  We propose a finite dimensional variational principle on triangulated
3-manifolds so that its critical points are related to solutions to Thurston's
gluing equation and Haken's normal surface equation. The action functional is
the volume. This is a generalization of an earlier program by Casson and Rivin
for compact 3-manifolds with torus boundary. Combining the result in this paper
and the work of Futer-Gu\'eritaud, Segerman-Tillmann and Luo-Tillmann, we
obtain a new finite dimensional variational formulation of the
Poncare-conjecture. This provides a step toward a new proof the Poincar\'e
conjecture without using the Ricci flow.
