  Convex geometry is a closure space $(G,\phi)$ with the anti-exchange
property. A classical result of Edelman and Jamison (1985) claims that every
finite convex geometry is a join of several linear sub-geometries, and the
smallest number of such sub-geometries necessary for representation is called
the convex dimension. In our work we find necessary and sufficient conditions
on a closure operator $\phi$ of convex geometry $(G,\phi)$ so that its convex
dimension equals 2, equivalently, they are represented by segments on a line.
These conditions can be checked in polynomial time in two parameters: the size
of the base set $|G|$ and the size of the implicational basis of $(G,\phi)$.
