Package gaiasky.util.math

Class QuaternionDouble

java.lang.Object

gaiasky.util.math.QuaternionDouble

All Implemented Interfaces:

Serializable

public class QuaternionDouble
extends Object
implements Serializable

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
double	w
double	x
double	y
double	z

Constructor Summary

Constructors

Constructor	Description
QuaternionDouble()
QuaternionDouble(double x, double y, double z, double w)	Constructor, sets the four components of the quaternion.
QuaternionDouble(com.badlogic.gdx.math.Quaternion quaternion)	Constructor, sets the quaternion components from the given quaternion.
QuaternionDouble(QuaternionDouble quaternion)	Constructor, sets the quaternion components from the given quaternion.
QuaternionDouble(Vector3d axis, double angle)	Constructor, sets the quaternion from the given axis vector and the angle around that axis in degrees.

Method Summary

Modifier and Type	Method	Description
QuaternionDouble	conjugate()	Conjugate the quaternion.
QuaternionDouble	cpy()
double	dot(double x, double y, double z, double w)	Get the dot product between this and the other quaternion (commutative).
static double	dot(double x1, double y1, double z1, double w1, double x2, double y2, double z2, double w2)	Get the dot product between the two quaternions (commutative).
double	dot(QuaternionDouble other)	Get the dot product between this and the other quaternion (commutative).
boolean	equals(Object obj)
QuaternionDouble	fromAxes(Vector3d xAxis, Vector3d yAxis, Vector3d zAxis)	fromAxes creates a Quaternion that represents the coordinate system defined by three axes.
QuaternionDouble	fromRotationMatrix(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)
double	getAngle()	Get the angle in degrees of the rotation this quaternion represents.
double	getAngleAround(double axisX, double axisY, double axisZ)	Get the angle in degrees of the rotation around the specified axis.
double	getAngleAround(Vector3d axis)	Get the angle in degrees of the rotation around the specified axis.
double	getAngleAroundRad(double axisX, double axisY, double axisZ)	Get the angle in radians of the rotation around the specified axis.
double	getAngleAroundRad(Vector3d axis)	Get the angle in radians of the rotation around the specified axis.
double	getAngleRad()	Get the angle in radians of the rotation this quaternion represents.
double	getAxisAngle(Vector3d axis)	Get the axis angle representation of the rotation in degrees.
double	getAxisAngleRad(Vector3d axis)	Get the axis-angle representation of the rotation in radians.
Vector3d	getDirection(Vector3d aux)	Gets the camera direction vector corresponding to this quaternion rotation.
int	getGimbalPole()	Get the pole of the gimbal lock, if any.
double	getPitch()	Get the pitch euler angle in degrees, which is the rotation around the x axis.
double	getPitchRad()	Get the pitch euler angle in radians, which is the rotation around the x axis.
double	getRoll()	Get the roll euler angle in degrees, which is the rotation around the z axis.
double	getRollRad()	Get the roll euler angle in radians, which is the rotation around the z axis.
void	getSwingTwist(double axisX, double axisY, double axisZ, QuaternionDouble swing, QuaternionDouble twist)	Get the swing rotation and twist rotation for the specified axis.
void	getSwingTwist(Vector3d axis, QuaternionDouble swing, QuaternionDouble twist)	Get the swing rotation and twist rotation for the specified axis.
Vector3d	getUp(Vector3d aux)	Gets the camera up vector corresponding to this quaternion rotation.
double	getYaw()	Get the yaw euler angle in degrees, which is the rotation around the y axis.
double	getYawRad()	Get the yaw euler angle in radians, which is the rotation around the y axis.
int	hashCode()
QuaternionDouble	idt()	Sets the quaternion to an identity QuaternionDouble
QuaternionDouble	inverse()	Sets the value of this quaternion to the quaternion inverse of itself.
boolean	isIdentity()
boolean	isIdentity(double tolerance)
double	len()
static double	len(double x, double y, double z, double w)
double	len2()
static double	len2(double x, double y, double z, double w)
QuaternionDouble	mul(double scalar)	Multiplies the components of this quaternion with the given scalar.
QuaternionDouble	mul(double x, double y, double z, double w)	Multiplies this quaternion with another one in the form of this = this * other
QuaternionDouble	mul(QuaternionDouble other)	Multiplies this quaternion with another one in the form of this = this * other
QuaternionDouble	mulAdd(QuaternionDouble q, double s)	Add quaternion q, scaled by s, to this quaternion (this = this + q * s)
QuaternionDouble	mulInverse(QuaternionDouble q1)	Multiplies this quaternion by the inverse of quaternion q1 and places the value into this quaternion.
QuaternionDouble	mulLeft(double x, double y, double z, double w)	Multiplies this quaternion with another one in the form of this = other * this
QuaternionDouble	mulLeft(QuaternionDouble other)	Multiplies this quaternion with another one in the form of this = other * this
QuaternionDouble	mulLeftInverse(QuaternionDouble q1)	Pre-multiplies this quaternion by the inverse of quaternion q and places the value into this quaternion.
void	nlerp(QuaternionDouble q2, double blend)	Normalized linear interpolation between the current instance and q2 using nlerp, and stores the result in the current instance.
QuaternionDouble	nor()	Normalizes this quaternion to unit length.
QuaternionDouble	set(double x, double y, double z, double w)	Sets the components of the quaternion
QuaternionDouble	set(com.badlogic.gdx.math.Quaternion quaternion)	Sets the quaternion components from the given quaternion.
QuaternionDouble	set(QuaternionDouble quaternion)	Sets the quaternion components from the given quaternion.
QuaternionDouble	set(Vector3d axis, double angle)	Sets the quaternion components from the given axis and angle around that axis.
QuaternionDouble	set(org.apfloat.Apfloat x, org.apfloat.Apfloat y, org.apfloat.Apfloat z, org.apfloat.Apfloat w)
QuaternionDouble	setEulerAngles(double yaw, double pitch, double roll)	Sets the quaternion to the given euler angles in degrees.
QuaternionDouble	setEulerAnglesRad(double yaw, double pitch, double roll)	Sets the quaternion to the given euler angles in radians.
QuaternionDouble	setFromAxes(boolean normalizeAxes, double xx, double xy, double xz, double yx, double yy, double yz, double zx, double zy, double zz)	Sets the QuaternionDouble from the given x-, y- and z-axis.
QuaternionDouble	setFromAxes(double xx, double xy, double xz, double yx, double yy, double yz, double zx, double zy, double zz)	Sets the QuaternionDouble from the given x-, y- and z-axis which have to be orthonormal.
QuaternionDouble	setFromAxis(double x, double y, double z, double degrees)	Sets the quaternion components from the given axis and angle around that axis.
QuaternionDouble	setFromAxis(Vector3d axis, double degrees)	Sets the quaternion components from the given axis and angle around that axis.
QuaternionDouble	setFromAxisRad(double x, double y, double z, double radians)	Sets the quaternion components from the given axis and angle around that axis.
QuaternionDouble	setFromAxisRad(Vector3d axis, double radians)	Sets the quaternion components from the given axis and angle around that axis.
QuaternionDouble	setFromCamera(Vector3d direction, Vector3d up)	Sets this quaternion from the given camera basis, using its direction and up vectors.
QuaternionDouble	setFromCross(double x1, double y1, double z1, double x2, double y2, double z2)	Set this quaternion to the rotation between two vectors.
QuaternionDouble	setFromCross(Vector3d v1, Vector3d v2)	Set this quaternion to the rotation between two vectors.
QuaternionDouble	setFromMatrix(boolean normalizeAxes, Matrix4d matrix)	Sets the QuaternionDouble from the given matrix, optionally removing any scaling.
QuaternionDouble	setFromMatrix(Matrix4d matrix)	Sets the QuaternionDouble from the given rotation matrix, which must not contain scaling.
void	slerp(QuaternionDouble end, double alpha)	Spherical linear interpolation between this quaternion and the end quaternion, based on the alpha value in the range [0,1].
void	slerp2(QuaternionDouble end, double alpha)	Second implementation of slerp, slightly different from the default one.
void	toMatrix(double[] matrix)	Fills a 4x4 matrix with the rotation matrix represented by this quaternion.
String	toString()
Vector3b	transform(Vector3b v)
Vector3d	transform(Vector3d v)	Transforms the given vector using this quaternion
double[]	values()	Returns the components of this quaternion as an array of [x, y, z, w].

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Details

x

public double x

y

public double y

z

public double z

w

public double w

Constructor Details

QuaternionDouble

public QuaternionDouble(double x,
 double y,
 double z,
 double w)

Constructor, sets the four components of the quaternion.

Parameters:

x - The x-component

y - The y-component

z - The z-component

w - The w-component

QuaternionDouble

public QuaternionDouble()

QuaternionDouble

public QuaternionDouble(QuaternionDouble quaternion)

Constructor, sets the quaternion components from the given quaternion.

Parameters:

quaternion - The quaternion to copy.

QuaternionDouble

public QuaternionDouble(com.badlogic.gdx.math.Quaternion quaternion)

Constructor, sets the quaternion components from the given quaternion.

Parameters:

quaternion - The quaternion to copy.

QuaternionDouble

public QuaternionDouble(Vector3d axis,
 double angle)

Constructor, sets the quaternion from the given axis vector and the angle around that axis in degrees.

Parameters:

axis - The axis

angle - The angle in degrees.

Method Details

len

public static double len(double x,
 double y,
 double z,
 double w)

Returns:

the euclidean length of the specified quaternion

len2

public static double len2(double x,
 double y,
 double z,
 double w)

dot

public static double dot(double x1,
 double y1,
 double z1,
 double w1,
 double x2,
 double y2,
 double z2,
 double w2)

Get the dot product between the two quaternions (commutative).

Parameters:

x1 - the x component of the first quaternion

y1 - the y component of the first quaternion

z1 - the z component of the first quaternion

w1 - the w component of the first quaternion

x2 - the x component of the second quaternion

y2 - the y component of the second quaternion

z2 - the z component of the second quaternion

w2 - the w component of the second quaternion

Returns:

the dot product between the first and second quaternion.

set

public QuaternionDouble set(double x,
 double y,
 double z,
 double w)

Sets the components of the quaternion

Parameters:

x - The x-component

y - The y-component

z - The z-component

w - The w-component

Returns:

This quaternion for chaining

set

public QuaternionDouble set(org.apfloat.Apfloat x,
 org.apfloat.Apfloat y,
 org.apfloat.Apfloat z,
 org.apfloat.Apfloat w)

set

public QuaternionDouble set(QuaternionDouble quaternion)

Sets the quaternion components from the given quaternion.

Parameters:

quaternion - The quaternion.

Returns:

This quaternion for chaining.

set

public QuaternionDouble set(com.badlogic.gdx.math.Quaternion quaternion)

Sets the quaternion components from the given quaternion.

Parameters:

quaternion - The quaternion.

Returns:

This quaternion for chaining.

set

public QuaternionDouble set(Vector3d axis,
 double angle)

Sets the quaternion components from the given axis and angle around that axis.

Parameters:

axis - The axis

angle - The angle in degrees

Returns:

This quaternion for chaining.

cpy

public QuaternionDouble cpy()

Returns:

a copy of this quaternion

len

public double len()

Returns:

the Euclidean length of this quaternion

toString

public String toString()

Overrides:

toString in class Object

setEulerAngles

public QuaternionDouble setEulerAngles(double yaw,
 double pitch,
 double roll)

Sets the quaternion to the given euler angles in degrees.

Parameters:

yaw - the rotation around the y-axis in degrees

pitch - the rotation around the x-axis in degrees

roll - the rotation around the z-axis degrees

Returns:

this quaternion

setEulerAnglesRad

public QuaternionDouble setEulerAnglesRad(double yaw,
 double pitch,
 double roll)

Sets the quaternion to the given euler angles in radians.

Parameters:

yaw - the rotation around the y axis in radians

pitch - the rotation around the x axis in radians

roll - the rotation around the z axis in radians

Returns:

this quaternion

getGimbalPole

public int getGimbalPole()

Get the pole of the gimbal lock, if any.

Returns:

positive (+1) for north pole, negative (-1) for south pole, zero (0) when no gimbal lock

getRollRad

public double getRollRad()

Get the roll euler angle in radians, which is the rotation around the z axis. Requires that this quaternion is normalized.

Returns:

the rotation around the z axis in radians (between -PI and +PI)

getRoll

public double getRoll()

Get the roll euler angle in degrees, which is the rotation around the z axis. Requires that this quaternion is normalized.

Returns:

the rotation around the z axis in degrees (between -180 and +180)

getPitchRad

public double getPitchRad()

Get the pitch euler angle in radians, which is the rotation around the x axis. Requires that this quaternion is normalized.

Returns:

the rotation around the x axis in radians (between -(PI/2) and +(PI/2))

getPitch

public double getPitch()

Get the pitch euler angle in degrees, which is the rotation around the x axis. Requires that this quaternion is normalized.

Returns:

the rotation around the x axis in degrees (between -90 and +90)

getYawRad

public double getYawRad()

Get the yaw euler angle in radians, which is the rotation around the y axis. Requires that this quaternion is normalized.

Returns:

the rotation around the y axis in radians (between -PI and +PI)

getYaw

public double getYaw()

Get the yaw euler angle in degrees, which is the rotation around the y axis. Requires that this quaternion is normalized.

Returns:

the rotation around the y axis in degrees (between -180 and +180)

len2

public double len2()

Returns:

the length of this quaternion without square root

nor

public QuaternionDouble nor()

Normalizes this quaternion to unit length.

Returns:

the quaternion for chaining.

conjugate

public QuaternionDouble conjugate()

Conjugate the quaternion.

Returns:

This quaternion for chaining

transform

public Vector3d transform(Vector3d v)

Transforms the given vector using this quaternion

Parameters:

v - Vector to transform

transform

public Vector3b transform(Vector3b v)

inverse

public QuaternionDouble inverse()

Sets the value of this quaternion to the quaternion inverse of itself. Warning: this quaternion will NOT be normalized. Note that if q not normalized, then q*qinverse=(0,0,0,1) whereas q*qconjugate =(0,0,0,Norm(q)*Norm(q))

Returns:

Quaternion

mul

public QuaternionDouble mul(QuaternionDouble other)

Multiplies this quaternion with another one in the form of this = this * other

Parameters:

other - QuaternionDouble to multiply with

Returns:

This quaternion for chaining

mul

public QuaternionDouble mul(double x,
 double y,
 double z,
 double w)

Multiplies this quaternion with another one in the form of this = this * other

Parameters:

x - the x component of the other quaternion to multiply with

y - the y component of the other quaternion to multiply with

z - the z component of the other quaternion to multiply with

w - the w component of the other quaternion to multiply with

Returns:

This quaternion for chaining

mulLeft

public QuaternionDouble mulLeft(QuaternionDouble other)

Multiplies this quaternion with another one in the form of this = other * this

Parameters:

other - QuaternionDouble to multiply with

Returns:

This quaternion for chaining

mulLeft

public QuaternionDouble mulLeft(double x,
 double y,
 double z,
 double w)

Multiplies this quaternion with another one in the form of this = other * this

Parameters:

x - the x component of the other quaternion to multiply with

y - the y component of the other quaternion to multiply with

z - the z component of the other quaternion to multiply with

w - the w component of the other quaternion to multiply with

Returns:

This quaternion for chaining

mulInverse

public QuaternionDouble mulInverse(QuaternionDouble q1)

Multiplies this quaternion by the inverse of quaternion q1 and places the value into this quaternion. The value of the argument quaternion is preserved (this = this * q^-1). Warning: this quaternion will NOT be normalized.

Parameters:

q1 - the other quaternion

Returns:

QuaternionDouble

mulLeftInverse

public QuaternionDouble mulLeftInverse(QuaternionDouble q1)

Pre-multiplies this quaternion by the inverse of quaternion q and places the value into this quaternion. The value of the argument quaternion is preserved (this = q^-1 * this). Warning: this quaternion will NOT be normalized.

Parameters:

q1 - the other quaternion

Returns:

QuaternionDouble

toMatrix

public void toMatrix(double[] matrix)

Fills a 4x4 matrix with the rotation matrix represented by this quaternion.

Parameters:

matrix - Matrix to fill

idt

public QuaternionDouble idt()

Sets the quaternion to an identity QuaternionDouble

Returns:

this quaternion for chaining

isIdentity

public boolean isIdentity()

Returns:

If this quaternion is an identity QuaternionDouble

isIdentity

public boolean isIdentity(double tolerance)

Returns:

If this quaternion is an identity QuaternionDouble

setFromAxis

public QuaternionDouble setFromAxis(Vector3d axis,
 double degrees)

Sets the quaternion components from the given axis and angle around that axis.

Parameters:

axis - The axis

degrees - The angle in degrees

Returns:

This quaternion for chaining.

setFromAxisRad

public QuaternionDouble setFromAxisRad(Vector3d axis,
 double radians)

Sets the quaternion components from the given axis and angle around that axis.

Parameters:

axis - The axis

radians - The angle in radians

Returns:

This quaternion for chaining.

setFromAxis

public QuaternionDouble setFromAxis(double x,
 double y,
 double z,
 double degrees)

Sets the quaternion components from the given axis and angle around that axis.

Parameters:

x - X direction of the axis

y - Y direction of the axis

z - Z direction of the axis

degrees - The angle in degrees

Returns:

This quaternion for chaining.

setFromAxisRad

public QuaternionDouble setFromAxisRad(double x,
 double y,
 double z,
 double radians)

Sets the quaternion components from the given axis and angle around that axis.

Parameters:

x - X direction of the axis

y - Y direction of the axis

z - Z direction of the axis

radians - The angle in radians

Returns:

This quaternion for chaining.

setFromMatrix

public QuaternionDouble setFromMatrix(boolean normalizeAxes,
 Matrix4d matrix)

Sets the QuaternionDouble from the given matrix, optionally removing any scaling.

setFromMatrix

public QuaternionDouble setFromMatrix(Matrix4d matrix)

Sets the QuaternionDouble from the given rotation matrix, which must not contain scaling.

setFromAxes

public QuaternionDouble setFromAxes(double xx,
 double xy,
 double xz,
 double yx,
 double yy,
 double yz,
 double zx,
 double zy,
 double zz)

Sets the QuaternionDouble from the given x-, y- and z-axis which have to be orthonormal.

Taken from Bones framework for JPCT, see http://www.aptalkarga.com/bones/ which in turn took it from Graphics Gem code at ftp://ftp.cis.upenn.edu/pub/graphics/shoemake/quatut.ps.Z.

Parameters:

xx - x-axis x-coordinate

xy - x-axis y-coordinate

xz - x-axis z-coordinate

yx - y-axis x-coordinate

yy - y-axis y-coordinate

yz - y-axis z-coordinate

zx - z-axis x-coordinate

zy - z-axis y-coordinate

zz - z-axis z-coordinate

setFromCamera

public QuaternionDouble setFromCamera(Vector3d direction,
 Vector3d up)

Sets this quaternion from the given camera basis, using its direction and up vectors.

Parameters:

direction - The camera direction vector.

up - The camera up vector.

Returns:

The quaternion representing the current camera orientation.

getDirection

public Vector3d getDirection(Vector3d aux)

Gets the camera direction vector corresponding to this quaternion rotation.

Parameters:

aux - The vector to put the result.

Returns:

The direction vector.

getUp

public Vector3d getUp(Vector3d aux)

Gets the camera up vector corresponding to this quaternion rotation.

Parameters:

aux - The vector to put the result.

Returns:

The up vector.

fromAxes

public QuaternionDouble fromAxes(Vector3d xAxis,
 Vector3d yAxis,
 Vector3d zAxis)

fromAxes creates a Quaternion that represents the coordinate system defined by three axes. These axes are assumed to be orthogonal and no error checking is applied. Thus, the user must ensure that the three axes being provided indeed represents a proper right-handed coordinate system.

Parameters:

xAxis - vector representing the x-axis of the coordinate system.

yAxis - vector representing the y-axis of the coordinate system.

zAxis - vector representing the z-axis of the coordinate system.

fromRotationMatrix

public QuaternionDouble fromRotationMatrix(double m00,
 double m01,
 double m02,
 double m10,
 double m11,
 double m12,
 double m20,
 double m21,
 double m22)

setFromAxes

public QuaternionDouble setFromAxes(boolean normalizeAxes,
 double xx,
 double xy,
 double xz,
 double yx,
 double yy,
 double yz,
 double zx,
 double zy,
 double zz)

Sets the QuaternionDouble from the given x-, y- and z-axis.

Taken from Bones framework for JPCT, see http://www.aptalkarga.com/bones/ which in turn took it from Graphics Gem code at ftp://ftp.cis.upenn.edu/pub/graphics/shoemake/quatut.ps.Z.

Parameters:

normalizeAxes - whether to normalize the axes (necessary when they contain scaling)

xx - x-axis x-coordinate

xy - x-axis y-coordinate

xz - x-axis z-coordinate

yx - y-axis x-coordinate

yy - y-axis y-coordinate

yz - y-axis z-coordinate

zx - z-axis x-coordinate

zy - z-axis y-coordinate

zz - z-axis z-coordinate

setFromCross

public QuaternionDouble setFromCross(Vector3d v1,
 Vector3d v2)

Set this quaternion to the rotation between two vectors.

Parameters:

v1 - The base vector, which should be normalized.

v2 - The target vector, which should be normalized.

Returns:

This quaternion for chaining

setFromCross

public QuaternionDouble setFromCross(double x1,
 double y1,
 double z1,
 double x2,
 double y2,
 double z2)

Set this quaternion to the rotation between two vectors.

Parameters:

x1 - The base vectors x value, which should be normalized.

y1 - The base vectors y value, which should be normalized.

z1 - The base vectors z value, which should be normalized.

x2 - The target vector x value, which should be normalized.

y2 - The target vector y value, which should be normalized.

z2 - The target vector z value, which should be normalized.

Returns:

This quaternion for chaining

nlerp

public void nlerp(QuaternionDouble q2,
 double blend)

Normalized linear interpolation between the current instance and q2 using nlerp, and stores the result in the current instance.

This method is often faster than slerp(QuaternionDouble, double), but less accurate.

Parameters:

q2 - the desired value when blend=1 (not null, unaffected).

blend - the fractional change amount.

slerp

public void slerp(QuaternionDouble end,
 double alpha)

Spherical linear interpolation between this quaternion and the end quaternion, based on the alpha value in the range [0,1]. Taken from. Taken from Bones framework for JPCT, see here.

Parameters:

end - the end quaternion.

alpha - alpha in the range [0,1].

slerp2

public void slerp2(QuaternionDouble end,
 double alpha)

Second implementation of slerp, slightly different from the default one.

Parameters:

end - The end quaternion.

alpha - The fractional change amount in [0,1].

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class Object

dot

public double dot(QuaternionDouble other)

Get the dot product between this and the other quaternion (commutative).

Parameters:

other - the other quaternion.

Returns:

the dot product of this and the other quaternion.

dot

public double dot(double x,
 double y,
 double z,
 double w)

Get the dot product between this and the other quaternion (commutative).

Parameters:

x - the x component of the other quaternion

y - the y component of the other quaternion

z - the z component of the other quaternion

w - the w component of the other quaternion

Returns:

the dot product of this and the other quaternion.

mul

public QuaternionDouble mul(double scalar)

Multiplies the components of this quaternion with the given scalar.

Parameters:

scalar - the scalar.

Returns:

this quaternion for chaining.

mulAdd

public QuaternionDouble mulAdd(QuaternionDouble q,
 double s)

Add quaternion q, scaled by s, to this quaternion (this = this + q * s)

Returns:

this quaternion for chaining.

getAxisAngle

public double getAxisAngle(Vector3d axis)

Get the axis angle representation of the rotation in degrees. The supplied vector will receive the axis (x, y and z values) of the rotation and the value returned is the angle in degrees around that axis. Note that this method will alter the supplied vector, the existing value of the vector is ignored. This will normalize this quaternion if needed. The received axis is a unit vector. However, if this is an identity quaternion (no rotation), then the length of the axis may be zero.

Parameters:

axis - vector which will receive the axis

Returns:

the angle in degrees

See Also:

• wikipedia
• calculation

getAxisAngleRad

public double getAxisAngleRad(Vector3d axis)

Get the axis-angle representation of the rotation in radians. The supplied vector will receive the axis (x, y and z values) of the rotation and the value returned is the angle in radians around that axis. Note that this method will alter the supplied vector, the existing value of the vector is ignored. This will normalize this quaternion if needed. The received axis is a unit vector. However, if this is an identity quaternion (no rotation), then the length of the axis may be zero.

Parameters:

axis - vector which will receive the axis

Returns:

the angle in radians

See Also:

• wikipedia
• calculation

getAngleRad

public double getAngleRad()

Get the angle in radians of the rotation this quaternion represents. Does not normalize the quaternion. Use getAxisAngleRad(Vector3d) to get both the axis and the angle of this rotation. Use getAngleAroundRad(Vector3d) to get the angle around a specific axis.

Returns:

the angle in radians of the rotation

getAngle

public double getAngle()

Get the angle in degrees of the rotation this quaternion represents. Use getAxisAngle(Vector3d) to get both the axis and the angle of this rotation. Use getAngleAround(Vector3d) to get the angle around a specific axis.

Returns:

the angle in degrees of the rotation

getSwingTwist

public void getSwingTwist(double axisX,
 double axisY,
 double axisZ,
 QuaternionDouble swing,
 QuaternionDouble twist)

Get the swing rotation and twist rotation for the specified axis. The twist rotation represents the rotation around the specified axis. The swing rotation represents the rotation of the specified axis itself, which is the rotation around an axis perpendicular to the specified axis.

The swing and twist rotation can be used to reconstruct the original quaternion: this = swing * twist

Parameters:

axisX - the X component of the normalized axis for which to get the swing and twist rotation

axisY - the Y component of the normalized axis for which to get the swing and twist rotation

axisZ - the Z component of the normalized axis for which to get the swing and twist rotation

swing - will receive the swing rotation: the rotation around an axis perpendicular to the specified axis

twist - will receive the twist rotation: the rotation around the specified axis

See Also:

• calculation

getSwingTwist

public void getSwingTwist(Vector3d axis,
 QuaternionDouble swing,
 QuaternionDouble twist)

Get the swing rotation and twist rotation for the specified axis. The twist rotation represents the rotation around the specified axis. The swing rotation represents the rotation of the specified axis itself, which is the rotation around an axis perpendicular to the specified axis.

The swing and twist rotation can be used to reconstruct the original quaternion: this = swing * twist

Parameters:

axis - the normalized axis for which to get the swing and twist rotation

swing - will receive the swing rotation: the rotation around an axis perpendicular to the specified axis

twist - will receive the twist rotation: the rotation around the specified axis

See Also:

• calculation

getAngleAroundRad

public double getAngleAroundRad(double axisX,
 double axisY,
 double axisZ)

Get the angle in radians of the rotation around the specified axis. The axis must be normalized.

Parameters:

axisX - the x component of the normalized axis for which to get the angle

axisY - the y component of the normalized axis for which to get the angle

axisZ - the z component of the normalized axis for which to get the angle

Returns:

the angle in radians of the rotation around the specified axis

getAngleAroundRad

public double getAngleAroundRad(Vector3d axis)

Get the angle in radians of the rotation around the specified axis. The axis must be normalized.

Parameters:

axis - the normalized axis for which to get the angle

Returns:

the angle in radians of the rotation around the specified axis

getAngleAround

public double getAngleAround(double axisX,
 double axisY,
 double axisZ)

Get the angle in degrees of the rotation around the specified axis. The axis must be normalized.

Parameters:

axisX - the x component of the normalized axis for which to get the angle

axisY - the y component of the normalized axis for which to get the angle

axisZ - the z component of the normalized axis for which to get the angle

Returns:

the angle in degrees of the rotation around the specified axis

getAngleAround

public double getAngleAround(Vector3d axis)

Get the angle in degrees of the rotation around the specified axis. The axis must be normalized.

Parameters:

axis - the normalized axis for which to get the angle

Returns:

the angle in degrees of the rotation around the specified axis

values

public double[] values()

Returns the components of this quaternion as an array of [x, y, z, w].

Returns:

The components of this quaternion as an array.