I'm working on a simple problem which is giving me some trouble right now. The problem is to build the lookat matrix for a camera in 3D. I ussume a left-handed coordinate system, i.e. z+ is pointing toward the screen. So, Eye being the point where the camera stands, At the point the camera is looking at, i construct an orthonormal basis for this new system like so :
Z = Normalize(At - Eye)
X = Normalize(Up x Z)
Y = Normalize(Z x X)
where x is the cross-product of two vectors and up is the original world ip vector (usually (0,1,0)).
Now, to build the matrix containing the rotation part of the transformation, i just build the matrix (X, Y, Z) where X, Y, X are the column vectors calculates above. This gives the following matrix :
[X.x Y.x Z.x 0]
[X.y Y.y Z.z 0]
[X.z Y.z Z.z 0]
[0 0 0 1]
To takes into account the translation to Eye, i then multiply this matrix by
[1 0 0 -Eye.x]
[0 1 0 -Eye.y]
[0 0 1 -Eye.z]
[0 0 0 1 ]
which gives
[X.x Y.x Z.x -(X.x*Eye.x + Y.x*Eye.y + Z.x*Eye.z)]
[X.y Y.y Z.z -(X.y*Eye.x + Y.y*Eye.y + Z.y*Eye.z)]
[X.z Y.z Z.z -(Z.z*Eye.x + Y.z*Eye.y + Z.z*Eye.z)]
[0 0 0 1 ]
The problem i have is that, when i look at the MSDN page for [font="Consolas, Courier, monospace"][size="4"]D3DXMatrixLookAtLH, [/font]the translation part had dot products. Yes, i'm using column major
matrices with column vectors, but it should be the same. In order to have those dot products, i would need to write my initial rotation matrix this way :
[X.x X.y X.z 0]
[Y.x Y.y Y.z 0]
[Z.x Z.y Z.z 0]
[0 0 0 1]
Did i write my rotation matrix wrong ?
