Pass to self or Dribble?

[Nu1]

In looking over the dribble rules and some scenarios in the case book, a scenario came to mind.

While standing in A's backcourt, A2 receives a pass from A1. A2 then throws the ball into A's front court (approx. 30 feet from where A2 was standing) where it touches the floor and (a) A2 runs, catches up with the ball and continues a dribble, or (b) A2 runs, catches up with the ball, and picks up the ball. What would the ruling be? Legal or not?

At first thought, this scenario seemed to be illegal, like a pass to one's self. But, after reading Rule 4-15-3 it seems this would be a legal beginning to a dribble ("throwing...the ball to the floor") and therefore would be legal in (a) or (b), as in (a) it is just a continuation of the dribble and in (b) it would be a legal ending to a dribble.

Thoughts and opinions please.