Quaternion - Cesium Documentation

new Quaternion(x, y, z, w)

A set of 4-dimensional coordinates used to represent rotation in 3-dimensional space.

Name	Type	Default	Description
`x`	Number	`0.0`	optional The X component.
`y`	Number	`0.0`	optional The Y component.
`z`	Number	`0.0`	optional The Z component.
`w`	Number	`0.0`	optional The W component.

See:

PackableForInterpolation

Source: Core/Quaternion.js, line 34

Members

staticQuaternion.IDENTITY

An immutable Quaternion instance initialized to (0.0, 0.0, 0.0, 1.0).

Source: Core/Quaternion.js, line 1078

staticQuaternion.packedInterpolationLength :Number

The number of elements used to store the object into an array in its interpolatable form.

Source: Core/Quaternion.js, line 250

staticQuaternion.packedLength :Number

The number of elements used to pack the object into an array.

Source: Core/Quaternion.js, line 190

staticQuaternion.ZERO

An immutable Quaternion instance initialized to (0.0, 0.0, 0.0, 0.0).

Source: Core/Quaternion.js, line 1072

w :Number

The W component.

Default Value: 0.0

Source: Core/Quaternion.js, line 61

x :Number

The X component.

Default Value: 0.0

Source: Core/Quaternion.js, line 40

y :Number

The Y component.

Default Value: 0.0

Source: Core/Quaternion.js, line 47

z :Number

The Z component.

Default Value: 0.0

Source: Core/Quaternion.js, line 54

Methods

staticQuaternion.add(left, right, result) → Quaternion

Computes the componentwise sum of two quaternions.

Name	Type	Description
`left`	Quaternion	The first quaternion.
`right`	Quaternion	The second quaternion.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 436

staticQuaternion.clone(quaternion, result) → Quaternion

Duplicates a Quaternion instance.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to duplicate.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided. (Returns undefined if quaternion is undefined)

Source: Core/Quaternion.js, line 319

staticQuaternion.conjugate(quaternion, result) → Quaternion

Computes the conjugate of the provided quaternion.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to conjugate.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 343

staticQuaternion.convertPackedArrayForInterpolation(packedArray, startingIndex, lastIndex, result)

Converts a packed array into a form suitable for interpolation.

Name	Type	Default	Description
`packedArray`	Number[]		The packed array.
`startingIndex`	Number	`0`	optional The index of the first element to be converted.
`lastIndex`	Number	`packedArray.length`	optional The index of the last element to be converted.
`result`	Number[]		optional The object into which to store the result.

Source: Core/Quaternion.js, line 261

staticQuaternion.divideByScalar(quaternion, scalar, result) → Quaternion

Divides the provided quaternion componentwise by the provided scalar.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to be divided.
`scalar`	Number	The scalar to divide by.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 613

staticQuaternion.dot(left, right) → Number

Computes the dot (scalar) product of two quaternions.

Name	Type	Description
`left`	Quaternion	The first quaternion.
`right`	Quaternion	The second quaternion.

Returns:

The dot product.

Source: Core/Quaternion.js, line 518

staticQuaternion.equals(left, right) → Boolean

Compares the provided quaternions componentwise and returns true if they are equal, false otherwise.

Name	Type	Description
`left`	Quaternion	optional The first quaternion.
`right`	Quaternion	optional The second quaternion.

Returns:

true if left and right are equal, false otherwise.

Source: Core/Quaternion.js, line 1031

staticQuaternion.equalsEpsilon(left, right, epsilon) → Boolean

Compares the provided quaternions componentwise and returns true if they are within the provided epsilon, false otherwise.

Name	Type	Description
`left`	Quaternion	optional The first quaternion.
`right`	Quaternion	optional The second quaternion.
`epsilon`	Number	The epsilon to use for equality testing.

Returns:

true if left and right are within the provided epsilon, false otherwise.

Source: Core/Quaternion.js, line 1052

staticQuaternion.exp(cartesian, result) → Quaternion

The exponential quaternion function.

Name	Type	Description
`cartesian`	Cartesian3	The cartesian.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new instance if one was not provided.

Source: Core/Quaternion.js, line 804

staticQuaternion.fastSlerp(start, end, t, result) → Quaternion

Computes the spherical linear interpolation or extrapolation at t using the provided quaternions. This implementation is faster than Quaternion#slerp, but is only accurate up to 10^-6.

Name	Type	Description
`start`	Quaternion	The value corresponding to t at 0.0.
`end`	Quaternion	The value corresponding to t at 1.0.
`t`	Number	The point along t at which to interpolate.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

See:

Quaternion#slerp

Source: Core/Quaternion.js, line 940

staticQuaternion.fastSquad(q0, q1, s0, s1, t, result) → Quaternion

Computes the spherical quadrangle interpolation between quaternions. An implementation that is faster than Quaternion#squad, but less accurate.

Name	Type	Description
`q0`	Quaternion	The first quaternion.
`q1`	Quaternion	The second quaternion.
`s0`	Quaternion	The first inner quadrangle.
`s1`	Quaternion	The second inner quadrangle.
`t`	Number	The time in [0,1] used to interpolate.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new instance if none was provided.

See:

Quaternion#squad

Source: Core/Quaternion.js, line 1006

staticQuaternion.fromAxisAngle(axis, angle, result) → Quaternion

Computes a quaternion representing a rotation around an axis.

Name	Type	Description
`axis`	Cartesian3	The axis of rotation.
`angle`	Number	The angle in radians to rotate around the axis.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 75

staticQuaternion.fromRotationMatrix(matrix, result) → Quaternion

Computes a Quaternion from the provided Matrix3 instance.

Name	Type	Description
`matrix`	Matrix3	The rotation matrix.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

See:

Matrix3.fromQuaternion

Source: Core/Quaternion.js, line 115

staticQuaternion.getAngle(quaternion) → Number

Computes the angle of rotation of the provided quaternion.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to use.

Returns:

The angle of rotation.

Source: Core/Quaternion.js, line 674

staticQuaternion.getAxis(quaternion, result) → Cartesian3

Computes the axis of rotation of the provided quaternion.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to use.
`result`	Cartesian3	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Cartesian3 instance if one was not provided.

Source: Core/Quaternion.js, line 641

staticQuaternion.innerQuadrangle(q0, q1, q2, result) → Quaternion

Computes an inner quadrangle point.

This will compute quaternions that ensure a squad curve is C¹.

Name	Type	Description
`q0`	Quaternion	The first quaternion.
`q1`	Quaternion	The second quaternion.
`q2`	Quaternion	The third quaternion.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new instance if none was provided.

See:

Quaternion#squad

Source: Core/Quaternion.js, line 848

staticQuaternion.inverse(quaternion, result) → Quaternion

Computes the inverse of the provided quaternion.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to normalize.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 421

staticQuaternion.lerp(start, end, t, result) → Quaternion

Computes the linear interpolation or extrapolation at t using the provided quaternions.

Name	Type	Description
`start`	Quaternion	The value corresponding to t at 0.0.
`end`	Quaternion	The value corresponding to t at 1.0.
`t`	Number	The point along t at which to interpolate.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 698

staticQuaternion.log(quaternion, result) → Cartesian3

The logarithmic quaternion function.

Name	Type	Description
`quaternion`	Quaternion	The unit quaternion.
`result`	Cartesian3	optional The object onto which to store the result.

Returns:

The modified result parameter or a new instance if one was not provided.

Source: Core/Quaternion.js, line 775

staticQuaternion.magnitude(quaternion) → Number

Computes magnitude for the provided quaternion.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to conjugate.

Returns:

The magnitude.

Source: Core/Quaternion.js, line 384

staticQuaternion.magnitudeSquared(quaternion) → Number

Computes magnitude squared for the provided quaternion.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to conjugate.

Returns:

The magnitude squared.

Source: Core/Quaternion.js, line 367

staticQuaternion.multiply(left, right, result) → Quaternion

Computes the product of two quaternions.

Name	Type	Description
`left`	Quaternion	The first quaternion.
`right`	Quaternion	The second quaternion.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 540

staticQuaternion.multiplyByScalar(quaternion, scalar, result) → Quaternion

Multiplies the provided quaternion componentwise by the provided scalar.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to be scaled.
`scalar`	Number	The scalar to multiply with.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 584

staticQuaternion.negate(quaternion, result) → Quaternion

Negates the provided quaternion.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to be negated.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 493

staticQuaternion.normalize(quaternion, result) → Quaternion

Computes the normalized form of the provided quaternion.

Name	Type	Description
`quaternion`	Quaternion	The quaternion to normalize.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 396

staticQuaternion.pack(value, array, startingIndex)

Stores the provided instance into the provided array.

Name	Type	Default	Description
`value`	Quaternion		The value to pack.
`array`	Number[]		The array to pack into.
`startingIndex`	Number	`0`	optional The index into the array at which to start packing the elements.

Source: Core/Quaternion.js, line 200

staticQuaternion.slerp(start, end, t, result) → Quaternion

Computes the spherical linear interpolation or extrapolation at t using the provided quaternions.

Name	Type	Description
`start`	Quaternion	The value corresponding to t at 0.0.
`end`	Quaternion	The value corresponding to t at 1.0.
`t`	Number	The point along t at which to interpolate.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

See:

Quaternion#fastSlerp

Source: Core/Quaternion.js, line 731

staticQuaternion.squad(q0, q1, s0, s1, t, result) → Quaternion

Computes the spherical quadrangle interpolation between quaternions.

Name	Type	Description
`q0`	Quaternion	The first quaternion.
`q1`	Quaternion	The second quaternion.
`s0`	Quaternion	The first inner quadrangle.
`s1`	Quaternion	The second inner quadrangle.
`t`	Number	The time in [0,1] used to interpolate.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new instance if none was provided.

Example:

// 1. compute the squad interpolation between two quaternions on a curve
var s0 = Cesium.Quaternion.innerQuadrangle(quaternions[i - 1], quaternions[i], quaternions[i + 1]);
var s1 = Cesium.Quaternion.innerQuadrangle(quaternions[i], quaternions[i + 1], quaternions[i + 2]);
var q = Cesium.Quaternion.squad(quaternions[i], quaternions[i + 1], s0, s1, t);

// 2. compute the squad interpolation as above but where the first quaternion is a end point.
var s1 = Cesium.Quaternion.innerQuadrangle(quaternions[0], quaternions[1], quaternions[2]);
var q = Cesium.Quaternion.squad(quaternions[0], quaternions[1], quaternions[0], s1, t);

See:

Quaternion#innerQuadrangle

Source: Core/Quaternion.js, line 894

staticQuaternion.subtract(left, right, result) → Quaternion

Computes the componentwise difference of two quaternions.

Name	Type	Description
`left`	Quaternion	The first quaternion.
`right`	Quaternion	The second quaternion.
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 465

staticQuaternion.unpack(array, startingIndex, result)

Retrieves an instance from a packed array.

Name	Type	Default	Description
`array`	Number[]		The packed array.
`startingIndex`	Number	`0`	optional The starting index of the element to be unpacked.
`result`	Quaternion		optional The object into which to store the result.

Source: Core/Quaternion.js, line 227

staticQuaternion.unpackInterpolationResult(array, sourceArray, startingIndex, lastIndex, result)

Retrieves an instance from a packed array converted with convertPackedArrayForInterpolation.

Name	Type	Default	Description
`array`	Number[]		The original packed array.
`sourceArray`	Number[]		The converted array.
`startingIndex`	Number	`0`	optional The startingIndex used to convert the array.
`lastIndex`	Number	`packedArray.length`	optional The lastIndex used to convert the array.
`result`	Quaternion		optional The object into which to store the result.

Source: Core/Quaternion.js, line 293

clone(result) → Quaternion

Duplicates this Quaternion instance.

Name	Type	Description
`result`	Quaternion	optional The object onto which to store the result.

Returns:

The modified result parameter or a new Quaternion instance if one was not provided.

Source: Core/Quaternion.js, line 1087

equals(right) → Boolean

Compares this and the provided quaternion componentwise and returns true if they are equal, false otherwise.

Name	Type	Description
`right`	Quaternion	optional The right hand side quaternion.

Returns:

true if left and right are equal, false otherwise.

Source: Core/Quaternion.js, line 1099

equalsEpsilon(right, epsilon) → Boolean

Compares this and the provided quaternion componentwise and returns true if they are within the provided epsilon, false otherwise.

Name	Type	Description
`right`	Quaternion	optional The right hand side quaternion.
`epsilon`	Number	The epsilon to use for equality testing.

Returns:

true if left and right are within the provided epsilon, false otherwise.

Source: Core/Quaternion.js, line 1113

toString() → String

Returns a string representing this quaternion in the format (x, y, z, w).

Returns:

A string representing this Quaternion.

Source: Core/Quaternion.js, line 1123