Converting 3D rotation to 2D rotation

Question

I've been trying to figure out the 2D rotation value as seen from orthographic "top" view for a 3D object with XYZ rotation values in Maya. Maybe another way to ask this could be: I want to figure out the 2D rotation of a 3D obj's direction.

Here is a simple image to illustrate my question: Sample image for the question

I've tried methods like getting the twist value of an object using quaternion (script pasted below), to this post I've found: Component of a quaternion rotation around an axis.

If I set the quaternion's X and Z values to zero, this method works half way. I can get the correct 2D rotation even when obj is rotated in both X and Y axis, but when rotated in all 3 axis, the result is wrong.

I am pretty new to all the quaternion and vector calculations, so I've been having difficulty trying to wrap my head around it.

;)

def quaternionTwist(q, axisVec):
    axisVec.normalize()

    # Get the plane the axisVec is a normal of
    orthonormal1, orthonormal2 = findOrthonormals(axisVec)

    transformed = rotateByQuaternion(orthonormal1, q)

    # Project transformed vector onto plane
    flattened = transformed - ((transformed * axisVec) * axisVec)
    flattened.normalize()

    # Get angle between original vector and projected transform to get angle around normal
    angle = math.acos(orthonormal1 * flattened)

    return math.degrees(angle)

q = getMQuaternion(obj)
# Zero out X and Y since we are only interested in Y axis.
q.x = 0
q.z = 0
up = om2.MVector.kYaxisVector
angle = quaternionTwist(q, up)

John Alexiou · Accepted Answer · 2021-05-22 22:25:32Z

1

Can you get the (x,y,z) coordinates of the rotated vector? Once you have them use the (x,y) values to find the angle with atan2(y,x).

answered May 22, 2021 at 22:25

John Alexiou

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1 Comment

Meatball Pie Over a year ago

This has helped me solve the problem. I have been overthinking when a simple atan on orientation vector was the solution. I've posted the final working code as a separate answer.

rwadman · Accepted Answer · 2021-05-22 10:03:22Z

0

I'm not familiar with the framework you're using, but if it does what it seems, I think you're almost there. Just don't zero out the X and Z components of the quaternion before calling quaternionTwist().

The quaternions q1 = (x,y,z,w) and q2 = (0, y, 0, w) don't represent the same rotation about the y-axis, especially since q2 written this way becomes unnormalized, so what you're really comparing is (x,y,z,w) with (0, y/|q2|, 0, w/|q2|) where |q2| = sqrt(y^2 + w^2).

answered May 22, 2021 at 10:03

rwadman

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Meatball Pie Over a year ago

Thanks for the explanation on the X and Z components. So, I've removed q.x = 0 and q.z = 0, however, I still cannot get the 2D rotation to match when I rotate the 3D obj's Z rotation. Rotating only X and Y does. I assume I am correctly retrieving the twist rotation about the axis vector (y-axis) but I feel like I am missing another step...

Meatball Pie · Accepted Answer · 2021-05-23 14:17:11Z

0

Here is a working code for Maya using John Alexiou's answer:

matrix = dagPath.inclusiveMatrix() #OpenMaya dagPath for an object
axis = om2.MVector.kZaxisVector
v = (axis * matrix).normal()
angle = math.atan2(v.x, v.z) #2D angle on XZ plane

answered May 23, 2021 at 14:17

Meatball Pie

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