# Pointer acceleration

libinput uses device-specific pointer acceleration methods, with the default being the Linear pointer acceleration. The methods share common properties, such as Velocity calculation.

This page explains the high-level concepts used in the code. It aims to provide an overview for developers and is not necessarily useful for users.

## Pointer acceleration profiles

The profile decides the general method of pointer acceleration. libinput currently supports three profiles: “adaptive”, “flat” and “custom”.

• The adaptive profile is the default profile for all devices and takes the current speed of the device into account when deciding on acceleration.

• The flat profile is simply a constant factor applied to all device deltas, regardless of the speed of motion (see The flat pointer acceleration profile).

• The custom profile allows the user to define a custom acceleration function, giving full control over accelerations behavior at different speed (see The custom acceleration profile).

Most of this document describes the adaptive pointer acceleration.

## Velocity calculation

The device’s speed of movement is measured across multiple input events through so-called “trackers”. Each event prepends a the tracker item, each subsequent tracker contains the delta of that item to the current position, the timestamp of the event that created it and the cardinal direction of the movement at the time. If a device moves into the same direction, the velocity is calculated across multiple trackers. For example, if a device moves steadily for 10 events to the left, the velocity is calculated across all 10 events.

Whenever the movement changes direction or significantly changes speed, the velocity is calculated from the direction/speed change only. For example, if a device moves steadily for 8 events to the left and then 2 events to the right, the velocity is only that of the last 2 events.

An extra time limit prevents events that are too old to factor into the velocity calculation. For example, if a device moves steadily for 5 events to the left, then pauses, then moves again for 5 events to the left, only the last 5 events are used for velocity calculation.

The velocity is then used to calculate the acceleration factor

## Acceleration factor

The acceleration factor is the final outcome of the pointer acceleration calculations. It is a unitless factor that is applied to the current delta, a factor of 2 doubles the delta (i.e. speeds up the movement), a factor of less than 1 reduces the delta (i.e. slows the movement).

Any factor less than 1 requires the user to move the device further to move the visible pointer. This is called deceleration and enables high precision target selection through subpixel movements. libinput’s current maximum deceleration factor is 0.3 (i.e. slow down to 30% of the pointer speed).

A factor higher than 1 moves the pointer further than the physical device moves. This is acceleration and allows a user to cross the screen quickly but effectively skips pixels. libinput’s current maximum acceleration factor is 3.5.

## Linear pointer acceleration

The linear pointer acceleration method is the default for most pointer devices. It provides deceleration at very slow movements, a 1:1 mapping for regular movements and a linear increase to the maximum acceleration factor for fast movements.

Linear pointer acceleration applies to devices with above 1000dpi resolution and after Normalization of relative motion is applied.

The image above shows the linear pointer acceleration settings at various speeds. The line for 0.0 is the default acceleration curve, speed settings above 0.0 accelerate sooner, faster and to a higher maximum acceleration. Speed settings below 0 delay when acceleration kicks in, how soon the maximum acceleration is reached and the maximum acceleration factor.

Extremely low speed settings provide no acceleration and additionally decelerate all movement by a constant factor.

## Pointer acceleration for low-dpi devices

Low-dpi devices are those with a physical resolution of less than 1000 dots per inch (dpi). The pointer acceleration is adjusted to provide roughly the same feel for all devices at normal to high speeds. At slow speeds, the pointer acceleration works on device-units rather than normalized coordinates (see Normalization of relative motion).

The image above shows the default pointer acceleration curve for a speed of 0.0 at different DPI settings. A device with low DPI has the acceleration applied sooner and with a stronger acceleration factor.

Touchpad pointer acceleration uses the same approach as the Linear pointer acceleration profile, with a constant deceleration factor applied. The user expectation of how much a pointer should move in response to finger movement is different to that of a mouse device, hence the constant deceleration factor.

The image above shows the touchpad acceleration profile in comparison to the Linear pointer acceleration. The shape of the curve is identical but vertically squashed.

## Pointer acceleration on trackpoints

The main difference between trackpoint hardware and mice or touchpads is that trackpoint speed is a function of pressure rather than moving speed. But trackpoint hardware is quite varied in how it reacts to user pressure and unlike other devices it cannot easily be normalized for physical properties. Measuring pressure objectively across a variety of hardware is nontrivial. See Trackpoints and Pointing Sticks for more details.

The deltas for trackpoints are converted units/ms but there is no common physical reference point for a unit. Thus, the same pressure on different trackpoints will generate different speeds and thus different acceleration behaviors. Additionally, some trackpoints provide the ability to adjust the sensitivity in hardware by modifying a sysfs file on the serio node. A higher sensitivity results in higher deltas, thus changing the definition of what is a unit again.

libinput attempts to normalize unit data to the best of its abilities, see The magic trackpoint multiplier. Beyond this, it is not possible to have consistent behavior across different touchpad devices.

The image above shows the trackpoint acceleration profile for the speed in units/ms.

## The flat pointer acceleration profile

In a flat profile, the acceleration factor is constant regardless of the velocity of the pointer and each delta (dx, dy) results in an accelerated delta (dx * factor, dy * factor). This provides 1:1 movement between the device and the pointer on-screen.

## Pointer acceleration on tablets

Pointer acceleration for relative motion on tablet devices is a flat acceleration, with the speed setting slowing down or speeding up the pointer motion by a constant factor. Tablets do not allow for switchable profiles.

## The custom acceleration profile

libinput supports a user-defined custom acceleration profile, which can be adjusted for different movement types supported by a device. Movement types include pointer movement, scrolling, etc. but the set of supported movement types depends on the device.

The custom pointer acceleration profile gives users full control over the acceleration behavior at different speeds. libinput exposes an acceleration function `f(x)` where the x axis is the device speed in device units per millisecond and the y axis is the pointer speed. By supplying the y axis values for this function, users can control the behavior of the device.

The user should take into account the native device dpi and screen dpi in order to achieve the desired behavior/feel.

The custom acceleration function is defined using `n` points which are spaced uniformly along the x axis, starting from 0 and continuing in constant steps. At least two points must be defined and there is an implementation-defined limit on how many points may be added.

Thus the points defining the custom function are: `(0 * step, f), (1 * step, f), ..., ((n-1) * step, f[n-1])` where `f` is a list of `n` values defining the output velocity for each input velocity. The acceleration factor is defined by the ratio of the output velocity to the input velocity. When a velocity value does not lie exactly on those points, a linear interpolation of the two closest points will be calculated. When a velocity value is greater than the max point defined, a linear extrapolation of the two biggest points will be calculated.

```input_delta = device delta units
delta_time = time in ms since last input_delta
input_speed = hypot(input_delta) / delta_time
output_speed = user_custom_function(input_speed)
acceleration_factor = output_speed / input_speed
output_delta = input_delta * acceleration_factor
```

An example is the curve of `0.0, 1.0` with a step of `1.0`. This curve is the equivalent of the flat acceleration profile with any input speed `N` mapped to the same pointer speed `N`. The curve `1.0, 1.0` neutralizes any input speed differences and results in a fixed pointer speed.

Another example is the custom acceleration function `x**2`, sampling the function at `4` points up to a maximum input speed of `9` will give us a custom function with a step of `3` and points `[0.0, 9.0, 36.0, 81.0]`:

More sampled points can be added to improve the accuracy of the user custom function.

Supported Movement types:

Movement type

Uses

supported by

Fallback

Catch-all default movement type

All devices

Motion

Used for pointer motion

All devices

Scroll

Used for scroll movement