Windows Mouse Acceleration Curve: SmoothMouseXCurve and SmoothMouseYCurve

Question

What is the format of the data of SmoothMouseXCurve and SmoothMouseYCurve in the registry key:

HKEY_CURRENT_USER\Control Panel\Mouse

score 10 · Accepted Answer · answered Jul 10 '11 at 03:09

The two registry keys contain the 5 coordinate pairs of a mouse acceleration graph inflection points (in this case, points in a graph that produce a curve). SmoothMouseXCurve contains the X coordinate points and SmoothMouseYCurve contain the Y coordinate points.

The first point is always 0,0, and refers to the beginning of the curved graph. So, if you inspect your values, you'll notice the first line of both registry values is 00,00,00,00,00,00,00,00. Each subsequent line introduces an inflection point in the graph. Any point after the fifth isn't required since Windows will extrapolate the remaining of the graph from these 5 points.

Each coordinate pair (each line of the five lines in the registry keys) is written in a 16.16 fixed point format (16 bit int + 16 bit fraction). As such you will always only use the first 4 hex of each line. 2 for the integer part and two for the fractional part.

EDIT: This is a somewhat old article on mouse acceleration in XP. It still applies to Vista and Windows 7. However, to my knowledge the formulas have changed slightly, for which reason if you intend to draw your own acceleration graphs, you shouldn't trust those formulas. In any case, it gives you an idea of the process that hasn't changed since then.

score 2 · Answer 2 · answered Feb 23 '22 at 14:36

And the article mentioned above, which is now dead, is archived, and gives the full technical explanation answer to the question.

Pointer Ballistics for Windows XP

Updated: October 31, 2002

Summary of Ballistic Performance

This paper describes the algorithms for the pointer ballistics for Microsoft Windows XP and is intended for hardware engineers, driver developers, test managers, and independent hardware vendors. The new algorithms overcome some of the limitations and fallbacks of the ballistic algorithms in the previous operating systems. The main feature results in smoother pointer movements regardless of the pointer speed setting.

Pointer Ballistics Objectives for Windows XP

The objectives of the pointer ballistics for Windows XP are to fix earlier problems and to:

Allow effective navigation of high-resolution and high-dpi screens while maintaining pointer precision at the pixel level.
Smooth the movement of the pointer.
Apply a gain factor to the velocity input based on the total vector, instead of the X and Y coordinates individually.
Minimize movement during object selection that would allow users to select objects one pixel apart
Remove the Advanced button and design a unified acceleration and velocity slider to simplify the user interface in the Mouse Properties dialog box.

Ballistics Problems Before Windows XP

Problems with pointer ballistics before Windows XP included the following:

Acceleration is applied separately to X-axis and Y-axis and thus biases the axis of greatest magnitude. For example, with the ballistics turned on, when moving pointing device in a perfect circle the resultant figure will look more like a square with rounded corners than a circle.
Users with high-resolution and high-dpi (dots per inch) screens require faster pointer speeds, and the old ballistics are not set up to handle fast pointer speeds and fine precision (being able to target every pixel). At high-speed pointer settings, the pointer skips pixels regardless of the velocity, making fine precision selection impossible.
The user interface for acceleration and speed settings is confusing because a majority of the users don't understand the meaning of the term "acceleration" in this context.

Basic Theory of Pointer Ballistics for Windows XP

For Windows XP, we designed a transfer function that relates the actual velocity of the mouse to the actual velocity of the pointer on the screen. Then an algorithm was applied to that transfer function to calculate the transferred pointer data. To improve design by giving physical meaning to the transfer function, the arbitrary units of the system were first converted to physical units.

Relating to Physical Units

Arbitrary units of the mouse were transformed to physical units by taking the X or Y value of the mouse called mickey and scaling it using the update rate of the mouse bus and the resolution of the pointing device:

The typical bus update rate for a USB mouse is 125 Hz, and the typical pointer resolution is 400 mickey/inch. The typical range of a mickey size per packet that coming from a mouse is between 0 and +50, though +127 is allowed in the packet structure. For example, if a standard USB mouse has a constant output of 3 mickey per packet, the physical velocity of that device is 0.9375 or about 1 inch/second.

To transfer the screen from arbitrary units to physical units the following relationship was used:

For example, a typical 17-inch monitor running at 1024 X 769 will have a resolution of about 80 dpi and a refresh rate of about 75 Hz. Thus, if the data is not transformed (default setting with no ballistics) from the previous example, then at 3 mickey per packet, the pointer physically moves at 2.8 inches/second on the screen. Thus, with a USB mouse and a 17-inch screen with the above specifications, there is a physical to virtual gain of 3 (2.8/9.375). In other words, the physical velocity of the pointer on the screen is three times faster than the physical velocity of the mouse.

The Parent Transfer Function

When the physical units were established, the parent transfer function was constructed based on a usability study. The parent transfer function is illustrated in the following graph:

The transfer function consists of five points. Four of the five points reside in the lower end of the mouse velocity spectrum. The velocities that go beyond the 4-inch limit are linearly extrapolated.

The Family of Curves

A family of curves is extrapolated from the parent curve to yield a transfer function with varying speed and acceleration properties, as shown in the graph below. The user selects one of these curves using the pointer speed slider in the MouseProperties dialog box (Pointer Options tab).

Precision Movement

The following figure shows a more detailed view of the critical inflection points of the transfer function graph.

The slope of the first line segment yields a physical-to-screen gain of less than one gain, providing the precision movement and ability to target every pixel on the screen, or subpixilation. Subpixilation is when the user has to move the mouse physically farther than the pointer moves on the screen, giving a high degree of precision and stability at low velocities. To achieve subpixilation, the divided remainder mouse counts have to be preserved and added into the next counts.

The following figure shows the same close-up with the family of curves. The most important feature to note is that regardless of whether a fast or slow curve is selected, the first set of points tends towards subpixilation, which means that the user is always able to target every pixel on the screen regardless of the mouse speed setting.

Calculating Acceleration

The transfer function is stored as a lookup table, and the points between the stored values are interpolated. The number used to look up the mouse X and Y translated values is the vector magnitude of incoming X and Y magnitudes. The ballistic algorithm used before Windows XP independently calculated the acceleration multiplier from X and Y. Therefore, the movement of the pointer was biased towards the greater axis, which resulted in rounded squares instead of perfect circles. To solve this problem, the vector magnitude of X and Y is now used to calculate the acceleration multiplier and is then applied to translate the X and Y data.

Fixed Point Math and Number Bounds

The ballistic Windows XP pointer algorithm resides between ring0 and ring3. Therefore, floating point math is not readily available, and because the Windows XP ballistics required the use of division with a remainder, fixed-point (16.16) integer math was used. This is important for the subpixilation and the increased smoothness of the pointer movement. Therefore, the maximum resultant number from two products is 2^16 (65536). While an overflow is possible, it is very unlikely. If an overflow ever becomes a problem in the future, the fixed point constants in the ballistics code are easily changed to support a 20.12 fixed-point format.

Changing the Transfer Function

The values of the parent curve are stored in a registry setting, its possible to modify and customized the curves and could be achieved easily with a GUI. These characteristics should allow programmers and users custom control of the pointer ballistics to meet a wide variety of needs. Five X and Y pairs are stored in 16.16 fixed point format.

Summary of the Ballistic Algorithm for Windows XP

The following list summarizes the ballistic algorithm used in Windows XP, in sequence:

When the system is started or the mouse speed setting is changed, the translation table is recalculated and stored. The parent values are stored in the registry and in physical units that are now converted to virtual units by scaling them based on system parameters: screen refresh rate, screen resolution, default values of the mouse refresh rate (USB 125 Hz), and default mouse resolution (400 dpi). (This may change in the future to actually reflect the pointer parameters.) Then the curves are speed-scaled based on the pointer slider speed setting in the Mouse Properties dialog box (Pointer Options tab).
Incoming mouse X and Y values are first converted to fixed-point 16.16 format.
The magnitude of the X and Y values is calculated and used to look up the acceleration value in the lookup table.
The lookup table consists of six points (the first is [0,0]). Each point represents an inflection point, and the lookup value typically resides between the inflection points, so the acceleration multiplier value is interpolated.
The remainder from the previous calculation is added to both X and Y, and then the acceleration multiplier is applied to transform the values. The remainder is stored to be added to the next incoming values, which is how subpixilation is enabled.
The values are sent on to move the pointer.
If the feature is turned off (by clearing the Enhance pointer precision check box underneath the mouse speed slider in the Mouse Properties dialog box [Pointer Options tab]), the system works as it did before without acceleration. All these functions are bypassed, and the system takes the raw mouse values and multiplies them by a scalar set based on the speed slider setting.