Hello!

Currently iam writing my Bachelor Thesis in Electronical Engineering and i had to program with Eigen.
I use Eigen mostly for geometric transformations in R³ space.

I represent a orientation by 2 vectors. A front and a up vector (i think similar to the viewpoint in openGL).
They are normalized, perpendicular and have their coordinate origin at (0,0,0)
Everythink works fine so far.

My Problem is, i had to write a function, which returns the difference between 2 orientations.
The best thing would be a rotations matrix, which transforms the first orientation into the other, but i have really no clue how to get this rotation matrix.

Is there a common algorithm or function i have overseen?

Thanks for any help!

Greetings

Form your full basis into 3x3 matrices B1 and B2, and then what your are looking for is simply B2 * B1.transpose().

Hi,

thats not exactly what i was looking for.
But thank you anyway! good support here.

But I've solved my problem.

Greetings

hm, then please post your solution.

no problem.

I divide the difference between 2 orientation into 2 rotations.

The first rotates the front vector of orientation1 into the front vector of orientation2.
For this I use "AngleAxis". I get the angle from the dot product of the front vectors (change formula to the angle).
And I get the axis to rotate from the cross product of the front vectors.

After the front vectors of orientation1 and orientation2 are in the same position i do the same thing with the upvector.

Finally i multiply the two rotations and i get the transformation to transform orientation1 into orientation2.

Sry for my bad english. Iam from germany

ok, then I well understood your question and my solution is simpler and faster (no trigo):

Code: Select all

Matrix3f R1, R2, Rdiff;
R1 << up1, front1, up1.cross(front1);
R2 << up2, front2, up2.cross(front2);
Rdiff = R2 * R1.transpose();


Thank your sir!

Your solution is much better!

could you post a link (wikipedia or something), where I can understand your formula.
I would like to understand why this works.

greetings

You have to understand what a basis is an that a unitary (or orthonormal) basis is the same as a rotation matrix. For instance, the matrix R1 stores as column your basis (up,front,left)_1. R1 * p transforms a point p expressed in your basis into the world space Since R1 is orthonormal, you can see it as the rotation that transforms the basis 1,0,0 ; 01,0 ; 0,0,1 to (up,front,left)_1. So to get the rotation difference between your two bases you simply cancel the first one and then apply the second one. Also recall that for a unitary matrix, its inverse is simply its transpose. Hope that helps.

After reading some articles and watching some youtube videos about it, I understand it well enough to handle it.

Thank for your advice!