DeviceOrientation Event Specification

1. Conformance requirements

All diagrams, examples, and notes in this specification are non-normative, as are all sections explicitly marked non-normative. Everything else in this specification is normative.

The key words "MUST", "MUST NOT", "REQUIRED", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in the normative parts of this document are to be interpreted as described in RFC2119. For readability, these words do not appear in all uppercase letters in this specification. [RFC2119]

Requirements phrased in the imperative as part of algorithms (such as "strip any leading space characters" or "return false and abort these steps") are to be interpreted with the meaning of the key word ("must", "should", "may", etc) used in introducing the algorithm.

Conformance requirements phrased as algorithms or specific steps may be implemented in any manner, so long as the end result is equivalent. (In particular, the algorithms defined in this specification are intended to be easy to follow, and not intended to be performant.)

User agents may impose implementation-specific limits on otherwise unconstrained inputs, e.g. to prevent denial of service attacks, to guard against running out of memory, or to work around platform-specific limitations.

Implementations that use ECMAScript to implement the APIs defined in this specification must implement them in a manner consistent with the ECMAScript Bindings defined in the Web IDL specification, as this specification uses that specification’s terminology. [WEBIDL]

The events introduced by this specification implement the Event interface defined in the DOM Specification, [DOM] . Implementations must therefore support this specification.

2. Introduction

This section is non-normative.

This specification provides two new DOM events for obtaining information about the physical orientation and movement of the hosting device. The information provided by the events is not raw sensor data, but rather high-level data which is agnostic to the underlying source of information. Common sources of information include gyroscopes, compasses and accelerometers.

The first DOM event provided by the specification, deviceorientation , supplies the physical orientation of the device, expressed as a series of rotations from a local coordinate frame.

The second DOM event provided by this specification, devicemotion , supplies the acceleration of the device, expressed in Cartesian coordinates in a coordinate frame defined in the device. It also supplies the rotation rate of the device about a local coordinate frame. Where practically possible, the event should provide the acceleration of the device’s center of mass.

The following code extracts illustrate basic use of the events.

window.addEventListener("deviceorientation", function(event) {
    // process event.alpha, event.beta and event.gamma
}, true);

{
  alpha: 90,
  beta: 0,
  gamma: 0
};

{
  alpha: 270 - alpha,
  beta: 0,
  gamma: 90
};

window.addEventListener("devicemotion", function(event) {
    // Process event.acceleration, event.accelerationIncludingGravity,
    // event.rotationRate and event.interval
}, true);

{
  x: 0,
  y: 0,
  z: 9.8
};

{
  x: 0,
  y: 0,
  z: -9.8
};

{
  acceleration: {x: v^2/r, y: 0, z: 0},
  accelerationIncludingGravity: {x: v^2/r, y: 9.8, z: 0},
  rotationRate: {alpha: 0, beta: 0, gamma: -v/r*180/pi}
};

3. Scope

This section is non-normative.

This specification is limited to providing DOM events for retrieving information describing the physical orientation and motion of the hosting device. The intended purpose of this API is to enable simple use cases such as those in Use-Cases section. The scope of this specification does not include providing utilities to manipulate this data, such as transformation libraries. Nor does it include providing access to low sensor data, or direct control of these sensors.

4. Model

4.1. Device Orientation

This specification expresses a device’s physical orientation as a series of rotations relative to an implementation-defined reference coordinate frame.

The sequence of rotation steps is a set of intrinsic Tait-Bryan angles of type Z - X' - Y'' ( [EULERANGLES] ) that are applied on the device coordinate system defined in [ACCELEROMETER] and summarized below:

• x is in the plane of the screen or keyboard and is positive towards the right hand side of the screen or keyboard.

• y is in the plane of the screen or keyboard and is positive towards the top of the screen or keyboard.

• z is perpendicular to the screen or keyboard, positive out of the screen or keyboard.

For a mobile device such as a phone or tablet, the device coordinate frame is defined relative to the screen in its standard orientation, typically portrait. This means that slide-out elements such as keyboards are not deployed, and swiveling elements such as displays are folded to their default position. If the orientation of the screen changes when the device is rotated or a slide-out keyboard is deployed, this does not affect the orientation of the coordinate frame relative to the device. For a laptop computer, the device coordinate frame is defined relative to the integrated keyboard.

Note: Users wishing to detect changes in screen orientation should refer to [SCREEN-ORIENTATION] .

Rotations must use the right-hand convention, such that positive rotation around an axis is clockwise when viewed along the positive direction of the axis.

Note: the coordinate system used by this specification differs from CSS Transforms 2 § 4 The Transform Rendering Model , where the y axis is positive to the bottom and rotations follow the left-hand convention. Additionally, rotateSelf() and rotate() , specified in [GEOMETRY-1] , apply rotations in an Z - Y' - X'' order, which differs from the order specified here.

A rotation represented by alpha , beta and gamma is carried out by the following steps:

1. Rotate the device frame around its z axis by alpha degrees, with alpha in [0, 360).

   

   

2. Rotate the device frame around its x axis by beta degrees, with beta in [-180, 180).

   

3. Rotate the device frame around its y axis by gamma degrees, with gamma in [-90, 90).

   

Note: This choice of angles follows mathematical convention, but means that alpha is in the opposite sense to a compass heading. It also means that the angles do not match the roll-pitch-yaw convention used in vehicle dynamics.

4.1.1. Choice of reference coordinate system

A device’s orientation is always relative to another coordinate system, whose choice influences the kind of information that the orientation conveys as well as the source of the orientation data.

Relative orientation is measured with an accelerometer and a gyroscope, and the reference coordinate system is arbitrary. Consequently, the orientation data provides information about changes relative to the initial position of the device.

Note: In native platform terms, this is similar to a relative OrientationSensor on Windows, a game rotation vector sensor on Android, or the xArbitraryZVertical option for Core Motion.

Absolute orientation is measured with an accelerometer, a gyroscope and a magnetometer, and the reference coordinate system is the Earth’s reference coordinate system .

Note: In native platform terms, this is similar to an absolute OrientationSensor on Windows, a rotation vector sensor on Android, or the xMagneticNorthZVertical option for Core Motion.

4.2. Device Motion

This specification expresses a device’s motion in space by measuring its acceleration and rotation rate, which are obtained from an accelerometer and a gyroscope. The data is provided relative to the device coordinate system summarized in the previous section.

Acceleration is the rate of change of velocity of a device with respect to time. Is is expressed in meters per second squared (m/s ² ).

Linear acceleration represents the device’s acceleration rate without the contribution of the gravity force. When the device is laying flat on a table, its linear acceleration is 0 m/s ² .

When the acceleration includes gravity , its value includes the effect of gravity and represents proper acceleration ( [PROPERACCELERATION] ). When the device is in free-fall, the acceleration is 0 m/s ² . This is less useful in many applications but is provided as a means of providing best-effort support by implementations that are unable to provide linear acceleration (due, for example, to the lack of a gyroscope).

Note: In practice, acceleration with gravity represents the raw readings obtained from an Motion Sensors Explainer § accelerometer , or the [G-FORCE] whereas linear acceleration provides the readings of a Motion Sensors Explainer § linear-acceleration-sensor and is likely a fusion sensor. [MOTION-SENSORS] and [ACCELEROMETER] both contain a more detailed discussion about the different types of accelerometers and accelerations that can be measured.

The rotation rate measures the rate at which the device rotates about a specified axis in the device coordinate system . As with device orientation, rotations must use the right-hand convention, such that positive rotation around an axis is clockwise when viewed along the positive direction of the axis. The rotation rate is measured in degrees per second (deg/s).

Note: [MOTION-SENSORS] and [GYROSCOPE] both contain a more detailed discussion of gyroscopes, rotation rates and measurements.

5. Permissions Policy integration

This specification defines the following policy-controlled features :

• " accelerometer ", whose default allowlist is " self ".

• " gyroscope ", whose default allowlist is " self ".

• " magnetometer ", whose default allowlist is " self ".

6. Permissions API integration

This specification defines the following default powerful features :

• " accelerometer "

• " gyroscope "

• " magnetometer "

7. Task Source

The task source for the tasks mentioned in this specification is the device motion and orientation task source .

8. API

8.1. deviceorientation Event

partial interface Window {
    [SecureContext] attribute EventHandler ondeviceorientation;
};
[Exposed=Window, SecureContext]
interface DeviceOrientationEvent : Event {
    constructor(DOMString type, optional DeviceOrientationEventInit eventInitDict = {});
    readonly attribute double? alpha;
    readonly attribute double? beta;
    readonly attribute double? gamma;
    readonly attribute boolean absolute;
    static Promise<PermissionState> requestPermission(optional boolean absolute = false);
};
dictionary DeviceOrientationEventInit : EventInit {
    double? alpha = null;
    double? beta = null;
    double? gamma = null;
    boolean absolute = false;
};

The ondeviceorientation attribute is an event handler IDL attribute for the ondeviceorientation event handler , whose event handler event type is deviceorientation .

The alpha attribute must return the value it was initialized to. It represents the rotation around the Z axis in the Z - X' - Y'' intrinsic Tait-Bryan angles described in § 4.1 Device Orientation .

The beta attribute must return the value it was initialized to. It represents the rotation around the X' axis (produced after the rotation around the Z axis has been applied) axis in the Z - X' - Y'' intrinsic Tait-Bryan angles described in § 4.1 Device Orientation .

The gamma attribute must return the value it was initialized to. It represents the rotation around the Y'' axis (produced after the rotation around the Z and X' axes have been applied in this order) in the Z - X' - Y'' intrinsic Tait-Bryan angles described in § 4.1 Device Orientation .

The absolute attribute must return the value it was initialized to. It indicates whether relative orientation or absolute orientation data is being provided.

A significant change in orientation indicates a difference in orientation values compared to the previous ones that warrants the firing of a deviceorientation or deviceorientationabsolute event. The process of determining whether a significant change in orientation has occurred is implementation-defined , though a maximum threshold for change of 1 degree is recommended. Implementations may also consider that it has occurred if they have reason to believe that the page does not have sufficiently fresh data.

Note: Implementations must take § 11 Automation into account to determine whether a significant change in orientation has occurred, so that a virtual sensor reading update causes it to be assessed.

If an implementation can never provide orientation information, the event should be fired with the alpha , beta and gamma attributes set to null, and the absolute attribute set to false.

8.2. deviceorientationabsolute Event

partial interface Window {
    [SecureContext] attribute EventHandler ondeviceorientationabsolute;
};

The ondeviceorientationabsolute attribute is an event handler IDL attribute for the ondeviceorientationabsolute event handler , whose event handler event type is deviceorientationabsolute .

A deviceorientationabsolute event is completely analogous to the deviceorientation event, except that it must always provide absolute orientation data.

If an implementation can never provide absolute orientation information, the event should be fired with the alpha , beta and gamma attributes set to null, and the absolute attribute set to true.

8.3. devicemotion Event

8.3.1. The DeviceMotionEventAcceleration interface

[Exposed=Window, SecureContext]
interface DeviceMotionEventAcceleration {
    readonly attribute double? x;
    readonly attribute double? y;
    readonly attribute double? z;
};

The DeviceMotionEventAcceleration interface represents the device’s acceleration as described in § 4.2 Device Motion . It has the following associated data:

x axis acceleration

The device’s acceleration rate along the X axis, or null. It is initially null.

y axis acceleration

The device’s acceleration rate along the Y axis, or null. It is initially null.

z axis acceleration

The device’s acceleration rate along the Z axis, or null. It is initially null.

The x getter steps are to return the value of this ’s x axis acceleration .

The y getter steps are to return the value of this ’s y axis acceleration .

The z getter steps are to return the value of this ’s z axis acceleration .

8.3.2. The DeviceMotionEventRotationRate interface

[Exposed=Window, SecureContext]
interface DeviceMotionEventRotationRate {
    readonly attribute double? alpha;
    readonly attribute double? beta;
    readonly attribute double? gamma;
};

The DeviceMotionEventRotationRate interface represents the device’s rotation rate as described in § 4.2 Device Motion . It has the following associated data:

x axis rotation rate

The device’s rotation rate about the X axis, or null. It is initially null.

y axis rotation rate

The device’s rotation rate about the Y axis, or null. It is initially null.

z axis rotation rate

The device’s rotation rate about the Z axis, or null. It is initially null.

The alpha getter steps are to return the value of this ’s x axis rotation rate .

The beta getter steps are to return the value of this ’s y axis rotation rate .

The gamma getter steps are to return the value of this ’s z axis rotation rate .

8.3.3. The DeviceMotionEvent interface

partial interface Window {
    [SecureContext] attribute EventHandler ondevicemotion;
};
[Exposed=Window, SecureContext]
interface DeviceMotionEvent : Event {
    constructor(DOMString type, optional DeviceMotionEventInit eventInitDict = {});
    readonly attribute DeviceMotionEventAcceleration? acceleration;
    readonly attribute DeviceMotionEventAcceleration? accelerationIncludingGravity;
    readonly attribute DeviceMotionEventRotationRate? rotationRate;
    readonly attribute double interval;
    static Promise<PermissionState> requestPermission();
};
dictionary DeviceMotionEventAccelerationInit {
    double? x = null;
    double? y = null;
    double? z = null;
};
dictionary DeviceMotionEventRotationRateInit {
    double? alpha = null;
    double? beta = null;
    double? gamma = null;
};
dictionary DeviceMotionEventInit : EventInit {
    DeviceMotionEventAccelerationInit acceleration;
    DeviceMotionEventAccelerationInit accelerationIncludingGravity;
    DeviceMotionEventRotationRateInit rotationRate;
    double interval = 0;
};

The ondevicemotion attribute is an event handler IDL attribute for the ondevicemotion event handler , whose event handler event type is devicemotion .

The acceleration attribute must return the value it was initialized to. When the object is created, this attribute must be initialized to null. It represents the device’s linear acceleration .

The accelerationIncludingGravity attribute must return the value it was initialized to. When the object is created, this attribute must be initialized to null. It represents the device’s acceleration with gravity .

The rotationRate attribute must return the value it was initialized to. When the object is created, this attribute must be initialized to null. It represents the device’s rotation rate .

The interval attribute must return the value it was initialized to. It represents the interval at which data is obtained from the underlying hardware and must be expressed in milliseconds (ms). It is constant to simplify filtering of the data by the Web application.

If an implementation can never provide motion information, the event should be fired with the acceleration , accelerationIncludingGravity and rotationRate attributes set to null.

9. Security and privacy considerations

The API defined in this specification can be used to obtain information from hardware sensors, such as accelerometer, gyroscope and magnetometer. Provided data may be considered as sensitive and could become a subject of attack from malicious web pages. The calibration of accelerometers, gyroscopes and magnetometers may reveal persistent details about the particular sensor hardware [SENSORID] . The main attack vectors can be categorized into following categories:

• Monitoring of a user input [TOUCH]

• Location tracking [INDOORPOS]

• User identification [FINGERPRINT]

In light of that, implementations may consider visual indicators to signify the use of sensors by the web page. Additionally, this specification requires users to give express permission for the user agent to provide device motion and/or orientation data via the requestPermission() API calls.

Furthermore, to minimize privacy risks, the chance of fingerprinting and other attacks the implementations must:

• fire events only when a navigable 's active document 's visibility state is " visible ",

• implement § 5 Permissions Policy integration so that events are fired on child navigables (including but not restricted to cross-origin ones) only if allowed by the top-level traversable ,

• fire events on a navigable 's active windows only when its relevant settings object is a secure context ,

• limit precision of attribute values as described in the previous sections.

Additionally, implementing these items may also have a beneficial impact on the battery life of mobile devices.

10. Use-Cases and Requirements

10.1. Use-Cases

10.1.1. Controlling a game

A gaming Web application monitors the device’s orientation and interprets tilting in a certain direction as a means to control an on-screen sprite.

10.1.2. Gesture recognition

A Web application monitors the device’s acceleration and applies signal processing in order to recognize certain specific gestures. For example, using a shaking gesture to clear a web form.

10.1.3. Mapping

A mapping Web application uses the device’s orientation to correctly align the map with reality.

10.2. Requirements

• The specification must provide data that describes the physical orientation in space of the device.

• The specification must provide data that describes the motion in space of the device.

• The specification must allow Web applications to register for changes in the device’s orientation.

• The specification must be agnostic to the underlying sources of orientation and motion data.

• The specification must use the existing DOM event framework.

11. Automation

This specification can pose a challenge to test authors, as the events defined here depend on the presence of physical hardware whose readings cannot be easily controlled.

To address this challenge, this document builds upon the [WEBDRIVER2] extension commands and infrastructure laid out by Generic Sensor API § 9 Automation . This was chosen over the option of developing completely new and independent infrastructure with separate extension commands because there is significant overlap between the two specifications: not only does testing the [GENERIC-SENSOR] specification present similar challenges, but many derived APIs (e.g. [GYROSCOPE] ) obtain and provide similar information.

This specification only requires implementations to support the Generic Sensor API § 9 Automation section of the [GENERIC-SENSOR] specification, not its interfaces and events.

11.1. Additional implementation requirements

Several aspects of the manner in which the user agent interacts with the underlying hardware or operating system are implementation-defined . For instance, the § 4 Model and § 8 API sections do not mandate:

• That readings must be retrieved in a specific way.

• When or how the user agent connects to one or more providers of readings.

• Which types or data structures need to be used to store readings.

• Whether readings obtained from the platform or operating system are shared across documents .

For automation support to work, specifically in the context of integrating with Generic Sensor API § 9 Automation , some of this behavior needs to be specified in more detail.

The Document interface must have a [[virtualSensorMapping]] internal slot, a map of virtual sensor types to orientation event platform sensor-likes . A orientation event platform sensor-like is a platform sensor-like struct with the following items:

• A sampling frequency (a number). It represents either the frequency with which the user agent either polls the underlying hardware for readings, or the frequency at which the underlying hardware should notify the user agent of new readings.

• A device sensor (a virtual sensor or null).

11.2. Device Orientation Automation

Automation support for the deviceorientation event is built upon virtual sensors that represent accelerometers, gyroscopes and, optionally, magnetometers.

Orientation data retrieved from the platform by the user agent comes from accelerometers, gyroscopes and, optionally, magnetometers. Contrary to motion data, however, these lower-level readings must be transformed into Euler angles in the formation described in § 4.1 Device Orientation . Furthermore, the platform might provide extra APIs to the user agent that already perform some of those conversions from raw acceleration and rotation data.

Therefore, instead of requiring implementations (and automation users) to provide orientation readings via lower-level virtual sensors which use different units of measurement, this specification defines extra virtual sensor types for relative and orientation data in the format used by this specification.

11.1.1. 11.2.1. Parse orientation reading data algorithm

11.1.2. 11.2.2. The "absolute-orientation" virtual sensor type

The per-type virtual sensor metadata map must have the following entry :

key

" absolute-orientation "

value

A virtual sensor metadata whose reading parsing algorithm is parse orientation data reading .

11.1.3. 11.2.3. The "relative-orientation" virtual sensor type

The per-type virtual sensor metadata map must have the following entry :

key

" relative-orientation "

value

A virtual sensor metadata whose reading parsing algorithm is parse orientation data reading .

11.2. 11.3. Device Motion Automation

The motion data retrieved from the platform by the user agent comes from accelerometers and gyroscopes. This specification defines certain per-type virtual sensor metadata entries that are shared with the [ACCELEROMETER] and [GYROSCOPE] specifications.

Accelerometer virtual sensors are used to provide acceleration with gravity data to the platform. Linear Acceleration virtual sensors are used to provide linear acceleration data to the platform. Gyroscope virtual sensors are used to provide rotation rate data to the platform.

11.2.1. 11.3.1. The "accelerometer" virtual sensor type

The per-type virtual sensor metadata map must have the following entry :

key

" accelerometer "

value

A virtual sensor metadata whose reading parsing algorithm is parse xyz reading .

11.2.2. 11.3.2. The "linear-acceleration" virtual sensor type

The per-type virtual sensor metadata map must have the following entry :

key

" linear-acceleration "

value

A virtual sensor metadata whose reading parsing algorithm is parse xyz reading .

11.2.3. 11.3.3. The "gyroscope" virtual sensor type

The per-type virtual sensor metadata map must have the following entry :

key

" gyroscope "

value

A virtual sensor metadata whose reading parsing algorithm is parse xyz reading .

A Examples

A.1 Calculating compass heading

This section is non-normative.

The following worked example is intended as an aid to users of the DeviceOrientation event.

Introduction section provided an example of using the DeviceOrientation event to obtain a compass heading when the device is held with the screen horizontal. This example shows how to determine the compass heading that the user is facing when holding the device with the screen approximately vertical in front of them. An application of this is an augmented-reality system.

More precisely, we wish to determine the compass heading of the horizontal component of a vector which is orthogonal to the device’s screen and pointing out of the back of the screen.

If v represents this vector in the rotated device body frame xyz, then v is as follows.

The transformation of v due to the rotation about the z axis can be represented by the following rotation matrix.

The transformation of v due to the rotation about the x axis can be represented by the following rotation matrix.

The transformation of v due to the rotation about the y axis can be represented by the following rotation matrix.

If R represents the full rotation matrix of the device in the earth frame XYZ, then since the initial body frame is aligned with the earth, R is as follows.

If v' represents the vector v in the earth frame XYZ, then since the initial body frame is aligned with the earth, v' is as follows.

The compass heading θ is given by

provided that β and γ are not both zero.

var degtorad = Math.PI / 180; // Degree-to-Radian conversion
function compassHeading( alpha, beta, gamma ) {
  var _x = beta  ? beta  * degtorad : 0; // beta value
  var _y = gamma ? gamma * degtorad : 0; // gamma value
  var _z = alpha ? alpha * degtorad : 0; // alpha value
  var cX = Math.cos( _x );
  var cY = Math.cos( _y );
  var cZ = Math.cos( _z );
  var sX = Math.sin( _x );
  var sY = Math.sin( _y );
  var sZ = Math.sin( _z );
  // Calculate Vx and Vy components
  var Vx = - cZ * sY - sZ * sX * cY;
  var Vy = - sZ * sY + cZ * sX * cY;
  // Calculate compass heading
  var compassHeading = Math.atan( Vx / Vy );
  // Convert compass heading to use whole unit circle
  if( Vy < 0 ) {
    compassHeading += Math.PI;
  } else if( Vx < 0 ) {
    compassHeading += 2 * Math.PI;
  }
  return compassHeading * ( 180 / Math.PI ); // Compass Heading (in degrees)
}

As a consistency check, if we set γ = 0, then

as expected.

Alternatively, if we set β = 90, then

as expected.

A.2 Alternate device orientation representations

This section is non-normative.

Describing orientation using Tait-Bryan angles can have some disadvantages such as introducing gimbal lock [GIMBALLOCK] . Depending on the intended application it can be useful to convert the Device Orientation values to other rotation representations.

The first alternate orientation representation uses rotation matrices. By combining the component rotation matrices provided in the worked example above we can represent the orientation of the device body frame as a combined rotation matrix.

If R represents the rotation matrix of the device in the earth frame XYZ, then since the initial body frame is aligned with the earth, R is as follows.

var degtorad = Math.PI / 180; // Degree-to-Radian conversion
function getRotationMatrix( alpha, beta, gamma ) {
  var _x = beta  ? beta  * degtorad : 0; // beta value
  var _y = gamma ? gamma * degtorad : 0; // gamma value
  var _z = alpha ? alpha * degtorad : 0; // alpha value
  var cX = Math.cos( _x );
  var cY = Math.cos( _y );
  var cZ = Math.cos( _z );
  var sX = Math.sin( _x );
  var sY = Math.sin( _y );
  var sZ = Math.sin( _z );
  //
  // ZXY rotation matrix construction.
  //
  var m11 = cZ * cY - sZ * sX * sY;
  var m12 = - cX * sZ;
  var m13 = cY * sZ * sX + cZ * sY;
  var m21 = cY * sZ + cZ * sX * sY;
  var m22 = cZ * cX;
  var m23 = sZ * sY - cZ * cY * sX;
  var m31 = - cX * sY;
  var m32 = sX;
  var m33 = cX * cY;
  return [
    m11,    m12,    m13,
    m21,    m22,    m23,
    m31,    m32,    m33
  ];
};

Another alternate representation of device orientation data is as Quaternions. [QUATERNIONS]

If q represents the unit quaternion of the device in the earth frame XYZ, then since the initial body frame is aligned with the earth, q is as follows.

var degtorad = Math.PI / 180; // Degree-to-Radian conversion
function getQuaternion( alpha, beta, gamma ) {
  var _x = beta  ? beta  * degtorad : 0; // beta value
  var _y = gamma ? gamma * degtorad : 0; // gamma value
  var _z = alpha ? alpha * degtorad : 0; // alpha value
  var cX = Math.cos( _x/2 );
  var cY = Math.cos( _y/2 );
  var cZ = Math.cos( _z/2 );
  var sX = Math.sin( _x/2 );
  var sY = Math.sin( _y/2 );
  var sZ = Math.sin( _z/2 );
  //
  // ZXY quaternion construction.
  //
  var w = cX * cY * cZ - sX * sY * sZ;
  var x = sX * cY * cZ - cX * sY * sZ;
  var y = cX * sY * cZ + sX * cY * sZ;
  var z = cX * cY * sZ + sX * sY * cZ;
  return [ w, x, y, z ];
}

We can check that a Unit Quaternion has been constructed correctly using Lagrange’s four-square theorem

as expected.

Acknowledgments

Lars Erik Bolstad, Dean Jackson, Claes Nilsson, George Percivall, Doug Turner, Matt Womer, Chris Dumez

12. Changes

This section summarizes substantial changes and notable editorial improvements to guide review. Full details are available from the commit log . Changes since the Candidate Recommendation 2016-08-18 :

• Add Permissions Policy integration, which supersedes the previous requirement of only firing events on iframes that were same-origin with the top-level frame

• Add note to implementers about bundling permission requests

• Export powerful features Accelerometer, Gyroscope and Magnetometer

• Add Permissions API integration, start requiring requestPermission() usage

• editorial: Define API section more normatively and with more dfns

• editorial: Reorder acceleration explanation in Device Motion Model section

• editorial: Update explanations of the device rotation and motion references

• editorial: Use more precise event handling terms, modernize others

• editorial: Refer to [SCREEN-ORIENTATION] instead of the orientation change event

• editorial: Reword requirements in "Security and privacy considerations"

• Mark use cases and requirements and examples sections non-normative

• Remove the oncompassneedscalibration event

• Update references to "triggered by user activation", now referred to as "transient activation"

• Align with DOM phrasing on firing events

• Add a note about acceleration properties for DeviceMotionEvent

• Add a note explaining how the coordinate system differs from the CSS coordinate system

• Require no more precise than 0.1 degrees, 0.1 degrees per second, 0.1 meters per second squared to mitigate a passive fingerprinting issue

• Update constructor definition in IDL with the Web IDL

• Add explicit [Exposed] to interfaces

• Update IDL dictionaries with new dictionary defaulting setup

• Note the deviceorientationabsolute event and its ondeviceorientationabsolute event handler IDL attribute have limited implementation experience

• Add requestPermission() API static operation to both DeviceOrientationEvent and DeviceMotionEvent

• Add [SecureContext] to event handlers ondeviceorientation, ondevicemotion and ondeviceorientationabsolute

• Restrict all interfaces to secure contexts

• Remove [NoInterfaceObject] from DeviceAcceleration and DeviceRotationRate

• Make security and privacy considerations normative

• Add the ondeviceorientationabsolute event handler attribute into the IDL block (was only in prose)

• Remove '?' from dictionary members of DeviceMotionEventInit

• Use [Exposed=Window] extended attribute