  Polarization-singularity C-points, a form of line singularities, are the
vectorial counterparts of the optical vortices of spatial modes and fundamental
optical features of polarization-spatial modes. Their generation in tailored
beams has been limited to lemon and star C-points that contain symmetric
dislocations in state-of-polarization patterns. In this article we present the
theory and laboratory measurements of two complementary methods to generate
isolated asymmetric C-points in tailored beams, of which symmetric lemons and
stars are limiting cases; and we report on the generation of monstars, an
asymmetric C-point with characteristics of both lemons and stars.
