angle between two points

Point2D.Double p = new Point2D.Double(4.0,3.0),

q=new Point2D.Double(-3.0,4.0);

double angle = Math.atan(p.x/p.y)-Math.atan(q.x/q.y);

System.out.println("angle(radians)="+angle+", (degrees)="+

angle/Math.PI*180);

bbrittaa at 2007-7-14 22:57:49 >

Your better off using atan2() and not atan() since the code above could cause dive by zero exceptions if either point has y=0.

Point2D.Double p = new Point2D.Double(4.0,3.0),

q=new Point2D.Double(-3.0,4.0);

double angle = Math.atan(p.y,p.x)-Math.atan(q.y,q.x);

System.out.println("angle(radians)="+angle+", (degrees)="+ angle/Math.PI*180);

eduar09a at 2007-7-14 22:57:49 >

Just out of curiosity, how on earth did you understand that question? I seem to remember that between any two points exists a LINE, but in order to have an angle you would have to have 3 points (one being the vertex). As I contemplate this question, my first thought is that the answer would depend on the placement of the "vertical line" and from which point on that vertical line you would be measuring the angle between the original two points. I am not challenging your answer, I am merely baffled that an answer could be formulated based on the VERY little information presented.

nochidsa at 2007-7-14 22:57:49 >

"measured from a vertical bar ?" I know how to measure an angle AOB where O is the origin, but I'm not sure what measuring from a bar might be.

The dot product of any two unit vectors is the cosine of the angle, so you can use that and avoid that pesky arctan.

theta = Math.acos(

(a.getX() * b.getX() + a.getY() * b.getY())

/ a.distance(0,0) / b.distance(0,0) );

pmuurray@bigpond.coma at 2007-7-14 22:57:49 >

Point2D.Double p = new Point2D.Double(4.0,3.0),

q=new Point2D.Double(-3.0,4.0);

double angle = Math.atan(p.y,p.x)-Math.atan(q.y,q.x);

System.out.println("angle(radians)="+angle+", (degrees)="+ angle/Math.PI*180);

Defend the hionour of atan2? Gaaah! you are making two[/d] calls to a math library! My code only needs to make one, to acos().

Firstly, of course, in the atan method the order of the operands is significant. In the dot product method, they are not. One gives "the angular distance from p to q", wheras the other gives "the angle between p and q".

Secondly, atan2 behaves ... oddly sometimes, I can never get straight whether the results are 0 to PI, or -PI/2 to PI/2. So if the angle is 60 degrees, you might get 60, -60, 120, -120, 300, -300 etc depending subtly on what the two points p and q contain, and all in floating point. You get the situation where the result flicks between two wildly different values when you move one of the points by a pixel, and the nature of the flick can change depending on which quarant the points are in. Been there, done that. The dot product method, by contrast, goes smoothly from 0 to PI.

Someone pass me a saucer of milk.

pmuurray@bigpond.coma at 2007-7-14 22:57:50 >

> Point well taken - one call to acos is better than atan2. That doesn't make it a superior function, that just says it's being used more efficiently by your algorithm. That's all I'm saying.

Look, I'm just engaging in a little macho swaggering and petty point-scoring. Don't mind me. :-)

pmuurray@bigpond.coma at 2007-7-19 5:12:30 >

> The "wild" nature you cite is due to the fact that

> atan2 is singular at +/-(pi/2), and it's periodic with

> period pi. It's not wild - a mathematician would say

> that's just the nature of the beast

tan is singular at +/-((2n+1)pi/2) and has period pi.

Neither atan nor atan2 is periodic. As the range of tan is from -infinity to +infinity, the domain of atan is the same. The 2D domain of atan2 allows atan2 to range over -pi to + pi, giving a result over any of the four quadrants:

public class Atan {

public static void main(String[] args) {

System.out.println(Math.toDegrees(Math.atan2(-1, -1)));

System.out.println(Math.toDegrees(Math.atan2(1, 1)));

System.out.println(Math.toDegrees(Math.atan2(1, 0)));

System.out.println(Math.toDegrees(Math.atan2(-1, 0)));

System.out.println(Math.toDegrees(Math.atan(-1 / -1)));

System.out.println(Math.toDegrees(Math.atan(1 / 1)));

System.out.println(Math.toDegrees(Math.atan(Double.POSITIVE_INFINITY)));

System.out.println(Math.toDegrees(Math.atan(Double.NEGATIVE_INFINITY)));

}

}

Pete_Kirkhama at 2007-7-19 5:12:30 >