Aligning an object's rotation to that of a vector.

[Adam Miels]

Hi All.

Not really a question specific to Python in Maya, but I am trying to
write this in python, and know that there are quite a few experienced
maya people on the list.

I was wondering if there was possibly a better way to do this.

I am querying a point on a surface, to get a normal vector, then
trying to use this vector to orient an objects rotation matrix so that
it points in the direction of surface.
I have written my own method to apply the transform as .setTransform
in pymel doesn't seem to work:

def mySetMatrix(anObject, aMatrix):

   select(anObject)

   xform(m=(aMatrix.a00,aMatrix.a01,aMatrix.a02,aMatrix.a03, \

   aMatrix.a10,aMatrix.a11,aMatrix.a12,aMatrix.a13, \

   aMatrix.a20,aMatrix.a21,aMatrix.a22,aMatrix.a23, \

   aMatrix.a30,aMatrix.a31,aMatrix.a32,aMatrix.a33))

I query the point on the surface with:

normalVector = aMesh.getClosestNormal(aPoint, 'world')[0]

and then use the X,Y,Z values of this vector to calculate the
following matrices:

rotate on x axis:
where X = atan2(Y,Z)

              1        0        0        0

              0 cosX -sinX 0

0 sinX cosX 0

0 0 0 1

rotate on y axis:
where Y = atan2(X,Z)

            cosY     0      sinY     0

              0 1 0 0

-sinY 0 cosX 0

0 0 0 1

rotate on z axis:
where Z = atan2(Y,X)

            cosZ -sinZ      0        0

            sinZ cosZ 0 0

0 0 1 0

0 0 0 1

and then assigning the resulting matrix (original Matrx) X (X Matrix)
X (Y Matrix) X (Z Matrix) to the original object.

Although this approach seems to make sense to me on paper, when I
implement it, I get matrices that end up scaling the object instead of
only affecting its rotations, and they point in the wrong directions.

I was wondering if anyone could point me in the right direction with
this one (literally :P ) ?

Regards,

Adam Miels.

[Chad Vernon]

You need more than one vector to set an orientation since there are infinite orientations that can spin around the normal.  You need at least 2 non-parallel vectors to create an orientation.

If you have a normal vector n and a tangent vector t, you can create an orthonormal basis by:

x = n ^ t
t = x ^ n

Then you can pick which axis is which for your matrix:
x.x  x.y  x.z  0
n.x  n.y  n.z  0
t.x   t.y   t.z  0
0      0     0   1

Chad

--
http://groups.google.com/group/python_inside_maya

[Adam Miels]

Hi Chad,

Thanks for your reply.

Is the ^ representing to the power of?

I am not really worried about the rotation around the normal at this
stage, so can I use the getFaceVertexBinormal to get the tangent?

I am not sure what the . in the matrix you drew represents, is this a
dot product?

Regards,

Adam.

> --
> http://groups.google.com/group/python_inside_maya

[Chad Vernon]

The ^ is a cross product.  n, t, and x are MVectors which are part of the Maya API. So, n.x, n.y, n.z are just the 3 components of the vector n.  You should be able to use either the binormal or the tangent.  You could also even use an adjacent vertex.

--

http://groups.google.com/group/python_inside_maya

[Adam Mechtley]

Hi Adam,

This short video basically visualizes Chad's explanation, if it is helpful

http://adammechtley.com/tutorials/rigging/aim-constraints/

[Adam Miels]

Hi Adam.

Thanks for the link to your video.

This did help explain the need to calculate the cross product twice.

Now to implement it :)

/adam.

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> http://groups.google.com/group/python_inside_maya
>