Tutorial details:
Written by: Flashjunki
Requirements: Flash 4
Download FLA (The method used to constrain to an arc here could be adapted to work with any algebraic formula.)

Here is a problem I had: I wanted to constrain a drag to an arc. Flash only allows you to constrain to a rectangle. So how do you do it? Well, the simple explanation is this:

1) Set up an arc using algebra. The blue line that the button follow is actually about 100 points. Each point is created via duplicate movie clip, then positioned according to the formula for an arc.
2) Using the bounds of your arc, start the drag of the red button within those constraints.
3) With a continuous action object embedded within the movie clip you are dragging, check the X position of the red button. Remember, you will always get valid values for your X position, because you set the drag to be constrained within the bounds of the arc.
4) Now, using the formula for an arc, calculate what Y would be. (You can see the formula in the frame labeled "drawarc" in the main timeline of the movie.)
5) Force the position of the red drag object to a certain x,y coordinate based on where the user drags the slider (x) and your calculated (y) value in the arc.

The complicated part comes here: the formula for an arc requires the calculation of a square root. Flash can't do this. However Newton had a formula for estimating a square root long before computers or calculators were ever invented. I used that. You can see that formula in the frame labeled "sqrt" on the main timeline.

What you require to understand how the top slider works:
A good grasp of Algebra, Geometry, and advanced Flash techniques such as Duplicating multiple Movie Clips (the arc is drawn from one point duplicated about a hundred times then properly positioned), "continuous action" actionscripting, the use of the Call statement and multiple timelines.

What you require to understand how the bottom slider works:
A grasp of how Button Actions and Tell Targets work.

The bottom slider was downloaded from somewhere on the net. The credit for it goes to Chris Glaubitz. I include it here so you can see the differences between how the two sliders work.

Final Notes on these sliders:
The top one, believe it or not, takes up less memory when stripped down and removed from the tutorial layers and the bottom slider layer. Only about 3K. It also works better, in my opinion. It is smoother and you can drag your mouse right off the slide area and it still works. Try that on the bottom one!

DISCLAIMER:
WARNING: I would rate the difficulty on this ".fla" VERY VERY VERY HARD. Even harder than more complicated effects I have generated in the past. Use at your own risk. I can't be held responsible for countless hundreds of hours wasted trying to modify this file!