June 23, 2008
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.