Focused Angular $N$-Body Event Generator (FANG)

We introduce FANG (Focused Angular $N$-body event Generator), a new Monte Carlo tool for efficient event generation in restricted Lorentz-Invariant Phase Space (LIPS). Unlike conventional approaches that sample the full $4\pi$ solid angle, FANG directly generates events in which selected final-state particles are constrained to fixed directions or finite angular regions in the laboratory frame. Because of the way the generator is constructed, angular constraints can be imposed directly in the laboratory frame while maintaining the correct LIPS structure, enabling differential and total cross sections or decay rates to be computed with high efficiency. The method is validated against analytic results and existing event generators, showing excellent agreement. By reducing the computational cost of full phase-space event generation by several orders of magnitude, FANG provides a robust and versatile framework applicable to particle, nuclear, and detector physics.