How can I get polar coordinates represented properly?

Question

I have the following hexagonal grid and trying to calculate the degrees to each edge hexagon from the center (light blue):

The blue highlighted hex is correct at 0 degrees and that quadrant (lower right) is correct. Here is my angle calculation method:

private static function calculateAngle(hex1:Hexagon, hex2:Hexagon):Number {
    // hex1 is always passed in as the grid center or start
    var diffY:Number = Math.abs(hex2.center.y) - Math.abs(hex1.center.y);
    var diffX:Number = Math.abs(hex2.center.x) - Math.abs(hex1.center.x);
    var radians:Number = Math.atan(diffY / diffX);

    return radians * 180 / Math.PI;
}

Why are the remaining angles (text in each hexagon) incorrect?

Answer 1

You're really close to correct; you just need to compensate for the periodicity of atan. The standard way to do this is to use atan2, which returns a signed angle in (-pi, pi] instead of an unsigned angle in [0, pi). You can do so like this:

var radians:Number = Math.atan2(
    hex2.center.y - hex1.center.y, hex2.center.x - hex1.center.x);

Note that I didn't include the call to abs in there: the signedness of those values is needed for atan2 to know which quadrant its in!

Edit: if you're looking for an angle in [0, pi], which represents the minimum angle between the center hex and the blue-highlighted hex, you can just take the absolute value of the result of atan2: return Math.abs(radians) * 180 / Math.PI; the question leaves it a little unclear as to which one you're asking for.