LWJGL - Problems implementing 'roll' in a

I've spent a couple weeks on this issue and can't seem to find a proper solution and need some advice.

I'm working on creating a Camera class using LWJGL/Java, and am using Quaternions to handle bearing (yaw), pitch and roll rotations. I'd like this camera to handle all 6 degrees of movement in 3D space, and roll. Bearing, Pitch and Roll are all quaternions. I multiply them into a 'change' quaternion, and create a translation matrix from that. I put that in a float buffer, and multiply the modelview matrix by my buffer containing the rotation matrix.

I can get the bearing and pitch rotations to work properly, but when I implement roll, I'm running into issues. Mainly, rotating around the Z-axis (rolling) doesn't seem to work. When ever I "roll" the camera, it seems to roll around the global Z axis instead of the local camera direction axis. I can usually get 2 of the 3 to work depending on the order I multiply the quaternions, but I can't get them working together.

Since they all work independently, I'm assuming there's something wrong with my orientation method where I combine them and build a rotation matrix. I'm having problems pasting the whole class in, so here are the methods and declarations relating to rotation:

private final static float DEGTORAD = (float)(Math.PI/180);    

//Eye - position of the camera in the 3D world.
private Vector3f eye;

//Camera axis vectors, calculated each time reorient() is called.
//Initialized to global x, y, and z axis initially.
private Vector3f up;
private Vector3f right;
private Vector3f direction;

//Angles of rotation (in degrees)    
private float pitchAngle;
private float bearingAngle;
private float rollAngle;

private Quaternion pitch;
private Quaternion bearing;
private Quaternion roll;

private FloatBuffer viewMatrixBuffer = BufferUtils.createFloatBuffer(16);
private Quaternion currentOrientation;

...

/**
 * Change the bearing (yaw)
 * @param bearing delta in degrees
 */
public void bearing(float bearingDelta){
    bearingAngle += bearingDelta;
    if(bearingAngle > 360){
        bearingAngle -= 360;
    }else if(bearingAngle < 0){
        bearingAngle += 360;
    }
    bearing.setFromAxisAngle(new Vector4f(0f, 1f, 0f, bearingAngle * DEGTORAD));
    bearing.normalise();
}

/**
 * Change the pitch
 * @param pitch delta in degrees
 */
public void pitch(float pitchDelta){
    pitchAngle += pitchDelta;
    if(pitchAngle > 360){
        pitchAngle -= 360;
    }else if(pitchAngle < 0){
        pitchAngle += 360;
    }
    pitch.setFromAxisAngle(new Vector4f(1f, 0f, 0f, pitchAngle * DEGTORAD));
    pitch.normalise();
}

/**
 * @param initialRoll
 */
public void roll(float initialRoll) {
    rollAngle += initialRoll;
    if(rollAngle > 360){
        rollAngle -= 360;
    }else if(rollAngle < 0){
        rollAngle += 360;
    }
    roll.setFromAxisAngle(new Vector4f(0, 0, 1, rollAngle * DEGTORAD));
    roll.normalise();
}

/**
 * Change direction to focus on a certain point in the world
 * @param eye
 */
public void lookThrough(){
    reorient();
    GL11.glMultMatrix(viewMatrixBuffer);
}    

public void reorient(){
    //Multiply in order: bearing, pitch, roll.  Non-commutative!
    Quaternion change = new Quaternion();
    Quaternion.mul(bearing, pitch, change);
    Quaternion.mul(roll, change, change);
    // orient the camera...
    Matrix4f rotationMatrix = getRotationMatrix(change);

    //Get the looking direction
    direction.x = rotationMatrix.m20;
    direction.y = rotationMatrix.m21;
    direction.z = rotationMatrix.m22;

    //Set the position
    rotationMatrix.m30 = eye.x;
    rotationMatrix.m31 = eye.y;
    rotationMatrix.m32 = eye.z;
    rotationMatrix.m33 = 1;

    rotationMatrix.invert();
    rotationMatrix.store(viewMatrixBuffer);

    viewMatrixBuffer.rewind();

    Vector3f.cross(new Vector3f(0,1,0), direction, null).normalise(right);
    Vector3f.cross(right, direction, null).normalise(up);               
}

Vector3f, Quaternion, and Matrix4f are all LWJGL classes, not custom made.

So my question is, given 3 Quaternions representing Bearing, Pitch and Roll, how do I modify the ModelView matrix to accurately represent these rotations?

EDIT: I feel that this is very close. See the Gist link in RiverC's comment. After rotating so many degrees, the view jumps around a lot before coming back to normal when rolling. The gist of it is there, but it's still slightly off.

回答1:

You're doing the multiplications in the wrong order.

For two rotations q1 and q2, if q2 is to follow q1 (since rotations are generally non-communitive) you multiply q2*q1.

In a gimbal style system such as controls for a FPS, the priority order is always yaw, pitch, roll. This would suggest the following math:

roll * pitch * yaw

As a java point, I would suggest not creating new Quaternions for every update but anyway

change = Quaternion.mul(Quaternion.mul(roll, pitch, change), yaw, change);

If you look at the code, the third Quaternion will just be overwritten with the result, so no need to reset it or recreate it each frame / update.

This rotational order thing is confusing, but if you look at the Wiki page on Quaternions, it's the general rule.

回答2:

I know this is old, but allow me a guess anyway. The problem is exactly what you said yourself:

When ever I "roll" the camera, it seems to roll around the global Z axis instead of the local camera direction axis.

It does so because you asked it to roll around vector (0,0,1), that is, the global Z axis.

This is what unit quaternions do: they rotate a vector (here a set of vectors, your rotation matrix) around an axis specified by their imaginary vectorial part (x,y,z) by some angle function of the w scalar (w = cos(angle/2)).

If I understand what you are trying to do, that is rolling your camera as when tilting your head from left to right, then you should build a roll quaternion around your direction vector:

 roll.setFromAxisAngle(new Vector4f(direction.x, direction.y, direction.z, rollAngle * DEGTORAD));

I'm assuming your direction vector is normalized, or that LWJGL knows what to do with a non-unitary axis vector when calling setFromAxisAngle.