Class: Quaternion

Quaternion

new Quaternion(xopt, yopt, zopt, wopt)

A set of 4-dimensional coordinates used to represent rotation in 3-dimensional space.
Parameters:
Name Type Attributes Default Description
x Number <optional>
 0.0 The X component.
y Number <optional>
 0.0 The Y component.
z Number <optional>
 0.0 The Z component.
w Number <optional>
 0.0 The W component.
Source:
See:
  • PackableForInterpolation

Members

(static, constant) IDENTITY :Quaternion

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

(static) packedInterpolationLength :Number

The number of elements used to store the object into an array in its interpolatable form.
Type:
  • Number
Source:

(static) packedLength :Number

The number of elements used to pack the object into an array.
Type:
  • Number
Source:

(static, constant) ZERO :Quaternion

An immutable Quaternion instance initialized to (0.0, 0.0, 0.0, 0.0).
Type:
Source:

w :Number

The W component.
Type:
  • Number
Default Value:
  • 0.0
Source:

x :Number

The X component.
Type:
  • Number
Default Value:
  • 0.0
Source:

y :Number

The Y component.
Type:
  • Number
Default Value:
  • 0.0
Source:

z :Number

The Z component.
Type:
  • Number
Default Value:
  • 0.0
Source:

Methods

(static) add(left, right, result) → {Quaternion}

Computes the componentwise sum of two quaternions.
Parameters:
Name Type Description
left Quaternion The first quaternion.
right Quaternion The second quaternion.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) clone(quaternion, resultopt) → {Quaternion}

Duplicates a Quaternion instance.
Parameters:
Name Type Attributes Description
quaternion Quaternion The quaternion to duplicate.
result Quaternion <optional>
 The object onto which to store the result.
Source:
Returns:
The modified result parameter or a new Quaternion instance if one was not provided. (Returns undefined if quaternion is undefined)
Type
Quaternion

(static) computeAngle(quaternion) → {Number}

Computes the angle of rotation of the provided quaternion.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to use.
Source:
Returns:
The angle of rotation.
Type
Number

(static) computeAxis(quaternion, result) → {Cartesian3}

Computes the axis of rotation of the provided quaternion.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to use.
result Cartesian3 The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Cartesian3

(static) computeInnerQuadrangle(q0, q1, q2, result) → {Quaternion}

Computes an inner quadrangle point.

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

Parameters:
Name Type Description
q0 Quaternion The first quaternion.
q1 Quaternion The second quaternion.
q2 Quaternion The third quaternion.
result Quaternion The object onto which to store the result.
Source:
See:
  • Quaternion#squad
Returns:
The modified result parameter.
Type
Quaternion

(static) conjugate(quaternion, result) → {Quaternion}

Computes the conjugate of the provided quaternion.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to conjugate.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) convertPackedArrayForInterpolation(packedArray, startingIndexopt, lastIndexopt, result)

Converts a packed array into a form suitable for interpolation.
Parameters:
Name Type Attributes Default Description
packedArray Array.<Number> 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.<Number> The object into which to store the result.
Source:

(static) divideByScalar(quaternion, scalar, result) → {Quaternion}

Divides the provided quaternion componentwise by the provided scalar.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to be divided.
scalar Number The scalar to divide by.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) dot(left, right) → {Number}

Computes the dot (scalar) product of two quaternions.
Parameters:
Name Type Description
left Quaternion The first quaternion.
right Quaternion The second quaternion.
Source:
Returns:
The dot product.
Type
Number

(static) equals(leftopt, rightopt) → {Boolean}

Compares the provided quaternions componentwise and returns true if they are equal, false otherwise.
Parameters:
Name Type Attributes Description
left Quaternion <optional>
 The first quaternion.
right Quaternion <optional>
 The second quaternion.
Source:
Returns:
true if left and right are equal, false otherwise.
Type
Boolean

(static) equalsEpsilon(leftopt, rightopt, epsilon) → {Boolean}

Compares the provided quaternions componentwise and returns true if they are within the provided epsilon, false otherwise.
Parameters:
Name Type Attributes Description
left Quaternion <optional>
 The first quaternion.
right Quaternion <optional>
 The second quaternion.
epsilon Number The epsilon to use for equality testing.
Source:
Returns:
true if left and right are within the provided epsilon, false otherwise.
Type
Boolean

(static) exp(cartesian, result) → {Quaternion}

The exponential quaternion function.
Parameters:
Name Type Description
cartesian Cartesian3 The cartesian.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) 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.
Parameters:
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 The object onto which to store the result.
Source:
See:
  • Quaternion#slerp
Returns:
The modified result parameter.
Type
Quaternion

(static) 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.
Parameters:
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 The object onto which to store the result.
Source:
See:
  • Quaternion#squad
Returns:
The modified result parameter or a new instance if none was provided.
Type
Quaternion

(static) fromAxisAngle(axis, angle, resultopt) → {Quaternion}

Computes a quaternion representing a rotation around an axis.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The modified result parameter or a new Quaternion instance if one was not provided.
Type
Quaternion

(static) fromHeadingPitchRoll(heading, pitch, roll, resultopt) → {Quaternion}

Computes a rotation from the given heading, pitch and roll angles. Heading is the rotation about the negative z axis. Pitch is the rotation about the negative y axis. Roll is the rotation about the positive x axis.
Parameters:
Name Type Attributes Description
heading Number The heading angle in radians.
pitch Number The pitch angle in radians.
roll Number The roll angle in radians.
result Quaternion <optional>
 The object onto which to store the result.
Source:
Returns:
The modified result parameter or a new Quaternion instance if none was provided.
Type
Quaternion

(static) fromRotationMatrix(matrix, resultopt) → {Quaternion}

Computes a Quaternion from the provided Matrix3 instance.
Parameters:
Name Type Attributes Description
matrix Matrix3 The rotation matrix.
result Quaternion <optional>
 The object onto which to store the result.
Source:
See:
Returns:
The modified result parameter or a new Quaternion instance if one was not provided.
Type
Quaternion

(static) inverse(quaternion, result) → {Quaternion}

Computes the inverse of the provided quaternion.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to normalize.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) lerp(start, end, t, result) → {Quaternion}

Computes the linear interpolation or extrapolation at t using the provided quaternions.
Parameters:
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 The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) log(quaternion, result) → {Cartesian3}

The logarithmic quaternion function.
Parameters:
Name Type Description
quaternion Quaternion The unit quaternion.
result Cartesian3 The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Cartesian3

(static) magnitude(quaternion) → {Number}

Computes magnitude for the provided quaternion.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to conjugate.
Source:
Returns:
The magnitude.
Type
Number

(static) magnitudeSquared(quaternion) → {Number}

Computes magnitude squared for the provided quaternion.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to conjugate.
Source:
Returns:
The magnitude squared.
Type
Number

(static) multiply(left, right, result) → {Quaternion}

Computes the product of two quaternions.
Parameters:
Name Type Description
left Quaternion The first quaternion.
right Quaternion The second quaternion.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) multiplyByScalar(quaternion, scalar, result) → {Quaternion}

Multiplies the provided quaternion componentwise by the provided scalar.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to be scaled.
scalar Number The scalar to multiply with.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) negate(quaternion, result) → {Quaternion}

Negates the provided quaternion.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to be negated.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) normalize(quaternion, result) → {Quaternion}

Computes the normalized form of the provided quaternion.
Parameters:
Name Type Description
quaternion Quaternion The quaternion to normalize.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) pack(value, array, startingIndexopt) → {Array.<Number>}

Stores the provided instance into the provided array.
Parameters:
Name Type Attributes Default Description
value Quaternion The value to pack.
array Array.<Number> The array to pack into.
startingIndex Number <optional>
 0 The index into the array at which to start packing the elements.
Source:
Returns:
The array that was packed into
Type
Array.<Number>

(static) slerp(start, end, t, result) → {Quaternion}

Computes the spherical linear interpolation or extrapolation at t using the provided quaternions.
Parameters:
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 The object onto which to store the result.
Source:
See:
  • Quaternion#fastSlerp
Returns:
The modified result parameter.
Type
Quaternion

(static) squad(q0, q1, s0, s1, t, result) → {Quaternion}

Computes the spherical quadrangle interpolation between quaternions.
Parameters:
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 The object onto which to store the result.
Source:
See:
  • Quaternion#computeInnerQuadrangle
Returns:
The modified result parameter.
Type
Quaternion
Example
// 1. compute the squad interpolation between two quaternions on a curve
var s0 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i - 1], quaternions[i], quaternions[i + 1], new Cesium.Quaternion());
var s1 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i], quaternions[i + 1], quaternions[i + 2], new Cesium.Quaternion());
var q = Cesium.Quaternion.squad(quaternions[i], quaternions[i + 1], s0, s1, t, new Cesium.Quaternion());

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

(static) subtract(left, right, result) → {Quaternion}

Computes the componentwise difference of two quaternions.
Parameters:
Name Type Description
left Quaternion The first quaternion.
right Quaternion The second quaternion.
result Quaternion The object onto which to store the result.
Source:
Returns:
The modified result parameter.
Type
Quaternion

(static) unpack(array, startingIndexopt, resultopt) → {Quaternion}

Retrieves an instance from a packed array.
Parameters:
Name Type Attributes Default Description
array Array.<Number> 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.
Source:
Returns:
The modified result parameter or a new Quaternion instance if one was not provided.
Type
Quaternion

(static) unpackInterpolationResult(array, sourceArray, startingIndexopt, lastIndexopt, resultopt) → {Quaternion}

Retrieves an instance from a packed array converted with convertPackedArrayForInterpolation.
Parameters:
Name Type Attributes Default Description
array Array.<Number> The array previously packed for interpolation.
sourceArray Array.<Number> The original packed 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.
Source:
Returns:
The modified result parameter or a new Quaternion instance if one was not provided.
Type
Quaternion

clone(resultopt) → {Quaternion}

Duplicates this Quaternion instance.
Parameters:
Name Type Attributes Description
result Quaternion <optional>
 The object onto which to store the result.
Source:
Returns:
The modified result parameter or a new Quaternion instance if one was not provided.
Type
Quaternion

equals(rightopt) → {Boolean}

Compares this and the provided quaternion componentwise and returns true if they are equal, false otherwise.
Parameters:
Name Type Attributes Description
right Quaternion <optional>
 The right hand side quaternion.
Source:
Returns:
true if left and right are equal, false otherwise.
Type
Boolean

equalsEpsilon(rightopt, epsilon) → {Boolean}

Compares this and the provided quaternion componentwise and returns true if they are within the provided epsilon, false otherwise.
Parameters:
Name Type Attributes Description
right Quaternion <optional>
 The right hand side quaternion.
epsilon Number The epsilon to use for equality testing.
Source:
Returns:
true if left and right are within the provided epsilon, false otherwise.
Type
Boolean

toString() → {String}

Returns a string representing this quaternion in the format (x, y, z, w).
Source:
Returns:
A string representing this Quaternion.
Type
String