Quaternion

Members

w :Number

The W component.

Default Value:

• 0.0

x :Number

The X component.

Default Value:

• 0.0

y :Number

The Y component.

Default Value:

• 0.0

z :Number

The Z component.

Default Value:

• 0.0

<static> IDENTITY

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

<static> packedInterpolationLength :Number

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

<static> packedLength :Number

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

<static> ZERO

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

Methods

clone

Duplicates this Quaternion instance.

Parameters:

Name	Type	Argument	Description
result	Quaternion	<optional>	The object onto which to store the result.

Returns:

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

equals

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

Parameters:

Name	Type	Argument	Description
right	Quaternion	<optional>	The right hand side quaternion.

Returns:

Boolean true if left and right are equal, false otherwise.

equalsEpsilon

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

Parameters:

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

Returns:

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

toString

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

Returns:

String A string representing this Quaternion.

<static> add

Computes the componentwise sum of two quaternions.

Parameters:

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

Returns:

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

<static> clone

Duplicates a Quaternion instance.

Parameters:

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

Returns:

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

<static> conjugate

Computes the conjugate of the provided quaternion.

Parameters:

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

Returns:

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

<static> convertPackedArrayForInterpolation

Converts a packed array into a form suitable for interpolation.

Parameters:

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

<static> divideByScalar

Divides the provided quaternion componentwise by the provided scalar.

Parameters:

Name	Type	Argument	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:

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

<static> dot

Computes the dot (scalar) product of two quaternions.

Parameters:

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

Returns:

Number The dot product.

<static> equals

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

Parameters:

Name	Type	Argument	Description
left	Quaternion	<optional>	The first quaternion.
right	Quaternion	<optional>	The second quaternion.

Returns:

Boolean true if left and right are equal, false otherwise.

<static> equalsEpsilon

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

Parameters:

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

Returns:

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

<static> exp

The exponential quaternion function.

Parameters:

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

Returns:

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

<static> fastSlerp

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.

Parameters:

Name	Type	Argument	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:

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

See:

• Quaternion#slerp

<static> fastSquad

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

Parameters:

Name	Type	Argument	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:

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

See:

• Quaternion#squad

<static> fromAxisAngle

Computes a quaternion representing a rotation around an axis.

Parameters:

Name	Type	Argument	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:

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

<static> fromRotationMatrix

Computes a Quaternion from the provided Matrix3 instance.

Parameters:

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

Returns:

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

See:

• Matrix3.fromQuaternion

<static> getAngle

Computes the angle of rotation of the provided quaternion.

Parameters:

Name	Type	Description
quaternion	Quaternion	The quaternion to use.

Returns:

Number The angle of rotation.

<static> getAxis

Computes the axis of rotation of the provided quaternion.

Parameters:

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

Returns:

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

<static> innerQuadrangle

Computes an inner quadrangle point.

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

Parameters:

Name	Type	Argument	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:

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

See:

• Quaternion#squad

<static> inverse

Computes the inverse of the provided quaternion.

Parameters:

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

Returns:

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

<static> lerp

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

Parameters:

Name	Type	Argument	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:

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

<static> log

The logarithmic quaternion function.

Parameters:

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

Returns:

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

<static> magnitude

Computes magnitude for the provided quaternion.

Parameters:

Name	Type	Description
quaternion	Quaternion	The quaternion to conjugate.

Returns:

Number The magnitude.

<static> magnitudeSquared

Computes magnitude squared for the provided quaternion.

Parameters:

Name	Type	Description
quaternion	Quaternion	The quaternion to conjugate.

Returns:

Number The magnitude squared.

<static> multiply

Computes the product of two quaternions.

Parameters:

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

Returns:

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

<static> multiplyByScalar

Multiplies the provided quaternion componentwise by the provided scalar.

Parameters:

Name	Type	Argument	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:

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

<static> negate

Negates the provided quaternion.

Parameters:

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

Returns:

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

<static> normalize

Computes the normalized form of the provided quaternion.

Parameters:

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

Returns:

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

<static> pack

Stores the provided instance into the provided array.

Parameters:

Name	Type	Argument	Default	Description
value	Quaternion			The value to pack.
array	Array			The array to pack into.
startingIndex	Number	<optional>	0	The index into the array at which to start packing the elements.

<static> slerp

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

Parameters:

Name	Type	Argument	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:

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

See:

• Quaternion#fastSlerp

<static> squad

Computes the spherical quadrangle interpolation between quaternions.

Parameters:

Name	Type	Argument	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:

Quaternion 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

<static> subtract

Computes the componentwise difference of two quaternions.

Parameters:

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

Returns:

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

<static> unpack

Retrieves an instance from a packed array.

Parameters:

Name	Type	Argument	Default	Description
array	Array			The packed array.
startingIndex	Number	<optional>	0	The starting index of the element to be unpacked.
result	Quaternion	<optional>		The object into which to store the result.

<static> unpackInterpolationResult

Retrieves an instance from a packed array converted with convertPackedArrayForInterpolation.

Parameters:

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