In 2D you have a single angle, a fixed rotation axis (so to say; in fact it is a fixed plane of rotation where the said axis is orthogonal to), and a free choosable origin (where the axis passes through, of course). Using 0 (i.e. the point where all co-ordinates are 0) as origin, the formulas for rotation look like
x' := x cos( a ) + y sin( a )
y' := -x sin( a ) + y cos( a )
If you write exactly this as matrix expression (using column vectors), you'll have
p' := R( a ) * p
so there is really nothing advanced at this level. However, as soon as you start to concatenate rotations, or (as in your case) want to compute rotational differences, matrix expression are much more handy than the scalar expressions using trigonometry terms. This gets more and more true when you consider other transformations, too, and when you work in spaces with more dimensions. I suggest you to look at matrix math (not in the broad sense but trimmed for the needs of CG) because after mastered the 3 or 4 hurdles geometric things gets much easier to deal with. Not to mention that there are several packages out there that already implement matrices and vectors for your convenience; you just have to learn how to use the stuff.

If you need help, please tell us how the both original rotations are defined, and how the difference shall look like to be used further.

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The way the rotations are defined is, they start at 0 pointing straight down, and then move counter-clockwise up to positive pi facing straight up. Then it changes to negative PI and goes back down to 0 at the bottom again. As far as I can tell, this is the standard way that rotation works in XNA. The co-ordinate system has the origin at the top left side of the screen, with positive X going to the right, and positive Y running straight down.

I'm never going to need to use this specific code for 3d, since this game is wholly 2d, so I don't think I need anything too fancy. Just a simple algorithm to get an angle from 2 points is what I need.

So the orientations are given as an origin and a distant point on the vector. Then you can use the atan2 function (see e.g. the illustration here on wikipedia and developer documentation of your favorite IDE). It is suitable to compute the angle of the vector with a horizontal reference line by relating the horizontal part of the vector with its vertical part. Doing so for both the original and the target point gives you 2 angles. Then compute the difference of the 2 angles and you have a measure for the rotation.

That...is exactly what I've been trying to do, and what I have in the example code I posted. The problem is, I can't get it to spit out the right number.

[quote name='AgentPaper' timestamp='1306365375' post='4815828']
That...is exactly what I've been trying to do, and what I have in the example code I posted. The problem is, I can't get it to spit out the right number.

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Well, as far as I can tell Atan and Atan2 are the same thing, only with Atan you need to divide the two values yourself, and in Atan2 you just input 2 values and it takes care of that. I guess I could try using Atan2, though I don't know how it would help.