Class: Quaternion

Members

(static, constant) IDENTITYQuaternion

Initialize as an immutable quaternion instance of (0.0, 0.0, 0.0, 1.0).

static packedInterpolationLengthNumber

The number of elements used to store objects in an array in an interpolated form.

static packedLengthNumber

The number of elements used to package an object into an array.

(static, constant) ZEROQuaternion

Initialize as an immutable quaternion instance of (0.0, 0.0, 0.0, 0.0).

wNumber

Part W.

Default Value:

0.0

Methods

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

Calculate the sum of the components of two quaternions.

Name	Type	Description
left	Quaternion	The first quaternion.
right	Quaternion	The second quaternion.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

static clone(quaternion, result){Quaternion}

Copy quaternion instances.

Name	Type	Description
quaternion	Quaternion	The quaternion to be copied.
result	Quaternion	optional The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters, or a new quaternion instance (if no quaternion instance is provided). If the quaternion is undefined, return undefined.

static computeAngle(quaternion){Number}

Calculate the rotation angle of the provided quaternion.

Name	Type	Description
quaternion	Quaternion	The quaternion to be used.

Returns:

Type	Description
Number	Rotation angle.

static computeAxis(quaternion, result){Cartesian3}

Calculate the rotation axis of the quaternion provided.

Name	Type	Description
quaternion	Quaternion	The quaternion to be used.
result	Cartesian3	The object that stores the results.

Returns:

Type	Description
Cartesian3	The modified result parameters.

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

Calculate an inner quadrilateral point. This will calculate quaternions to ensure that the lineup curve is C1.

Name	Type	Description
q0	Quaternion	The first quaternion.
q1	Quaternion	The second quaternion.
q2	Quaternion	The third quaternion.
result	Quaternion	The object that stores the results.

See:

• Quaternion#squad

Returns:

Type	Description
Quaternion	The modified result parameters.

static conjugate(quaternion, result){Quaternion}

Calculate the conjugate number of the quaternion provided.

Name	Type	Description
quaternion	Quaternion	A quaternion used for conjugation.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

static convertPackedArrayForInterpolation(packedArray, startingIndex, lastIndex, result)

Convert the packaged array into a form suitable for interpolation.

Name	Type	Default	Description
packedArray	Array.<Number>		Package the 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	Array.<Number>		The object in which to store the results.

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

Divide the provided scalar component by the provided quaternion.

Name	Type	Description
quaternion	Quaternion	The quaternion to be divided.
scalar	Number	The scalar to be divided by.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

static dot(left, right){Number}

Calculate the point (scalar) product of two quaternions.

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

Returns:

Type	Description
Number	Dot product.

static equals(left, right){Boolean}

Compare the components of the provided quaternions, return true if they are equal, otherwise return false.

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

Returns:

Type	Description
Boolean	If they are equal, it is true; otherwise, it is false.

static equalsEpsilon(left, right, epsilon){Boolean}

Compare the components of the provided quaternions, return true if they are within the provided range of ε, otherwise return false.

Name	Type	Description
left	Quaternion	optional The first quaternion.
right	Quaternion	optional The second quaternion.
epsilon	Number	Tolerance values used for equation testing.

Returns:

Type	Description
Boolean	If within the provided tolerance range, it is true; Otherwise, it is false.

static exp(cartesian, result){Quaternion}

Exponential quaternion function.

Name	Type	Description
cartesian	Cartesian3	cartesian。
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

static fastSlerp(start, end, t, result){Quaternion}

Calculate spherical linear interpolation or extrapolation at t using the provided quaternions. This implementation is faster than Quaternion # slip, but can only be precise to 10-6.

Name	Type	Description
start	Quaternion	Corresponding to the value of t at 0.0.
end	Quaternion	Corresponding to the value of t at 1.0.
t	Number	The point interpolated along t.
result	Quaternion	The object that stores the results.

See:

• Quaternion#slerp

Returns:

Type	Description
Quaternion	The modified result parameters.

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

Calculate the spherical quadrilateral interpolation between quaternions. A faster implementation than Quaternion # squad, but not very accurate.

Name	Type	Description
q0	Quaternion	The first quaternion.
q1	Quaternion	The second quaternion.
s0	Quaternion	The first quadrilateral.
s1	Quaternion	The second quadrilateral.
t	Number	The time used for interpolation in [0,1].
result	Quaternion	The object that stores the results.

See:

• Quaternion#squad

Returns:

Type	Description
Quaternion	The modified result parameters, if not provided, will be a new instance.

static fromAxisAngle(axis, angle, result){Quaternion}

Calculate the quaternion representing rotation around an axis.

Name	Type	Description
axis	Cartesian3	Rotating axis.
angle	Number	The angle of rotation around the axis (in radians).
result	Quaternion	optional The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters, or a new quaternion instance (if not provided).

static fromHeadingPitchRoll(headingPitchRoll, result){Quaternion}

Calculate the rotation angle based on the given azimuth, elevation, and roll angles. The azimuth angle is the rotation around the negative Z-axis. The pitch angle is the rotation angle around the negative y-axis. Rolling is the rotation around the positive x-axis.

Name	Type	Description
headingPitchRoll	HeadingPitchRoll	Rotation represented by azimuth, pitch, and roll.
result	Quaternion	optional The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters, or a new quaternion instance (if not provided).

static fromRotationMatrix(matrix, result){Quaternion}

Calculate quaternions based on the provided Matrix3 instance.

Name	Type	Description
matrix	Matrix3	Rotation matrix
result	Quaternion	optional The object that stores the results.

See:

• Matrix3.fromQuaternion

Returns:

Type	Description
Quaternion	The modified result parameters, or a new quaternion instance (if not provided).

static inverse(quaternion, result){Quaternion}

Calculate the inverse of the quaternion provided.

Name	Type	Description
quaternion	Quaternion	To standardize quaternions.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

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

Calculate the linear interpolation or extrapolation value 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=1.0.
t	Number	The point interpolated along t.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

static log(quaternion, result){Cartesian3}

Logarithmic quaternion function.

Name	Type	Description
quaternion	Quaternion	Unit quaternion.
result	Cartesian3	The object that stores the results.

Returns:

Type	Description
Cartesian3	The modified result parameters.

static magnitude(quaternion){Number}

Calculate the magnitude of the quaternion provided.

Name	Type	Description
quaternion	Quaternion	To conjugate quaternions.

Returns:

Type	Description
Number	The magnitude.

static magnitudeSquared(quaternion){Number}

Calculate the square of the amplitude of the quaternion provided.

Name	Type	Description
quaternion	Quaternion	To conjugate quaternions.

Returns:

Type	Description
Number	The square of the amplitude.

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

Calculate the product of two quaternions.

Name	Type	Description
left	Quaternion	The first quaternion.
right	Quaternion	The second quaternion.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

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

Multiply the provided quaternion by the provided scalar as a component.

Name	Type	Description
quaternion	Quaternion	The quaternion to be scaled.
scalar	Number	The scalar to be multiplied with.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

static negate(quaternion, result){Quaternion}

Deny the quaternion provided.

Name	Type	Description
quaternion	Quaternion	The quaternion to be negated.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

static normalize(quaternion, result){Quaternion}

Calculate the standardized form of the quaternion provided.

Name	Type	Description
quaternion	Quaternion	To standardize quaternions.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

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

Store the provided instance in the provided array.

Name	Type	Default	Description
value	Quaternion		The value to be packaged.
array	Array.<Number>		The array to be loaded.
startingIndex	Number	0	optional Start packaging the array index of elements.

Returns:

Type	Description
Array.<Number>	The array that has been loaded.

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

Calculate 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=1.0.
t	Number	The point interpolated along t.
result	Quaternion	The object that stores the results.

See:

• Quaternion#fastSlerp

Returns:

Type	Description
Quaternion	The modified result parameters.

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

Calculate the spherical quaternion interpolation between quaternions.

Name	Type	Description
q0	Quaternion	The first quaternion.
q1	Quaternion	The second quaternion.
s0	Quaternion	The first quadrilateral.
s1	Quaternion	The second quadrilateral.
t	Number	The time used for interpolation in [0,1].
result	Quaternion	The object that stores the results.

See:

• Quaternion#computeInnerQuadrangle

Returns:

Type	Description
Quaternion	The modified result parameters.

Example

// 1. compute the squad interpolation between two quaternions on a curve
var s0 = SuperMap3D.Quaternion.computeInnerQuadrangle(quaternions[i - 1], quaternions[i], quaternions[i + 1], new SuperMap3D.Quaternion());
var s1 = SuperMap3D.Quaternion.computeInnerQuadrangle(quaternions[i], quaternions[i + 1], quaternions[i + 2], new SuperMap3D.Quaternion());
var q = SuperMap3D.Quaternion.squad(quaternions[i], quaternions[i + 1], s0, s1, t, new SuperMap3D.Quaternion());

// 2. compute the squad interpolation as above but where the first quaternion is a end point.
var s1 = SuperMap3D.Quaternion.computeInnerQuadrangle(quaternions[0], quaternions[1], quaternions[2], new SuperMap3D.Quaternion());
var q = SuperMap3D.Quaternion.squad(quaternions[0], quaternions[1], quaternions[0], s1, t, new SuperMap3D.Quaternion());

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

Calculate the difference between the components of two quaternions.

Name	Type	Description
left	Quaternion	The first quaternion.
right	Quaternion	The second quaternion.
result	Quaternion	The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters.

static unpack(array, startingIndex, result){Quaternion}

Retrieve instances from the packaged array.

Name	Type	Default	Description
array	Array.<Number>		Package the array.
startingIndex	Number	0	optional The starting index of the element to be decompressed.
result	Quaternion		optional The object in which to store the results.

Returns:

Type	Description
Quaternion	The modified result parameters or a new Quaternion instance (if not provided).

static unpackInterpolationResult(array, sourceArray, firstIndex, lastIndex, result){Quaternion}

Read instances from the packaged array converted using convertPackedArrayForInterpolation.

Name	Type	Default	Description
array	Array.<Number>		The array previously packaged for interpolation.
sourceArray	Array.<Number>		The original packaging array.
firstIndex	Number	0	optional The firstIndex used when converting arrays.
lastIndex	Number	packedArray.length	optional Used to convert the last index of an array.
result	Quaternion		optional The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters, or a new quaternion instance (if not provided).

clone(result){Quaternion}

Copy this quaternion instance.

Name	Type	Description
result	Quaternion	optional The object that stores the results.

Returns:

Type	Description
Quaternion	The modified result parameters, or a new quaternion instance (if not provided).

equals(right){Boolean}

Compare the components of this quaternion with the provided quaternion. If they are equal, return true; otherwise, return false.

Name	Type	Description
right	Quaternion	optional The quaternion on the right.

Returns:

Type	Description
Boolean	If they are equal, it is true; otherwise, it is false.

equalsEpsilon(right, epsilon){Boolean}

Compare the components of this quaternion with the provided quaternion, return true if within the provided tolerance range, otherwise return false.

Name	Type	Description
right	Quaternion	optional The quaternion on the right.
epsilon	Number	Tolerance values used for equation testing.

Returns:

Type	Description
Boolean	If within the provided tolerance range, it is true; Otherwise, it is false.

toString(){String}

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

Returns:

Type	Description
String	The string representing this quaternion.