  A protagonist here is a new-type invariant for type II degenerations of K3
surfaces, which is explicit PL (piecewise linear) convex function from the
interval with at most 18 non-linear points. Forgetting its actual function
behaviour, it also classifies the type II degenerations into several
combinatorial types, depending on the type of root lattices as appeared in
classical examples.
  From differential geometric viewpoint, the function is obtained as the
density function of the limit measure on the collapsing hyperKahler metrics to
conjectural segments, as in the work of Honda-Sun-Zhang. On the way, we also
reconstruct a moduli compactification of elliptic K3 surfaces in the works of
Brunyate, Ascher-Bejleri, Alexeev-Brunyate-Engel in a more elementary manner,
analyze the cusps more explicitly.
  We also interpret the glued hyperKahler fibration of
Hein-Sun-Viaclovsky-Zhang as a special case from our viewpoint, discuss other
cases, and possible relations with Landau-Ginzburg models in the mirror
symmetry context.
