If you are talking about curve drawn at authoring time - there is no way to read graphics data.

Not if the line was drawn at authoring on Flash stage.

If the line was drawn at runtime, on the other hand, you can store coordinates and commands in arrays and read these arrays as needed.

you can listen for a MouseEvent.MOUSE_MOVE.  From this event you can tell the x and y location of the mouse.  from there its some simple math.  take two of the 3 or more points given and form an equation in the form of y = mx + b.  once you find your m and b for the equation, just plug in x for your third point.  If the answer is y then it's on the line.  otherwise its part of a curve.  the mouse event won't fire every millisecond though, so you will only get some of the points of the mouse move depending on how fast the user moves the mouse.  To control that, you can raise your lower your frame rate.  the faster the frame rate, the more often the mouseEvent will fire.  (or so I think, that last part might only be on enterFrame events)

"anyone knows a better/simpler solution. I just want to know if the mouse  movement is forming a circle/curve or so. It doesn't need to be  accurate."

What would be implications if you, say, know user's intentions? How your program will react to establishing this knowledge?

As I said in my previous post - each iteration of mouse move is recorded as integers. This means, in part, that the line between two consequent recorded mouse positions is ALWAY a straight line no matter how small.

I guess it is up to you to define, based on the task you need to implement, what constitutes curve - this is the main challenge I think. I see many different ways to look at it.Say, I scatter 100 randomly positioned points over some plane. What does program have to see - circle encompassing all the points, square, ellipse?

Once curve definition is in place - developing algorithm and math formulas will be more straightforward.

mouse coordinates likely will NOT be on a straight line

. It might be better to calculate the angle of turn between pts 1, 2 and pts 2,3 to see if it is a clear turn left or right