libinput: Absolute axes

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Absolute axes

Devices with absolute axes are those that send positioning data for an axis in a device-specific coordinate range, defined by a minimum and a maximum value.

Compare this to relative devices (e.g. a mouse) that can only detect directional data, not positional data.

libinput supports three types of devices with absolute axes:

- multi-touch screens
- single-touch screens
- graphics tablets

Touchpads are technically absolute devices but libinput converts the axis values to directional motion and posts events as relative events. Touchpads do not count as absolute devices in libinput.

For all absolute devices in libinput, the default unit for x/y coordinates is in mm off the top left corner on the device, or more specifically off the device's sensor. If the device is physically rotated from its natural position and this rotation was communicated to libinput (e.g. by setting the device left-handed), the coordinate origin is the top left corner of in the current rotation.

# Handling of absolute coordinates

In most use-cases, absolute input devices are mapped to a single screen. For direct input devices such as touchscreens the aspect ratio of the screen and the device match. Mapping the input device position to the output position is thus a simple mapping between two coordinates. libinput provides the API for this with

- libinput_event_pointer_get_absolute_x_transformed() for pointer events
- libinput_event_touch_get_x_transformed() for touch events

libinput's API only provides the call to map into a single coordinate range. If the coordinate range has an offset, the compositor is responsible for applying that offset after the mapping. For example, if the device is mapped to the right of two outputs, add the output offset to the transformed coordinate.

# Devices without x/y resolution

An absolute device that does not provide a valid resolution is considered buggy and must be fixed in the kernel. Some touchpad devices do not provide resolution, those devices are correctly handled within libinput (touchpads are not absolute devices, as mentioned above).

# Calibration of absolute devices

Absolute devices may require calibration to map precisely into the output range required. This is done by setting a transformation matrix, see libinput_device_config_calibration_set_matrix() which is applied to each input coordinate.

\[ \begin{pmatrix} cos\theta & -sin\theta & xoff \\ sin\theta & cos\theta & yoff \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ 1 \end{pmatrix} \]

\(\theta\) is the rotation angle. The offsets \(xoff\) and \(yoff\) are specified in device dimensions, i.e. a value of 1 equals one device width or height. Note that rotation applies to the device's origin, rotation usually requires an offset to move the coordinates back into the original range.

The most common matrices are:

- 90 degree clockwise: \( \begin{pmatrix} 0 & -1 & 1 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)
- 180 degree clockwise: \( \begin{pmatrix} -1 & 0 & 1 \\ 0 & -1 & 1 \\ 0 & 0 & 1 \end{pmatrix} \)
- 270 degree clockwise: \( \begin{pmatrix} 0 & 1 & 0 \\ -1 & 0 & 1 \\ 0 & 0 & 1 \end{pmatrix} \)
- reflection along y axis: \( \begin{pmatrix} -1 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)

See Wikipedia's Transformation Matrix article for more information on the matrix maths. See libinput_device_config_calibration_get_default_matrix() for how these matrices must be supplied to libinput.

Once applied, any x and y axis value has the calibration applied before it is made available to the caller. libinput does not provide access to the raw coordinates before the calibration is applied.

# Why x/y coordinates are not normalized

x/y are not given in normalized coordinates ([0..1]) for one simple reason: the aspect ratio of virtually all current devices is something other than 1:1. A normalized axes thus is only useful to determine that the stylus is e.g. at 78% from the left, 34% from the top of the device. Without knowing the per-axis resolution, these numbers are meaningless. Worse, calculation based on previous coordinates is simply wrong: a movement from 0/0 to 50%/50% is not a 45% degree line.

This could be alleviated by providing resolution and information about the aspect ratio to the caller. Which shifts processing and likely errors into the caller for little benefit. Providing the x/y axes in mm from the outset removes these errors.