  We have carried out a Monte Carlo simulation of a modified version of Vicsek
model for the motion of self-propelled particles in two dimensions. In this
model the neighborhood of interaction of a particle is a sector of the circle
with the particle at the center (rather than the whole circle as in the
original Vicsek model). The sector is centered along the direction of the
velocity of the particle, and the half-opening angle of this sector is called
the `view-angle'. We vary the view-angle over its entire range and study the
change in the nature of the collective motion of the particles. We find that
ordered collective motion persists down to remarkably small view-angles. And at
a certain critical view-angle the collective motion of the system undergoes a
first order phase transition to a disordered state. We also find that the
reduction in the view-angle can in fact increase the order in the system
significantly. We show that the directionality of the interaction, and not only
the radial range of the interaction, plays an important role in the
determination of the nature of the above phase transition.
