Quaternion Object Rotation

Garrick Winter · 2012-03-22T17:04:08

So I'm trying to code something similar to a 3D space sim, where I want six degrees of freedom. Apparently the best way to achieve 6DoF is with quaternions, so I've spent the last two days reading up about them and trying to get some code to work. I am using SFML 1.6 and OpenGL, nothing else. I have a Quaternion class that I'm fairly certain is mathematically correct, and can create a quaternion from an axis and an angle; it normalizes itself, and the multiplication operator is overloaded to perform a proper multiplication. However, don't understand how to transform the player's input into a quaternion representing a change in rotation. The player can input changes into the Pitch, Yaw and Roll, potentially all three at once. The object they are controlling is supposed to then rotate according to this input along its LOCAL axes. Suppose the player wanted to change the Pitch by 30°, the Yaw by 45° and the Roll by 10° all at the same time (I'm using that example because it's the most complex possible situation my code will have to deal with). So I have these nice little values, 30-45-10 (which I could also convert to radians), but what do I do with them? I've read dozens of tutorials, and what little I can make sense of them seems to indicate I need to make the change quaternion like this (pseudocode): Qaternion xChange = Quaternion.FromAxisAngle(30, 1, 0, 0); Qaternion yChange = Quaternion.FromAxisAngle(45, 0, 1, 0); Qaternion zChange = Quaternion.FromAxisAngle(10, 0, 0, 1); Qaternion totalChange = zChange * yChange * xChange; Where FromAxisAngle takes the parameters (float Angle, float X, float Y, float Z). Then I apparently need to perform this on the object's current Orientation, also a quaternion: Orientation = totalChange * Orientation; And finally derive a matrix from Orientation and pass that to glMultMatrix(). Unfortunately, my current code doesn't really work. Trying to change the yaw or roll just makes the object shiver, and trying to change the pitch makes the object spin correctly for a moment and then start to roll and grow enormously large at the same time. The thing is, deep down I know my code shouldn't work, because quaternion multiplications are non-commutative. I can't just willy-nilly multiply quaternions for three different orientations with one another - the order will end up influencing the result, right? What do I do when a particular axis isn't supposed to be rotating at the moment? I've got this not-working system in place, but I've tried half a dozen other configurations that don't work either. Rotation is the user-input rotation around the X,Y,Z axes respectively. I'n not doing any translation at the moment. void Entity::Transform(sf::Vector3<float> Translation, sf::Vector3<float> Rotation) { if (Rotation.x != 0) { Quaternion Offset = Quaternion(); Offset.FromAxisAngle(Rotation.x, 1, 0, 0); m_Orientation = Offset * m_Orientation; } if (Rotation.y != 0) { Quaternion Offset = Quaternion(); Offset.FromAxisAngle(Rotation.y, 0, 1, 0); m_Orientation = Offset * m_Orientation; } if (Rotation.z != 0) { Quaternion Offset = Quaternion(); Offset.FromAxisAngle(Rotation.z, 0, 0, 1); m_Orientation = Offset * m_Orientation; } //Derive a rotation matrix m_Orientation.RotationMatrix(m_RotationMatrix); } Can somebody tell me how I'm supposed to transform my player input into the appropriate quaternion transformations? Note that I've also tried directly creating a quaternion from stored PYR variables, but this didn't work and I was told by someone reading my code that that was the wrong way to implement this sort of thing (unfortunately, his explanation of the right way to do it was extremely vague, at least to me).

Math and Physics Programming

Started by GarrickW March 16, 2012 01:02 PM

13 comments, last by GarrickW 12 years, 1 month ago

alvaro

21,604

March 22, 2012 02:35 PM

What part of that code is initialization that you do once and what part is something you do in each iteration of the loop? Or do you do all of that every time?

GarrickW

115

Author

March 22, 2012 02:39 PM

What part of that code is initialization that you do once and what part is something you do in each iteration of the loop? Or do you do all of that every time?

The input code above is performed every time, assuming a certain flag is true. Rotation is then passed to the entity that is supposed to be rotating. Is that bad?

EDIT: Just to be sure, I changed the code such that it is executed regardless of the flag, and the same problem occurs.

alvaro

21,604

March 22, 2012 03:10 PM

I would remove the input and pretend the user is pressing "Down" constantly. Then either debug the program step by step and see if variables have the values you expect, or add logging to your code so you can see what it's doing. The advantage of doing it with logging is that you can then post the log here if you need help.

GarrickW

115

Author

March 22, 2012 03:18 PM

All right, I'll do some more intensive debugging and get back with the results.

GarrickW

115

Author

March 22, 2012 05:04 PM

Found it!

It turns out my implementation of quaternions wasn't correct after all. The code for quaternion multiplication I had was either wrong, or I copied it wrong. Either way, fixing it by referring to this site helped: http://www.arcsynthesis.org/gltut/Positioning/Tut08%20Quaternions.html

For the record, the correct quaternion multiplication code I now use is:

Quaternion Quaternion::operator* (Quaternion OtherQuat)

{

    float A = (OtherQuat.a * a) - (OtherQuat.x * x) - (OtherQuat.y * y) - (OtherQuat.z * z);

    float X = (OtherQuat.a * x) + (OtherQuat.x * a) + (OtherQuat.y * z) - (OtherQuat.z * y);

    float Y = (OtherQuat.a * y) + (OtherQuat.y * a) + (OtherQuat.z * x) - (OtherQuat.x * z);

    float Z = (OtherQuat.a * z) + (OtherQuat.z * a) + (OtherQuat.x * y) - (OtherQuat.y * x);

    Quaternion NewQuat = Quaternion();

    NewQuat.a = A;

    NewQuat.x = X;

    NewQuat.y = Y;

    NewQuat.z = Z;

    return NewQuat;

}

Many thanks to you, alvaro! I otherwise would have just assumed this was beyond my capabilities.

The object now rotates easily along all its local axes, no matter what previous rotations took place. Awesome!

Quaternion Object Rotation

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