  Segmented strings in flat space are piecewise linear classical string
solutions. Kinks between the segments move with the speed of light and their
worldlines form a lattice on the worldsheet. This idea can be generalized to
AdS$_3$ where the embedding is built from AdS$_2$ patches. The construction
provides an exact discretization of the non-linear string equations of motion.
  This paper computes the area of segmented strings using cross-ratios
constructed from the kink vectors. The cross-ratios can be expressed in terms
of either left-handed or right-handed variables. The string equation of motion
in AdS$_3$ is reduced to that of an integrable time-discretized relativistic
Toda-type lattice. Positive solutions yield string embeddings that are unique
up to global transformations. In the appendix, the Poincare target space energy
is computed by integrating the worldsheet current along kink worldlines and a
formula is derived for the integrated scalar curvature of the embedding.
