  This survey paper contains an elementary exposition of Casson and Rivin's
technique for finding the hyperbolic metric on a 3-manifold M with toroidal
boundary. We also survey a number of applications of this technique.
  The method involves subdividing M into ideal tetrahedra and solving a system
of gluing equations to find hyperbolic shapes for the tetrahedra. The gluing
equations decompose into a linear and non-linear part. The solutions to the
linear equations form a convex polytope A. The solution to the non-linear part
(unique if it exists) is a critical point of a certain volume functional on
this polytope. The main contribution of this paper is an elementary proof of
Rivin's theorem that a critical point of the volume functional on A produces a
complete hyperbolic structure on M.
