# Posts tagged ‘Articulation’

Just a quick theoretical idea – I’ve been thinking that a rotation is basically the reflection or product of a direction indirectly or directly controlled by its spin.  This seems simple to understand in theory but in practice its more complex. Im coming to terms that rotation is really an illusion of a direction or a side product.

Thinking about this more in my notes, we can hypothesize that if a rotation is really just a direction, then we can seperate it into two parts: the direction and the spin and more importantly have direction controlled by anything, namely the tangent of a spline or curve. This seems amazingly simple now, the curviture of a spline dictating the direction of a quaternion about a hemisphere. But detaching yourself to thinking this way is really hard.

In this way we can treat the wrist and spine articulation the same – the spin (or twist in the conventional sence) is just used to dictate the direction of the system, with a spine you’d use the tangent of the curve itself,  with the wrist the hand  is the direction.

I don’t know if this is new but I’m calling it double strung quaternions (DSQ). Its a method to reinforce a rotation relative to a transform space. In lamens terms it trys to make rotations true to our way of seeing them in a control. I’ve been looking into ik spine systems and hopefully this maybe a way towards helping out with rotation issues. Here’s a demo using z as its direction.

(click on the above image to view it the demonstration)

Bugs im noticing are that it uses linear distances to work our the quernions, quatDrivers as I call them (they can infact drive any value with distances) – i get some slight wobblying, but i think this can be cured using a value-space normalisation method like so:

1. a = 10, b = 20
2. summation = 30
3. norm a = .33 norm b = .66
4. multiplication by the norm gives a = 3.33r and b = 13.66r

This is a derived final value which might yeild better results. The whole system is enclosable and useable across a variety of articulation problems.

So I’ve been looking into using quats to simulate joint rotation and deformation. What I’ve found out is that most joints of a human can fall into two systems: single and double quaternion systems. If a bone system doesn’t twist using its bone like the forearm then it can fall into a single quat system, which dictates just a direction , resolution of the twist happens naturally when two perpendicular axis’ come together at 90 degrees.

If a system has a twist dictated by bones in conjunction with muscle deformation, then one quaternion is needed to dictate the twist space the second ‘deformation’ quat rides on. With this we can say that twist is not only dictated by the resolution of the system it exists in, but by the spin this system dictates. The order of which system drives each space is important.