// HACKER NEWS — CYBERSECURITY
Smooth Move: Taming Trajectories with Polynomials
This article is all about movement.
Of a vehicle, or a robot, or something like a 3D printer.
A 3D printer is really just a specialized robot with a hot glue gun
which it can move in multiple directions while squirting out molten
plastic.
Our robot, or print head, has a position in space and also a velocity
which is how fast it is moving and an acceleration which is how rapidly
that velocity is changing.
Velocity is just the derivative
of position: how fast is our position changing.
Acceleration is the derivative
of velocity: how rapidly our velocity is increasing or decreasing.
These are all vectors in that they have
both magnitude and direction
but for (many) 3D printers and machines each axis is a separate mechanism, so this
article is for now going to talk about them as if they were scalars, eg:
just a positive or negative number.
Jerk is the derivative of
acceleration, which might seem like a pretty abstract thing to be worried about.
But imagine a mass in a box under constant acceleration.
Springs inside the box are pushing the mass to cause it to accelerate too.
But if we change the size or direction of the acceleration, the mass is going
to slide around until it reaches a new equilibrium.
Now imagine the box is your skull and the mass is your brain. Jerk is real!
There’s also higher derivatives which are sometimes called
Snap, Crackle and Pop.
Snap (sometimes called Jounce) is the rate of change of Jerk; Crackle is the rate
of change of Snap, etc.
I don’t have as neat an illustration of what these physically mean but there seems to be a consensus that
they, and presumably even higher derivatives, have an effect on vibration and so on of
mechanisms, and so they should be minimized too.