How to make an Atan2() for DM?

ID:156485
 
Sep 25 2010, 3:44 pm
How would I make an Atan2() proc for DM
#1 Sep 25 2010, 3:59 pm
http://www.byond.com/developer/forum/?id=455650&view=0

Oh, and Arctan:

proc/arctan(m) return arcsin(m/sqrt(1+m*m))
#2 Sep 25 2010, 3:59 pm
I assume you're trying to find an angle between two points? I'm sure there are more efficient ways of doing this but I used some stuff I learned from Calculus to develop a Get_Angle() proc which uses inverse cosine and some vector math to determine the angle between point (x0,y0) and point (x1,y1).

Anyways here it is:
/*
Angle returns the angle between the origin (x0, y0) and a point (x1, y1).
The angle will be a number in degrees between 0 and 359
*/
proc/Angle (x0, y0, x1, y1)
{
    var/quadrant_modifier = 0
    var/list/vector1 = list(x1-x0, y1-y0)
    var/list/vector2
    if(vector1[2] < 0)
    {
        vector2 = list(-1,0)
        quadrant_modifier = 180
    }
    else vector2 = list(1,0)
    var/angle = (arccos (Dot_Product (vector1, vector2) / (Magnitude (vector1) * Magnitude (vector2)))) + quadrant_modifier
    return angle
}

/*
Dot_Product performs an equation from vector calculus. This equation is
essential for determining the angle between two vectors.
*/
proc/Dot_Product (vector1[2], vector2[2])
{
    var/product = (vector1[1] * vector2[1]) + (vector1[2] * vector2[2])
    return product
}

/*
Magnitude determines the magnitude of a vector. Magnitude is essential
for determining the angle between two vectors
*/
proc/Magnitude (vector[2])
{
    return sqrt((vector[1]**2)+(vector[2]**2))
}
#3 Sep 25 2010, 4:17 pm
In response to Cody123100 (#2)
Ily Cody.
#4 Sep 25 2010, 4:41 pm
ZOMG rage in the cage, I just found out jt_vectors already does this.

I'm a highschool freshman, smd.
#5 Sep 25 2010, 4:59 pm
In response to DarkCampainger (#1)
atan2() (or arctan2() or arctangent2() or whatever you want to call it) is different from just the arctangent function. atan() takes just one argument, which is the ratio y/x. However, the issue here is that the domain and range is then limited to half of the unit circle: y/x = -y/-x, and -y/x = y/-x. The range of the function, therefore, is only -pi/2 to pi/2. The atan2() function solves this by taking two arguments - y and x - and then using that to give a full range.

Granted, it's only a small difference in terms of lines of code (as shown by Lummox's example) but it really makes things neater and less prone to error.

Also that's a really poor explanation in retrospect. Anybody who's actually a mathematician able to say things properly?
#6 Sep 25 2010, 5:06 pm
In response to Garthor (#5)
Yep, that's why I linked to Lummox's snippet. I just threw the arctan() function in because his code relies on it, and most people don't know it by heart.
#7 Sep 26 2010, 2:32 am
In response to Garthor (#5)
Not a mathematician, but yeah, we basically have the atan2 function because atan can't tell between opposite directions. Atan2 properly accounts for signs (it's a four-quadrant arctan).