arctangent formula

[Draxxarguest]

On the old board I saved a copy of the following post (as I sort of like collecting formulas for some reason) and had some questions on it:

--begin quote----:
subject: "2D Angle Between 2 Objects"

rad = Math.atan2(targety-originy, targetx-originx);
deg = Math.round((rad*180/Math.PI));
rot = deg+90;


Assuming your origin graphic is pointed up at 0 degrees.
rot = _rotation, or the rotation (360) of your graphic,
which will point it towards the target. originx/y and
targetx/y is the x and y pixel coordinates of your
origin and target objects respectively.


----end quote----

My question is how does the atan2 function work exactly? Does it sort out the "arctangent problem" mentioned here:
hyperphysics.phy-astr.gsu.edu/hbase/ttrig.html#c3

..in other words does it handle figuring out what quadrant the angle is in case arctangent returns a negative number?

[Draxxarguest]

Basically my question was what would the formula be for regular tangent (Math.atn vs. Math.atn2).

I wrote up some code that seems to handle it, but it's much longer and a little buggy perhaps.

// Cartesian Coordinate System (Flash has an inverted y!)
//.................-y..............
//..................|...............
//............2....|...1..........
// x-_______|_______x+
//..................|..............
//............3....|...4th quadrant
//..................|..............
//.................+y............


// translate to 0,0
// this is so you can find out what quadrant(1-4) the
// originx/y ship is in
originx = originx - targetx;
originy = originy - targety;
targetx = 0;
targety = 0;

// handle div. by zero
if((targetx - originx) ==0){
rad = Math.atan((targety-originy) / .0001);
}else{
rad = Math.atan((targety-originy) / (targetx-originx));
}
deg = rad * (180/Math.PI);

quadrant = 0;
if (originx> 0 and originy < 0) {
quadrant = 1; // angle is between 0 and 90 degrees
deg = deg - 90;
}
if (originx < 0 and originy < 0) {
quadrant = 2; // angle is between 90 and 180 degrees
deg = (deg * (-1)) + 180;
}
if (originx < 0 and originy> 0) {
quadrant = 3; // angle is between 180 and 270 degrees
deg = deg + 90;
}
if (originx > 0 and originy > 0) {
quadrant = 4; // angle is between 270 and 360 degrees (or 0 again)
deg = deg + 270;
}
// handle x or y = 0
if (originx == 0 and originy > 0){
deg = 270; // angle is pointing straight down
}
if (originx == 0 and originy < 0){
deg = 90; // angle is pointing straight up
}
if (originx > 0 and originy == 0){
deg = 0; // angle is pointing to the right
}
if (originx < 0 and originy == 0){
deg = 180; // angle is pointing left
}

rot = deg;

this._rotation = rot;

[Draxxarguest]

Just figured out the bug I had in the code above...
The line following "quadrant = 2" should say:
deg = deg + 90;
...likewise the "quadrant = 4" line could be simplified to:
deg = deg - 90;
.... vs. deg = deg + 270... but it's the same result.

I know the original code is much simpler. I just like to figure out things the hard way I guess. Not all progamming languages have the atn2 function built in (especially old languages). So I like to back engineer what a function does sometimes, just for wider compatability to other languages.