Java: Determin angle between two points

Question

OK firstly apologies as I know this kind of question has been asked before more than once. However even after looking at the other questions and answers I have been unable to get this to work for my situation. See below for an example:

All I am simply trying to is work out the angle between P1 and P2 assuming that 0 degrees is as shown above so that I can point an arrow between the 2 in the correct direction. So I do something like this...

Point p1 = new Point(200,300); Point p2 = new Point(300,200);
double difX = p2.x - p1.x; double difY = p2.y - p1.y;
double rotAng = Math.toDegrees(Math.atan2(difY,difX));

Which comes out as: -45, where it should be 45? However it is not simply a case I don't think of it returning a negative result, as for example if I changed P1 to 300,300 (below P2) then the angle should be 0, but is returned as -90.

So I am just wondering if anyone can point out what I am doing wrong to calculate this, or is it even possible to do it this way?

Hetero

You should put this into a function and compute and compare with your expectations the angles for points O and P2 that are closer together. The principal idea to employ atan2 is good. – Chagres

Hmm 0 isn't meant to be a point, just what I would expect 0 degrees to point at from P1. Experimenting with a method/function for this now though with setting P1 as 0,0 but not sure that's what u meant :o – Hetero

No, I was referring to the location around the 0 or O mark. – Chagres

Ooh sorry, yeh that makes more sense. so the 0,0 position/mark I guess would be 200,200 in this case. – Hetero

Answer 1

atan2(Y,X) computes in the standard Cartesian coordinate system with anti-clockwise positive orientation the angle of the point (X,Y) against the ray through (1,0). Which means that X is the coordinate along the zero-angle ray, in your situation X=-difY, and Y is the coordinate in the direction of (small) positive angles, which gives, with your preference for the depicted angle to be 45°, Y=difX. Thus

double rotAng = Math.toDegrees(Math.atan2(difX,-difY));

Chagres

Answer 2

You are confusing with the coordinates system used in geometry vs. one used on computer screen. In geometry you are regular that 0,0 is a point in the left bottom corner. However 0,0 on screen is left - upper corner.

Now, rotate your picture according coordinates of screen and see that the angle is calculated correctly.

So, in general case you can choose one of the following solutions: 1. recalculate corrdinates of your points to screen coordinats and back. 2. if your problem is in angles only you can add π/2 (90 degrees) to your result.

Floatable

Oh? That I didn't think of and would likely explain it. I have through my experimentation tried simply adding 90 to the result, but it doesn't always give the right answer still. Not sure how to follow your advice at the moment though as would need to look into how to convert point coordinates to screen ones... ^ – Hetero

The conversion is simple. X is the same. Y is (screen height - y). – Floatable

"but it doesn't always give the right answer still" in what case? – Bauske

@Floatable what has screen height got to do with it? These points can be regarded as directions, so is sufficient to just negate them. – Bauske

@Floatable Oooh of course, sorry like you say the y position is simply reversed. I will try that thank you. Weston: I had tried modifying the result of the atan2 calculation such as adding 90 to it. I think it worked most times but as P1 and P2 are not fixed it sometimes didn't. Need to test again in case I was wrong though. – Hetero

Thank you @Alex and Weston your explanations helped me understand what I was doing wrong so have now got it working :) – Hetero

Answer 3

With your line double difX = p2.x - p1.x; double difY = p2.y - p1.y;, you are calculating your angle from p2 to 0, so -45 is a correct answer. Try to reverse p1 with p2.

Also, if P1 is changed to 300,300, then you have an angle from 0 ( 0 to P1 and P1 to P2). The angle is indeed 90 or -90 depending if you are seeing from P2 to 0 or 0 to P2.

Heap

So it seems, thanks for pointing that out, which is what LutzL also did below, which is what I ended up doing and now seems to work. Thanks! – Hetero