Animating rod rest position

[josemendez]

Thank you for the help. Is there any existing code in obi for converting a quaternion(rotation of a joint of an animated rig) into a Darboux vector?

You have ObiUtils.RestDarboux(Quaternion q1, Quaternion q2). It takes two rotation quaternions as input, and outputs the Darboux vector that describes the change in curvature and torsion from q1 to q2. So you can take one joint as q2, its parent as q1, pass them to this function and you will get a Darboux vector.

Also out of curiosity, what is the point of having a rest position with rotational velocity? doesn't a rest position always have no rotational velocity?

A rod is basically a curve, right? On a curve, you can define a orthonormal frame (3 unit vectors orthogonal to each other) at any point:
- A vector that's tangent to the curve, pointing to the "direction" of the curve (tangent vector)
- A vector pointing "inside" or "outside" the curve (normal vector)
- A vector orthogonal to the other 2 (binormal vector)

This is known as the Frenet-Serret frame. If you want to describe how the shape of the curve changes between two points, you need to somehow compare two Frenet frames. This is where the Darboux vector comes into play.

Back to your original question: The Darboux vector determines the frame's change in curvature and torsion between two points. Both curvature and torsion are rotations (curvature is rotation around the normal/binormal frame vectors, and torsion is rotation around the tangent vector), so the Darboux vector is directly proportional to the curve's angular momentum. That's why it can be understood as an angular velocity vector.