  Curve pseudo-visibility graphs generalize polygon and pseudo-polygon
visibility graphs and form a hereditary class of graphs. We prove that every
curve pseudo-visibility graph with clique number $\omega$ has chromatic number
at most $3\cdot 4^{\omega-1}$. The proof is carried through in the setting of
ordered graphs; we identify two conditions satisfied by every curve
pseudo-visibility graph (considered as an ordered graph) and prove that they
are sufficient for the claimed bound. The proof is algorithmic: both the clique
number and a colouring with the claimed number of colours can be computed in
polynomial time.
