Angle between two lines in 2D

Question

Hey, I've got a problem dealing with the Vector2.Angle and the Vector3.Angle The thing is during runtime I define three points A,B and C which are in 2D world.

and eventually two lines will be used , (A,B) and (B,C) I'm trying to figure out the angle between those two lines. I've tried Vector2.Angle(B-A,C-B) and bunch of others, but I think I don't understand the essential concept of the Angle() method.

The picture will illustrate my point! Click Here

how to calculate Alpha ??

Thanks for your time

Answer 1

Answer by rutter · Jun 24, 2014 at 07:04 PM

So you're describing a shape like this?

Three points

It's important to note that vectors have both length and direction. The vector from A to B is not the same as the vector from B to A. They have equal length, but opposite direction.

So, this bit:

 Vector2.Angle(B-A,C-B)

That's not running the comparison you might expect, because one of your vectors is pointing "backwards". You end up calculating the supplementary angle:

Supplementary angle

So, what you probably want is this:

 Vector2.Angle(B-A, B-C);

three points.png (3.0 kB)

three points supp (1).png (4.3 kB)

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ziadantar90 · Jun 25, 2014 at 08:27 AM 0

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Awesome man.... Thanks a lot, it did the trick

Have a good one !

Answer 2

Answer by Zoodinger · Jun 24, 2014 at 01:24 PM

The dot product between two vectors returns the cosine of the angle.

 float dot = Vector2.Dot(A, B);
 float angleInRadians = Mathf.Acos(dot);
 float angle = Mathf.Rad2Deg(angleInRadians); //to degrees

Note: A and B need to be NORMALIZED for this to work!

Keep in mind that this will only produce angles between 0 and 180 degrees. You'll need to do some additional trickery to compensate for that. For 2d vectors this is not too hard:

 Vector3 cross = Vector3.Cross(new Vector3(A.x, A.y, 0), new Vector3(B.x, B.y, 0));

cross.z will be positive if the rotation is clockwise or negative if the rotation is counter-clockwise. Or the other way around, I'm not sure :P. Either way, you'll be able to figure out what to do in case you want to detect angles larger than 180 degrees.

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Answer 3

Answer by Ankit Priyarup · Jun 24, 2014 at 03:14 PM

It's very simple with physics. Let two lines be vector a and vector b then the angle cos theta will equal to A.B(dot product)/a mode cross product to b mode.

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ziadantar90 · Jun 24, 2014 at 06:42 PM 0

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The problem is I can't seem to struct the lines A line from A to B is for example : Vector2 AB = A+B; or Vector2 AB = A-B or something else ?!

I mean logically I know it and mathematically but to apply it in unity that's where's my pickle

Angle between two lines in 2D

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