Expressing a quaternion with zero rotation

Hi!

How do you do this? Up to now all formulas I've seen will cause the x y and z parts to collapse by sin(theta/2) if theta is 0. So how do you express say an orientation straight down the x-axis with no rotation about that axis? Thanks ;)

A zero rotation quaternion would be the unit quaternion.

Thanks mate. Out of curiousity what would its values be for an orientation down the x-axis? I did some research on unit quats but got more confused :)

What do you mean an orientation down the x - axis?

I think the question is, how can you produce a quaternion which points down the x-axis but expresses a rotation of 0? The answer is there's no such thing -- a rotation of 0 about the x-axis is a rotation of 0 about any axis. It's like asking which way the zero vector is pointing. It doesn't point anywhere at all.

O_o

Left-handed devils or right-handed devils?

*shrug*

Either way, I'd say a rotation of 90 degrees should suit you.

Soma

Quote:

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how can you produce a quaternion which points down the x-axis but expresses a rotation of 0?

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Wow. If that's his question, he wasn't kidding about being confused.

Soma

You'd better believe it!!!! I got it figured in the end, thanks guys ;)

Some code from my quaternion camera. Most of it taken from various tutorials on the internet and then plugged in to my existing system. Don't ask me how quaternions work b/c the math behind them is complex. I just know properties of them and various operations that can be performed on them. So this is one of those things in my book that 'just works'.

Code:

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void X3DCamera::Pitch(float angle)
{
    D3DXQUATERNION quat = m_qRot;
    D3DXQuaternionRotationAxis(&quat,TransformVector(&m_qRot,
                          &D3DXVECTOR3(1.0f, 0.0f, 0.0f)),
                          angle);
   
    m_qRot *= quat;
    D3DXQuaternionNormalize(&m_qRot,&m_qRot);
    m_inTransition = true;
}

void X3DCamera::Yaw(float angle)
{
    m_yaw += angle;
    D3DXMATRIX matRot;
    D3DXQUATERNION quat;
    D3DXMatrixRotationY(&matRot,m_yaw);
    D3DXQuaternionRotationMatrix(&quat,&matRot);

    D3DXQuaternionRotationAxis(&quat,TransformVector(&quat,
                              &D3DXVECTOR3(0.0f, 1.0f, 0.0f)),
                                                  angle);
   
    m_qRot *= quat;
    D3DXQuaternionNormalize(&m_qRot,&m_qRot);
    m_inTransition = true;
}

void X3DCamera::Roll(float angle)
{
    D3DXQUATERNION quat = m_qRot;
    D3DXQuaternionRotationAxis(&quat,TransformVector(&m_qRot,
                          &D3DXVECTOR3(0.0f, 0.0f, 1.0f)),
                          angle); 
    m_qRot *= quat;
    D3DXQuaternionNormalize(&m_qRot , &m_qRot);
    m_inTransition = true;
}

D3DXVECTOR3* X3DCamera::TransformVector(D3DXQUATERNION *pOrientation, D3DXVECTOR3 *pAxis)
{
    D3DVECTOR vNewAxis;
    D3DXMATRIX matRotation;

    // Build a matrix from the quaternion.
    D3DXMatrixRotationQuaternion(&matRotation, pOrientation);

    // Transform the queried axis vector by the matrix.
    vNewAxis.x = pAxis->x * matRotation._11 + pAxis->y * matRotation._21 + pAxis->z * 
    matRotation._31 + matRotation._41;

    vNewAxis.y = pAxis->x * matRotation._12 + pAxis->y * matRotation._22 + pAxis->z *
    matRotation._32 + matRotation._42;

    vNewAxis.z = pAxis->x * matRotation._13 + pAxis->y * matRotation._23 + pAxis->z *
    matRotation._33 + matRotation._43;

    memcpy(pAxis, &vNewAxis, sizeof(vNewAxis)); // Copy axis.
    return(pAxis);
}

void X3DCamera::GetViewMatrix(D3DXMATRIX *outMatrix)
{
    D3DXMATRIX matRot;
    D3DXQuaternionNormalize(&m_qRot,&m_qRot);
    D3DXMatrixRotationQuaternion(&matRot,&D3DXQUATERNION(-m_qRot.x,-m_qRot.y,-m_qRot.z,m_qRot.w));
   
    D3DXVECTOR3 vecLook(matRot._13,matRot._23,matRot._33);
    D3DXVECTOR3 vecOrbitPos = m_vecTargetPos + vecLook * -m_fCamDist;
    D3DXMATRIX matOrbit;
    D3DXMatrixTranslation(&matOrbit,-vecOrbitPos.x,-vecOrbitPos.y,-vecOrbitPos.z);
   
    D3DXMATRIX matTrans;
    D3DXMatrixTranslation(&matTrans,-Pos.x,-Pos.y,-Pos.z);
   
    m_matView = matOrbit * matRot * matTrans;
    *outMatrix = m_matView;
}

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That's really nice! Can i copy that please?

O_o

I don't imagine that he would've posted the example if he didn't intend for you to make use of it.

Soma

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I don't imagine that he would've posted the example if he didn't intend for you to make use of it.

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Hehe. :) One would think that such a conclusion was obvious but perhaps not. :D

Or it could even be described as being polite......

And i don't see why something you sweated over to make should just be acquired by someone without asking your permission first ;)