Angle in 360 degrees

Question

I coded this code here:

     double cosine = (v1.x*v2.x+v1.y*v2.y)/(150*150);               
     double radian = Math.acos(cosine);
     double angle = Math.toDegrees(radian);

V1 and V2 are two vectors, which are simple Point(s)() to keep it simple. Now I calc. the angle between them and it works well. But over 180 deg. , it turns back to 179,178... But I want to have 360°.

The Problem is that for example radian won't get negative, so that I'm able to put it in an if-Segment...

Thanks for advice.

This seems more of a math problem than a coding problem. How would you do this with paper and pencil? — azurefrog
– azurefrog, Commented Sep 24, 2014 at 15:03
yes, i think it's a math problem, too. The way I coded it is the way I would do it on paper(I learned it that way). It seems that the beginning line just give me the smaller angle. — Billabong
– Billabong, Commented Sep 24, 2014 at 15:09
acos always return a value for the first two quadrants. You will have to decide the quadrant you are in from your vertices and then adapt your result accordingly. — Dawnkeeper
– Dawnkeeper, Commented Sep 24, 2014 at 15:16

Grimxn · Accepted Answer · 2014-09-25 08:57:27Z

2

You're using the dot product of the two vectors to calculate the angle between them, but, since the dot product is commutative a.b = b.a - therefore, there is no way to get the sense of the angle, only its magnitude (as you've found out) - acos is ambiguous over 180º.

Try instead using atan2. It should be something like :

double theta1 = Math.atan2(v1.y, v1.x);
double theta2 = Math.atan2(v2.y, v2.x);
double theta = theta1 - theta2;

Note that atan2 always returns an answer in -pi ... pi, so you will have to add pi to make it in the range 0 ... 2.0 * pi.

edited Sep 25, 2014 at 8:57

answered Sep 24, 2014 at 15:17

Grimxn

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1 Comment

Teepeemm Over a year ago

You don't want to add pi. You want to add 2*pi if it's less than 0.

MBo · Accepted Answer · 2014-09-24 15:21:12Z

1

You can get full-range angle (-Pi..Pi for the most of math libraries) using both scalar product and cross product:

radian = Math.atan2(v1.x*v2.y-v1.y*v2.x, v1.x*v2.x+v1.y*v2.y)

answered Sep 24, 2014 at 15:21

MBo

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4 Comments

Billabong Over a year ago

Ah I see. okay, but I still have to check if it's <0 or something like that?

Billabong Over a year ago

mh, well i changed it and there are values from 0<->180 and 0<->-179

Billabong Over a year ago

I solved it with: double diff = 180+Math.toDegrees(radian); if(radian<0){ angle = 180+diff; }

MBo Over a year ago

It would better to add 360 once (if negative) - to get angle needed to turn v1 counterclockwise until v2

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