A star is tidally stretched into an elongated stream after being disrupted by a supermassive black hole (BH). Using an approximate tidal equation, we calculate the stream's thickness evolution along its 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. We explore a wide parameter space of orbital angular momenta, inclinations, and BH spins to obtain the properties of stream intersection. Two collision modes are identified: in similar to half of the cases, the collision occurs near the pericentre at an angle close to 0(o) ('rear-end' mode) and the other half have collisions far from the pericentre with collision angles close to 180(o) ('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's mass is shock heated in an offset collision. Many of the numerical results can be analytically understood in a post-Newtonian picture, where we find the reason for stream collision to be a geometric one. Future hydrodynamic simulations including recombination are needed to understand the long-term effects of pressure forces which are neglected here.