We study Cerenkov-type second-harmonic generation in a two-dimensional quasi-periodically poled LiNbO3 crystal. We employ a new geometry of interaction to observe simultaneous emission of multidirectional nonlinear Cerenkov radiation with comparable intensities. This opens a way to control the angle of Cerenkov emission by tailoring the nonlinearity of the material, which is otherwise intrinsically defined by dielectric constants of the medium and their dispersion. (C) 2012 Optical Society of America