Quaternion Rotation Help

Question

So I'm making a little engine with DirectX 11 and C++. (Some other help from other API's as well) DirectX has this function XMMatrixRotationQuaternion(XMVECTOR quaternion). I know nothing about this so excuse my cluelessness. I have a few questions about them that maybe someone could help me with.

• Do I use XMMatrixRotationQuaternion(XMVECTOR quaternion) and multiply the resultant Matrix with my scaling matrix and translation matrix to get my transformation matrix?

• How can I convert an angle (let's say in radians) to a quaternion. I've tried to look at this and what I got was something like this(I have a feeling this isn't anywhere close to correct)...

• Lastly, do I need to normalize that XMFLOAT3 axis?

  static XMVECTOR XMConvertToQuaternion(XMFLOAT3 axis, float radian)
  {
     return XMVectorSet(cos(radian/2), sin(radian/2)*cos(axis.x), sin(radian/2)*cos(axis.y), sin(radian/2)*cos(axis.z));
  }
  

Answer 1

Do I use XMMatrixRotationQuaternion(XMVECTOR quaternion) and multiply the resultant Matrix with my scaling matrix and translation matrix to get my transformation matrix?

I believe so. At least that's what I do with D3D9. (D3DXMatrixRotationQuaternion) You might already know but multiplication order should be : scalingMatrix * rotationMatrix * translationMatrix

For converting an angle to a quaternion, you can use:

XMQuaternionRotationAxis XMQuaternionRotationNormal (which, as its name suggests, requires the axis vector to be normalized.)

http://msdn.microsoft.com/en-us/library/windows/desktop/microsoft.directx_sdk.quaternion.xmquaternionrotationaxis(v=vs.85).aspx http://msdn.microsoft.com/en-us/library/windows/desktop/microsoft.directx_sdk.quaternion.xmquaternionrotationnormal(v=vs.85).aspx

Answer 2

I'd expect the conversion to be more like:

static XMVECTOR XMConvertToQuaternion(XMFLOAT3 axis, float radian)
{
   return XMVectorSet(sin(radian/2)*axis.x, sin(radian/2)*axis.y, sin(radian/2)*axis.z, cos(radian/2));
}

in particular there is no need to push the coordinates through a cos and the w should be the last coordinate, there is a micro optimization that stores the sin(radian/2) in a temporary variable but I expect an optimizer to be able to deal with it.