Input devices should allow users to configure a velocity mapping curve (which could be negative to reverse the motion). X-Widows had a crude threshold-based mouse acceleration scheme, but it's better to have an arbitrary curve, like the TrackPoint uses, that can be optimized for the particular user, input device, screen size, and scrolling or pointing task at hand.

https://wiki.archlinux.org/index.php/Mouse_acceleration

One of the patented (but probably expired by now) aspects of the Trackpoint is that it has a very highly refined pressure=>cursor speed transfer function, that has a couple of plateaus in it that map a wide range of pressures to one slow or fast but constant speed. The slow speed notch is good for precise predictable fine positioning, and the fast speed notch is tuned to be just below eye tracking speed, so you don't lose sight of the cursor. But you can push even harder than the fast plateau to go above the eye tracking plateau and flick the cursor really fast if you want, or push even lighter than the slow plateau, for super fine positioning. (The TrackPoint sensor is outrageously more sensitive than it needs to be, so it can sense very soft touches, or even your breath blowing on it.)

Here's a description of Ted Selker's work and all the refinement that went into the TrackPoint, that he developed at IBM Almaden Research Lab:

https://news.ycombinator.com/item?id=9438461

Highlights:

In 1984 he observed that it took 0.75 - 1.75 seconds to reposition the hand from the keyboard to the mouse, which is a long time for something that you do quite often. `

He tried many different ideas and built several prototypes, then later when he was working at IBM Alameda Research Lab, he had a chance to refine the idea into a product.

He had his father, a material scientist, help by designing the special non-skid rubber that the clitoris was made from.

IBM wouldn't let him ship it until it was measurably as efficient as a mouse for common tasks.

The thing going for it was that it eliminated the 0.75 - 1.75 second hand repositioning penalty, but of course the fundamental problem with it that you can't get around is that it's a relative positioning device, not an absolute positioning device like a mouse. So he had to come up with ways of overcoming that problem.

The trackpoint performs very well for mixed typing and pointing tasks, since you switch between typing and pointing so often, and that adds up to a lot of time, and is a very common way of using computers. The mouse is still better for tasks that are mostly pointing and clicking, but it takes up some prime real-estate on your desk, and there are many situations where a mouse is impossible to use with a laptop.

He also made the observation that when the cursor moved above eye tracking speed, you tended to lose track of it. And also the observation that some of the time you needed to position it finely around a small area, and other times you needed to move it quickly across a large area.

So he came up with a pressure-to-speed "transfer function" that had a non-linear mapping from how hard you were pressing it to how fast the cursor moved.

The mapping had a plateau at "predictable fine positioning speed" (i.e. there was a wide range of light pressure that would map to moving the cursor at one exact slow predictable speed, so you could smoothly cruise the cursor around with a light touch at a speed that was good for exact positioning. Then after the plateau of light pressure, it sloped up smoothly until just below eye tracking speed, where there was another plateau, mapping a wide range of harder pressure to a fast-but-not-so-fast-that-you-lose-track-of-it speed, for coarse positioning without losing the cursor. And then above that there was a fast speed for quickly flicking the cursor to the other side of the screen.

Once I was sitting in a coffee shop in Mountain View hacking on my Thinkpad, and Ted and his wife Ellen rolled in, sat down, and started chatting. Ted noticed that my Thinkpad's Joy Button was all worn down, and he was mortified and quickly excused himself to go out to the car. Ellen rolled her eyes and shrugged, explaining that he was always like that. Then he came back with a big bag of red Joy Buttons, and replaced my worn-out one right there in the coffee shop, and gave me a few extras as spares!