  We present a novel method to generate a synthetic distribution of objects
(mock) on a spherical surface (i.e. a sky), by using a real distribution. The
resulting surrogate map mimics the clustering features of the real data,
including the effects of non-uniform exposure, if any. The method is
model-independent, also preserving the angular correlation function, as well as
the angular power spectrum, of the original data. It can be reliably adopted to
mimic the angular clustering of objects distributed on a spherical surface and
it can be easily extended to include further information, as the spatial
clustering of objects distributed inside a sphere. Applications to real data
are presented and discussed. In particular, we consider the distribution of
galaxies recently presented in the 2MASS Redshift Survey (2MRS) catalog.
