how to get 4x4 orientation matrix in BGE

Hi,
when I use Object.matrix_world in the Blender Python API (bpy), I get a 4x4 matrix which includes translation, rotation and scale. That’s basically what I need.
When I call KX_GameObject.worldOrientation in the BGE, I just get a 3x3 matrix that does not seem to change when the translation or the scale of the object changes. Is there a way to get the bpy-style 4x4 matrix in the game engine?
Thanks so much! And sorry for the about 1000th question about matrices.

I’m pretty sure the Wiki has the components of a 4x4 matrix somwhere.

By the way in a 3D Space the orientation matrix is 3x3 (see http://en.wikipedia.org/wiki/Rotation_matrix)

It contains the scaling too which are the diagonal terms (see http://en.wikipedia.org/wiki/Scaling_(geometry)).

To include the translation transformation you must extend the matrix to 3X4 (or 4x3? I can’t remeber). But it is easier to calculate with 4x4 Matrices so the Matrix can be extended to 4x4. Read http://en.wikipedia.org/wiki/Translation_matrix for details.

I forgot:
you create a Matrix with the scale parts only,
a matrix with the translation parts only and
a matrix with the rotation parts only.

Then multiply them to get the final transformation matrix.
Be aware the order of the multiplication is important (translationscalerotation != scalerotationtranslation).

That is all.

Monster

I guess you could put it together yourself in a function, something like this matches the matrix returned by the bpy

from mathutils import Matrix
def get_4x4(obj):
    ori = obj.worldOrientation
    pos = obj.worldPosition
    scale = obj.scaling
    rx = list(scale.x*ori[0])
    rx.append(0)
    ry = list(scale.y*ori[1])
    ry.append(0)
    rz = list(scale.z*ori[2])
    rz.append(0)
    rw = list(pos)
    rw.append(1)
    return Matrix([rx,ry,rz,rw])