We analyze here the issue of local versus the global visibility of a
singularity that forms in gravitational collapse of a dust cloud, which has
important implications for the weak and strong versions of the cosmic
censorship hypothesis. We find conditions as to when a singularity will be only
locally naked, rather than being globally visible, thus preseving the weak
censorship hypothesis. The conditions for formation of a black hole or naked
singularity in the Szekeres quasi-spherical collapse models are worked out. The
causal behaviour of the singularity curve is studied by examining the outgoing
radial null geodesics, and the final outcome of collapse is related to the
nature of the regular initial data specified on an initial hypersurface from
which the collapse evolves. An interesting feature that emerges is the
singularity in Szekeres spacetimes can be ``directionally naked''.Comment: Latex file, 32 pages, 12 postscript figures. To appear in the Journal
of General Relativity and Gravitatio