  This work uncovers the tropical analogue for measured laminations of the
convex hull construction of decorated Teichmueller theory, namely, it is a
study in coordinates of geometric degeneration to a point of Thurston's
boundary for Teichmueller space. This may offer a paradigm for the extension of
the basic cell decomposition of Riemann's moduli space to other contexts for
general moduli spaces of flat connections on a surface. In any case, this
discussion drastically simplifies aspects of previous related studies as is
explained. Furthermore, a new class of measured laminations relative to an
ideal cell decomposition of a surface is discovered in the limit. Finally, the
tropical analogue of the convex hull construction in Minkowski space is
formulated as an explicit algorithm that serially simplifies a triangulation
with respect to a fixed lamination and has its own independent applications.
