Getting an object's local axes in worldspace?

[ohmboy]

hi all!

i am, as usual, having some problems with MEL and could use your help...

my question is: how can i get the 3 vectors (or float[]) that represent an object's local axes, in worldspace?
In other words, create for instace a cube and translate it to position (1,1,1). Now rotate it over Y by +90 degrees. Finally, check the "Display Local Axis" found in the attribute editor.
So:
the cube's local X axis is thus, with respect to WorldSpace coordinate system equal to (0,0,-1)
the cube's local Y axis is (0,1,0)
the cube's local Z axis is (1,0,0)

Is there any MEL command that can give me these values, regardless of the rotations that the object has undergone? Or do i need to write my own script to compute these vectors? If so, where do i start? For example, how can i get the orientation of any of the local axes?

Any input greatly appreciated!

thanks

alexander

[failure]

Multiply axis vectors with localToWorld matrix of the transform node

[andersegleus]

You can either get the transform's worldMatrix (wm) attribute using getAttr, or use the "xform -query -worldSpace -matrix" command.

In either case you get an array of 16 floats, which is in fact the flattened (i.e. in array form, not matrix) world space transformation matrix. if this matrix is
{M00, M021, M02, M03, M04, M05, M06, M07, M08, M09, M10, M11, M12, M13, M14, M15},
then it looks like this in matrix form:

| M00 M01 M02 M03 |
| M04 M05 M06 M07 |
| M08 M09 M10 M11 |
| M12 M13 M14 M15 |

Ok, So how does this answer your question?
Well, the nice thing about the world transformation matrix is that the elements translate very easily into the direction, scale, shear and translation of the local axes in world space:

Translation: {M12, M13, M14}
Direction of x-axis: {M00, M01, M02}
Direction of y-axis: {M04, M05, M06}
Direction of z-axis: {M08, M09, M10}

In short, the axes directions are stored in the upper left 3x3 submatrix, and the translation is stored in the left subvector of the bottom row.

Afaik, the last column of the matrix ({M03, M07, M11, M15}) is always {0, 0, 0, 1}, because the matrix is affine (don't ask me what that means though).

So, when you get the flattened matrix using getAttr or xform, you can determine the axes in vector form like this:

float $flatMatrix [16] = xform -q -ws -m $the\_object;
vector $wTranslation = <>;
vector $wLocalXAxis = <>;
vector $wLocalYAxis = <>;
vector $wLocalZAxis = <>;

note: getting the axes this way doesn't guarantee that the axes are unitized (i.e. their magnitude is 1), or perpendicular. If the object is scaled, this will reflect in the values (the axes' magnitude will not be 1). Same thing with shear (the axes will not be perpendicular to eachother).