  Synchronization is one of the emerging collective phenomena in interacting
particle systems. Its ubiquitous presence in nature, science, and technology
has fascinated the scientific community over the decades. Moreover, a great
deal of research has been, and is still being, devoted to understand various
physical aspects of the subject. In particular, the study of interacting
\textit{active} particles has led to exotic phase transitions in such systems
which have opened up a new research front-line. Motivated by this line of work,
in this paper, we study the directional synchrony among self-propelled
particles. These particles move inside a bounded region, and crucially their
directions are also coupled with spatial degrees of freedom. We assume that the
directional coupling between two particles is influenced by the relative
spatial distance which changes over time. Furthermore, the nature of the
influence is considered to be both short and long-ranged. We explore the phase
transition scenario in both the cases and propose an approximation technique
which enables us to analytically find the critical transition point. The
results are further supported with numerical simulations. Our results have
potential importance in the study of active systems like bird flocks, fish
schools and swarming robots where spatial influence plays a pertinent role.
