  When a star is tidally disrupted by a supermassive black hole (BH), the gas
debris is stretched into an elongated stream. The longitudinal motion of the
stream follows geodesics in the Kerr spacetime and the evolution in the
transverse dimensions is decoupled from the longitudinal motion. Using an
approximate tidal equation, we calculate the evolution of the stream thickness
along the geodesic, during which we treat the effect of nozzle shocks as a
perfect bounce. Intersection occurs when the thickness exceeds the closest
approach separation. This algorithm allows us to explore a wide parameter space
of orbital angular momenta, inclinations, and BH spins to obtain the properties
of stream intersection. We identify two collision modes, split evenly among all
cases: "rear-end" collisions near the pericenter at an angle close to $0$ and
"head-on" collisions far from the pericenter at an angle close to $\pi$. The
intersection typically occurs between consecutive half-orbits with a delay time
that spans a wide range (from months up to a decade). The intersection radius
generally increases with the orbital angular momentum and depends less strongly
on the inclination and BH spin. The thickness ratio of the colliding ends is of
order unity. The transverse separation is a small fraction of the sum of the
two thicknesses, so a large fraction of the stream is shock-heated in an offset
collision. Many of the numerical results can be analytically understood in a
post-Newtonian picture, where the orientation of an elliptical orbit undergoes
apsidal and Lense-Thirring precessions. Instead of thickness inflation due to
energy dissipation at nozzle shocks as invoked in earlier works, we find the
physical reason for stream collision to be a geometric one. After the
collision, we expect the gas to undergo secondary shocks and form an accretion
disk, generating bright electromagnetic emission.
