Jump to content
  • Advertisement
Sign in to follow this  

Calculate Euler rotation angles between 2 points

This topic is 2921 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

I need to calculate the 3 Euler angles (yaw, pitch, roll) between 2 points.

The picture below shows the way I rotate. These are the angles I need to calculate.
(The only difference is I'm rotating the object in the order X,Y,Z and not Z,Y,X)


This is the code I'm using but its not working for me:

// x, y, z represent a fractional value between -[1] and [1]
// a "unit vector" of the point I need to rotate towards

yaw = Math.atan2( y, x )
pitch = Math.atan2( z, Math.sqrt( x * x + y * y ) )

[Edited by - Jenko on October 22, 2010 10:04:08 PM]

Share this post

Link to post
Share on other sites
I have also been doing a lot a research on the internet about that topic. I'm currently looking for a way to do this with QUATERNIONS and I decided to post that here instead of starting a new thread since it's basicaly the same question but with another system.

So here's what I currently found:


//Given two vectors, find the angle difference between them in quaternion

vector $V1 = << my first vector >>;
vector $V2 = << my second vector >>;

float $d = dot($V1, $V2);
vector $axis = cross($V1, $V2);

float $W = sqrt(norm($V1) * norm($V1) * norm($V2) * norm($V2) + $d);

float $X = ($axis.x);
float $Y = ($axis.y);
float $Z = ($axis.z);

// So my quaternion is now $X, $Y, $Z, $W ... transform that in a vector

vector $xyz = << $X, $Y, $Z >>;

vector $result = (2 * $W*$W -1)*$V1 + 2*dot($V1,$xyz)*$xyz + 2 * $W * cross($V1,$xyz);

// $result is my resulting vector


It's weird because this is almost working, if I rotate on vector on a specific axis in relation to my other vector, the resulting vector seems to rotate correctly but all other axis won't work ! It gives awkward results. But if I move my two vectors as if they were stick one to the other, the resulting vector will react as if it was stick to my 2 vectors. So I think I'm not doing something correct here but I just don't know what.

And finally, here's the same thing with euler angles. I got it to work but I wanted a more optimized method.

// Calculate Euler rotation angles between 2 vectors .. we use Rodrigues formula

vector $V1 = << my first vector >>;
vector $V2 = << my second vector >>;

vector $axis;
float $angle;

$angle = acos($V1*$V2);
$axis = normalizeVector((cross($V1,$V2)));

matrix $axis_skewed[3][3] = <<
0, (-$axis.z), ($axis.y) ;
($axis.z), 0, (-$axis.x) ;
(-$axis.y), ($axis.x), 0 >>;

matrix $eye3[3][3] = <<
1, 0, 0;
0, 1, 0;
0, 0, 1 >>;

// here's Rodrigues
$R = $eye3 + sin($angle)*$axis_skewed + (1-cos($angle))*$axis_skewed*$axis_skewed;

matrix $vectorMatr[3][1];
$vectorMatr[0][0] = ($V1.x);
$vectorMatr[1][0] = ($V1.y);
$vectorMatr[2][0] = ($V1.z);

// $result is the resulting vector

$result = ($R * $vectorMatr);


In conclusion, my quaternion method is still not working but seems more promising than my other method which is working but might be slow. I'm looking for a better solution.

Share this post

Link to post
Share on other sites
mfiorilli, thanks for the Euler method.

Do I assume correctly that the resultant vector stores the X and Y euler rotations into the vector's x and y properties?

However since I'm not programming this in C++ nor do I have your vector library, I'm having some trouble understanding what you've done here:

$R = $eye3 + sin($angle)*$axis_skewed + ([[1]]-cos($angle))*$axis_skewed*$axis_skewed;

// do you add all the properties of the eye3 matrix?
// do you multiply with all the properties of the axis_skewed matrix?
// etc..
// and what is R? a vector or matrix? or number?

and here:

$result = ($R * $vectorMatr);

// do you multiply the vector with the matrix to get the resultant vector using standard matrix multiplying?

If you could post your matrix/vector library I could use its code since my platform does not compute operators (* / + -) and call functions behind the scenes.

Share this post

Link to post
Share on other sites
Sign in to follow this  

  • Advertisement

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

We are the game development community.

Whether you are an indie, hobbyist, AAA developer, or just trying to learn, GameDev.net is the place for you to learn, share, and connect with the games industry. Learn more About Us or sign up!

Sign me up!