Get eye, target and up vectors from view matrix

In Direct3D, I'm using the Matrix.LookAtLH function to compute the view matrix.

I am using this for the camera, which I orbit around a target by moving the origin to the target position开发者_C百科, rotating, and then moving the origin back to (0,0,0).

This is multiplied to the matrix that was originally computed from LookAtLH.

Is there a way I can, after a few of these operations, decompose the matrix to get the eye position, target position, and up vector?

---

View matricies are very easy to extract data from. Check out the documentation for the function you used (I've used the documentation for D3DXMatrixLookAtLH):

http://msdn.microsoft.com/en-us/library/bb205342%28v=vs.85%29.aspx

As you can see towards the bottom of the page, the matrix is internally generated like so:

zaxis = normal(At - Eye)
xaxis = normal(cross(Up, zaxis))
yaxis = cross(zaxis, xaxis)

 xaxis.x           yaxis.x           zaxis.x          0
 xaxis.y           yaxis.y           zaxis.y          0
 xaxis.z           yaxis.z           zaxis.z          0
-dot(xaxis, eye)  -dot(yaxis, eye)  -dot(zaxis, eye)  1

Bear in mind, this is only valid for DirectX; transpose the above matrix when porting the same calculations to OpenGL because the coordinate system in DirectX is backwards to the norm.

---

Two options :

• Long and difficult : extract eye, up and lookAt from the new computed matrix
• Easy version : apply your transformations (translation, rotation, translation) to a copy of your eye, up, and lookAt. This way you will get very easily the new vectors.