  A triangulation of a point configuration is regular if it can be given by a
height function, that is every point gets lifted to a certain height and
projecting the lower convex hull gives the triangulation. Checking regularity
of a triangulation usually is done by solving a linear program. However when
checking many flip-connected triangulations for regularity, one can instead ask
which flips preserve regularity. When traversing the flip graph for enumerating
all regular triangulations, this allows for vast reduction of the linear
programs needing to be solved. At the same time the remaining linear programs
will be much smaller.
