33 papers since.