Given a geodesic lamination with finitely many leaves in a closed surface of genus at least 2, I'll construct a very explicit parametrization of the Hitchin component of this surface. In essence, this parametrization is an extension of Thurston's shearing coordinates for the Teichmueller space of a closed surface, combined with Fock-Goncharov's coordinates for the moduli space of positive framed local systems of a punctured surface. This is joint work with Francis Bonahon.