SOLVED Rotate object around world axis regardless of orientation

Hello!

I'm having a hard time wrapping my brain around this script I'm trying to write.

I want to rotate a cube along the floor in the direction that it's being animated. The problem I'm running into is that I need to be able to specify the rotation around the world axis (just like how the rotate tool does) so that when the cube is oriented in any direction, I can still rotate properly with the animation.

Here's some pseudo code and a screen grab. Any help would be greatly appreciated!

# Rolling
distTraveled = pos - PREV_POS
numRevs.x = (distTraveled.x / circumfrence.x)
numRevs.z = (distTraveled.z / circumfrence.z)
outRot = numRevs * c4d.utils.DegToRad(360.0)
objMx = rotObj.GetMl()
rotMx = c4d.utils.MatrixRotY(-outRot.z) * c4d.utils.MatrixRotZ(outRot.x)
rotObj.SetMl(objMx * rotMx)

https://microsoft-my.sharepoint-df.com/✌/p/cosorgen/ESTEQCvARE1Nn4F3qnKfCC8B1nahC5Y3iHhSvgOtkhO0DQ?e=xhrNCK

This code almost works, but some of the time the cube rotates the wrong direction (although on the right axis).

Thanks so much @ferdinand! You all at Maxon are the best. Sorry my code is a shit show, just a quick hack at a rolling cube rig.

For anyone in the future looking for this solution here's what I needed:

    # Rolling
    distTraveled = pos - PREV_POS
    numRevs.x = (distTraveled.x / circumfrence.x)
    numRevs.z = (distTraveled.z / circumfrence.z)
    outRot = numRevs * c4d.utils.DegToRad(360.0)
    objMx = rotObj.GetMl()
    worldXInLocal = ~objMx * c4d.Vector(1, 0, 0)
    worldZInLocal = ~objMx * c4d.Vector(0, 0, 1)
    xTrans = c4d.utils.RotAxisToMatrix(worldXInLocal, -outRot.z)
    zTrans = c4d.utils.RotAxisToMatrix(worldZInLocal, outRot.x)
    rotObj.SetMl(objMx * xTrans * zTrans)

I needed the cube to be able to roll the correct way regardless of orientation. Admittedly this was a simple matrix transform issue that anyone who actually understood graphics programming would've known. (LOL not me)

Here's the full scene for anyone interested. test_cube_roll.c4d

Hello @codysorgenfrey,

thank you for reaching out to us. Your question is a bit hard to answer, given the abstract nature of the provided code and the absence of a specific setup/file. I would however point out that:

  1. This number of revisions expressed as a vector, i.e., separated onto axis, strikes me as a bit odd, since this is not how rotation works ^^
  2. Using BaseObject.GetMl() can make things harder to compute, depending on your setup. I would stay in world space.
  3. Most importantly I would point that you do not seem to take order of rotation into account, i.e., that matrix multiplication is not commutative, i.e., M * N != N * M which might get in the way in your second to last line, as you do not make this dependent on the travel direction.

I personally would also take a more "transform" oriented approach. As it much easier to just rotate a vector than figuring out into which direction you are now traveling and what that means for constructing a transform in "the proper way". I have provided below a quick solution as Python scripting tag, which is more meant to line out the approach rather than being a full solution (which we cannot provide). My solution requires an "aligned-with-world-frame" orientation for the start of travel. It would not be too hard to fix this, you must account for that additional delta before applying the final transform. I am just running a bit of time here, especially since this question is a bit out of scope of support (as it is just a math question).

If you need further help, also with the "alignment" condition, just ask 😉

Cheers,
Ferdinand

The result:
abc.gif

The file: rot_cube.c4d

The code:

import c4d
import math

# Global non-static variables are a really bad idea. Please replace this
# in a production environment with a more safe approach by for example
# storing this as a user-data parameter or just as an element in a
# BaseContainer of a node.
PREVIOUS_POSITION = None

NULL_VECTOR = c4d.Vector()
UP_VECTOR = c4d.Vector(0, 1, 0)

def main():
    """
    """
    # Get out when the tag is not attached to a BaseObject
    node = op.GetObject()
    if node is None:
        return

    # Get out when the position cache, PREVIOUS_POSITION, has not been yet
    # initialized.
    global PREVIOUS_POSITION
    if PREVIOUS_POSITION is None:
        PREVIOUS_POSITION = node.GetMg().off
        return

    # Compute the position delta and get out when it is the null/zero vector,
    # i.e., nothing happened.
    nodeMg = node.GetMg()
    currentPosition = nodeMg.off
    positionDelta = currentPosition - PREVIOUS_POSITION
    if positionDelta == NULL_VECTOR:
        return

    # Now we are going to compute the angle of rotation similarly to what you
    # did as a ratio of arc length (of travel) to circumference.

    # Compute the circumference of the traveling object as the maximum radius
    # of its bounding box. This also could be done for a non spherical case,
    # but would get quite a bit more complicated.
    boundingBoxRadii = node.GetRad()
    travelObjectCircumference = 2 * math.pi * max(boundingBoxRadii.x,
                                                  boundingBoxRadii.y,
                                                  boundingBoxRadii.z)

    # The traveled distance since the last update, i.e., the arc-length of the
    # angle of rotation.
    travelDistance = positionDelta.GetLength()

    # The angle of rotation, based on the arc-length to angle of rotation
    # relation:
    #
    #   arc_length        theta
    # --------------- = ---------
    #  circumference       2π
    #
    theta = travelDistance / travelObjectCircumference * 2 * math.pi

    # Now we are going to construct a transform for that angle. First we are
    # going to construct our axis rotation which is orthogonal to the travel
    # vector and an arbitrary up-vector, i.e., we simply assume one degree or
    # otherwise would have to also track the banking of the traveling object.

    axisRot = ~positionDelta % UP_VECTOR

    # Now we are just computing our final desired transform, we could do this,
    # i.e., constructing a transform out of an axis and an angle, manually but
    # since the Python SDK does offer RotAxisToMatrix, we are going to be lazy
    # and just use that :)
    transform = c4d.utils.RotAxisToMatrix(axisRot, theta)

    # Now we are just going to write this into the object's transform in world
    # space, i.e., what Cinema does call its global matrix.
    mg = node.SetMg(nodeMg * transform)

    # And we have to update our position cache at the end.
    PREVIOUS_POSITION = currentPosition

Thanks so much @ferdinand! You all at Maxon are the best. Sorry my code is a shit show, just a quick hack at a rolling cube rig.

For anyone in the future looking for this solution here's what I needed:

    # Rolling
    distTraveled = pos - PREV_POS
    numRevs.x = (distTraveled.x / circumfrence.x)
    numRevs.z = (distTraveled.z / circumfrence.z)
    outRot = numRevs * c4d.utils.DegToRad(360.0)
    objMx = rotObj.GetMl()
    worldXInLocal = ~objMx * c4d.Vector(1, 0, 0)
    worldZInLocal = ~objMx * c4d.Vector(0, 0, 1)
    xTrans = c4d.utils.RotAxisToMatrix(worldXInLocal, -outRot.z)
    zTrans = c4d.utils.RotAxisToMatrix(worldZInLocal, outRot.x)
    rotObj.SetMl(objMx * xTrans * zTrans)

I needed the cube to be able to roll the correct way regardless of orientation. Admittedly this was a simple matrix transform issue that anyone who actually understood graphics programming would've known. (LOL not me)

Here's the full scene for anyone interested. test_cube_roll.c4d

Hello @codysorgenfrey,

without any further questions, we will consider this topic as solved by Monday and flag it accordingly.

Thank you for your understanding,
Ferdinand