  Delaunay flip is an elegant, simple tool to convert a triangulation of a
point set to its Delaunay triangulation. The technique has been researched
extensively for full dimensional triangulations of point sets. However, an
important case of triangulations which are not full dimensional is surface
triangulations in three dimensions. In this paper we address the question of
converting a surface triangulation to a subcomplex of the Delaunay
triangulation with edge flips. We show that the surface triangulations which
closely approximate a smooth surface with uniform density can be transformed to
a Delaunay triangulation with a simple edge flip algorithm. The condition on
uniformity becomes less stringent with increasing density of the triangulation.
If the condition is dropped completely, the flip algorithm still terminates
although the output surface triangulation becomes "almost Delaunay" instead of
exactly Delaunay.
