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When a star is tidally disrupted by a supermassive black hole (BH) at the center of a galaxy, the gas debris is stretched into an elongated cold stream. The longitudinal motion of the stream accurately follows geodesics in the Kerr spacetime and the stream 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. Self-intersection occurs when the closest approach separation is smaller than the stream thickness. 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: in about half of the cases, the collision occurs near the pericenter at an angle close to 0 o (the "rear-end" mode) and the other half has collisions far from the pericenter with collision angles close to 180 o (the "head-on" mode). 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 two colliding ends is of order unity and 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 precession. 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.

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