  A simple, geometrical construction is given for three-dimensional spacetimes
with negative cosmological constant that contain two particles colliding
head-on. Depending on parameters like particle masses and distance, the
combined geometry will the that of a particle, or of a black hole. In the black
hole case the horizon is calculated. It is found that that the horizon
typically starts at a point and spreads into a closed curve with corners, which
propagate along spacelike caustics and disappear as the horizon passes the
particles.
