6.3 No Rail after Contact
If no ball is pocketed on a shot, the cue ball must contact an object ball, and after that contact at least one ball (cue ball or any object ball) must be driven to a rail, or the shot is a foul. (See 8.4 Driven to a Rail.)
and here:
6.7 Double Hit / Frozen Balls
If the cue stick contacts the cue ball more than once on a shot, the shot is a foul. If the cue ball is close to but not touching an object ball and the cue tip is still on the cue ball when the cue ball contacts that object ball, the shot is a foul. If the cue ball is very close to an object ball, and the shooter barely grazes that object ball on the shot, the shot is assumed not to violate the first paragraph of this rule, even though the tip is arguably still on the cue ball when ball-ball contact is made.
However, if the cue ball is touching an object ball at the start of the shot, it is legal to shoot towards or partly into that ball (provided it is a legal target within the rules of the game) and if the object ball is moved by such a shot, it is considered to have been contacted by the cue ball. (Even though it may be legal to shoot towards such a touching or “frozen” ball, care must be taken not to violate the rules in the first paragraph if there are additional balls close by.)
The cue ball is assumed not to be touching any ball unless it is declared touching by the referee or opponent. It is the shooter’s responsibility to get the declaration before the shot. Playing away from a frozen ball does not constitute having hit that ball unless specified in the rules of the game.
.
