Sign in to follow this  

Want to make sure i get this correctly...

This topic is 4853 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

Hi, for the past year in college i've struggled in physics with vector math... After looking at some tutorials on the net, i've started to understand more and more vector physics... I wanted to make sure i understood some stuff before moving on: Calculating an angle between 2 vectors: let's say u and v are 2 non-colinear vectors in 2D space. The Dot product u.v = x1 * x2 + y1 * y2 It could also be reprensented as u.v= |u||v|*cos theta, theta being the angle between the 2 vectors... So if i want to calculate the angle between the 2 vectors, i have to normalize them both, so now |u| = |v| = 1, thus u.v=cos theta So the angle between the two would then be ArcCosine(u.v) when u and v are normalised... Correct? I imagine this would also work in 3D... I wanted to make sure i made no mistake... As I said, i've struggled with it in the past (especially in physics, trying to grasp the concepts of point mechanics while at the same time not understanding whta half the vector stuff meant... :( ) thanks...

Share this post


Link to post
Share on other sites
Thanks, heh

I have to retake first semester physics because i failed it, i hope this time it won't be as hard as the first... The first lesson last year was all about this vector math stuff, and at that moment i knew i was gonna fail :(

All i actually remembered were some stuff like how to calculate a cross product (with an easy to remember formula, wich is always good :) )

Well, as you said, i'm gonna carry on with making my game :)

Share this post


Link to post
Share on other sites
as a side note, to get the angle between two vectors in 2D i use the arc tangent, which saves normalisation.

...ok, since I started....

similar to the dot product, is the cross product. At least in 2D.

a x b = |A|*|B|*sin(a, b) = ax*by - ay*bx

so sin (a, b) = (a x b) / (|a|*|b|)

sin (a, b) = (ax*by - ay*bx) / (|a|*|b|)
cos (a, b) = (ax*bx + ay*by) / (|a|*|b|)

tan (a, b) = sin(a, b) / cos(a, b) = (ax*by - ay*bx) / (ax*bx + ay*by);

angle(a, b) = atan((ax*by - ay*bx) / (ax*bx + ay*by));

or in code,

angle(a, b) = atan2(ax*by - ay*bx, ax*bx + ay*by);

which gives me the angle in the range [-PI, PI], whereas acos()., asin(), atan() return angles in a half-range. And acos() has some issues...

acos(ac)
if ac close to 1, there can be some accuracy issues. Also if ac > 1 (like ac = 1.0000001f), it will fail.
similarly

asin(as)
if as close to 0, there can be some accuracy issues. Also if as > 1 (like as = 1.0000001f), it will fail.

there are no such issues when using atan2(). it's the best of both worlds and more :)


but be careful with the cross product in 3D, it's a vector (in 2D, sort of too...), so you can't really use it that way.

best of luck ;)

Share this post


Link to post
Share on other sites
Well since i was looking at ways to do it in 3D, i think i'll go with the acos routine, making sure to check for errors and adapting the code to include that it only returns angles from 0 to 180...

Anyways, i haven't started doing anything complicated in 3D yet, i need to learn some OpenGL first as well as more algorithms to help me understand how to make my 3D engine, wich is still a long ways off ;)

Share this post


Link to post
Share on other sites

This topic is 4853 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this