All Superinterfaces:

Cloneable, Serializable
```
public interface Quaternion
extends Cloneable, Serializable
```
A 4 element unit quaternion represented by x, y, z, w coordinates. The quaternion is always normalized.
Other Rotation Representations

Other representations of an rotation are available from this class: axis-angle, and Euler angles.
Axis Angles
The axis–angle representation of a rotation parameterizes a rotation in a three-dimensional Euclidean space by two values: a unit vector, indicating the direction of an axis of rotation, and an angle describing the magnitude of the rotation about the axis. The rotation occurs in the sense prescribed by the (left/right)-hand rule.
Euler Angles
The term "Euler Angle" is used for any representation of 3 dimensional rotations where the rotation is decomposed into 3 separate angles.
There is no single set of conventions and standards in this area, therefore the following conventions was choosen:
- angle applied first: heading;
- angle applied second: attitude;
- angle applied last: bank
Examples: NASA aircraft standard and telescope standard
Version:

17.0 2020-01-04 14:41:43

Author:

Stéphane GALLAND

Maven Group Id:

org.arakhne.afc.core

Maven Artifact Id:

mathgeom

Nested Class Summary

Nested Classes
Modifier and Type	Interface	Description
`static class`	`Quaternion.AxisAngle`	A representation of axis-angle.
`static class`	`Quaternion.EulerAngles`	A representation of Euler Angles.

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	Description
`void`	`conjugate()`	Sets the value of this quaternion to the conjugate of itself.
`void`	`conjugate(Quaternion q1)`	Sets the value of this quaternion to the conjugate of quaternion q1.
`boolean`	`epsilonEquals(Quaternion t1, double epsilon)`	Returns true if the L-infinite distance between this tuple and tuple t1 is less than or equal to the epsilon parameter, otherwise returns false.
`double`	`getAngle()`	Replies the rotation angle represented by this quaternion.
`Vector3D<?,?>`	`getAxis()`	Replies the rotation axis-angle represented by this quaternion.
`Quaternion.AxisAngle`	`getAxisAngle()`	Replies the rotation axis represented by this quaternion.
`Quaternion.EulerAngles`	`getEulerAngles()`	Replies the Euler's angles that corresponds to the quaternion.
`Quaternion.EulerAngles`	`getEulerAngles(CoordinateSystem3D system)`	Replies the Euler's angles that corresponds to the quaternion.
`double`	`getW()`	Replies the W coordinate.
`double`	`getX()`	Replies the X coordinate.
`double`	`getY()`	Replies the Y coordinate.
`double`	`getZ()`	Replies the Z coordinate.
`void`	`interpolate(Quaternion q1, double alpha)`	Performs a great circle interpolation between this quaternion and the quaternion parameter and places the result into this quaternion.
`void`	`interpolate(Quaternion q1, Quaternion q2, double alpha)`	Performs a great circle interpolation between quaternion q1 and quaternion q2 and places the result into this quaternion.
`void`	`inverse()`	Sets the value of this quaternion to the quaternion inverse of itself.
`void`	`inverse(Quaternion q1)`	Sets the value of this quaternion to quaternion inverse of quaternion q1.
`void`	`mul(Quaternion q1)`	Sets the value of this quaternion to the quaternion product of itself and q1 (this = this * q1).
`void`	`mul(Quaternion q1, Quaternion q2)`	Sets the value of this quaternion to the quaternion product of quaternions q1 and q2 (this = q1 * q2).
`void`	`mulInverse(Quaternion q1)`	Multiplies this quaternion by the inverse of quaternion q1 and places the value into this quaternion.
`void`	`mulInverse(Quaternion q1, Quaternion q2)`	Multiplies quaternion q1 by the inverse of quaternion q2 and places the value into this quaternion.
`void`	`normalize()`	Normalizes the value of this quaternion in place.
`void`	`normalize(Quaternion q1)`	Sets the value of this quaternion to the normalized value of quaternion q1.
`void`	`set(double x, double y, double z, double w)`	Set the quaternion coordinates.
`void`	`set(Quaternion quat)`	Set the quaternion coordinates.
`void`	`setAxisAngle(double x1, double y1, double z1, double angle)`	Sets the value of this quaternion to the equivalent rotation of the Axis-Angle arguments.
`void`	`setAxisAngle(Vector3D<?,?> axis, double angle)`	Sets the value of this quaternion to the equivalent rotation of the Axis-Angle arguments.
`void`	`setEulerAngles(double attitude, double bank, double heading)`	Set the quaternion with the Euler angles.
`void`	`setEulerAngles(double attitude, double bank, double heading, CoordinateSystem3D system)`	Set the quaternion with the Euler angles.
`void`	`setEulerAngles(Quaternion.EulerAngles angles)`	Set the quaternion with the Euler angles.
`void`	`setFromMatrix(Matrix3d m1)`	Sets the value of this quaternion to the rotational component of the passed matrix.
`void`	`setFromMatrix(Matrix4d m1)`	Sets the value of this quaternion to the rotational component of the passed matrix.
`void`	`setW(double w)`	Set the W coordinate.
`void`	`setX(double x)`	Set the X coordinate.
`void`	`setY(double y)`	Set the Y coordinate.
`void`	`setZ(double z)`	Set the Z coordinate.

- Method Detail
  - getX
```
@Pure
double getX()
```
    Replies the X coordinate.
    
    Returns:
    
    x
  - setX
```
void setX(double x)
```
    Set the X coordinate.
    
    Parameters:
    
    x - x coordinate.
  - getY
```
@Pure
double getY()
```
    Replies the Y coordinate.
    
    Returns:
    
    y
  - setY
```
void setY(double y)
```
    Set the Y coordinate.
    
    Parameters:
    
    y - y coordinate.
  - getZ
```
@Pure
double getZ()
```
    Replies the Z coordinate.
    
    Returns:
    
    z
  - setZ
```
void setZ(double z)
```
    Set the Z coordinate.
    
    Parameters:
    
    z - z coordinate.
  - getW
```
@Pure
double getW()
```
    Replies the W coordinate.
    
    Returns:
    
    w
  - setW
```
void setW(double w)
```
    Set the W coordinate.
    
    Parameters:
    
    w - w coordinate.
  - epsilonEquals
```
@Pure
boolean epsilonEquals(Quaternion t1,
                      double epsilon)
```
    Returns true if the L-infinite distance between this tuple and tuple t1 is less than or equal to the epsilon parameter, otherwise returns false. The L-infinite distance is equal to MAX[abs(x1-x2), abs(y1-y2)].
    
    Parameters:
    
    t1 - the tuple to be compared to this tuple
    
    epsilon - the threshold value
    
    Returns:
    
    true or false
  - conjugate
```
void conjugate(Quaternion q1)
```
    Sets the value of this quaternion to the conjugate of quaternion q1.
    
    Parameters:
    
    q1 - the source vector
  - conjugate
```
void conjugate()
```
    Sets the value of this quaternion to the conjugate of itself.
  - mul
```
void mul(Quaternion q1,
         Quaternion q2)
```
    Sets the value of this quaternion to the quaternion product of quaternions q1 and q2 (this = q1 * q2). Note that this is safe for aliasing (e.g. this can be q1 or q2).
    
    Parameters:
    
    q1 - the first quaternion
    
    q2 - the second quaternion
  - mul
```
void mul(Quaternion q1)
```
    Sets the value of this quaternion to the quaternion product of itself and q1 (this = this * q1).
    
    Parameters:
    
    q1 - the other quaternion
  - mulInverse
```
void mulInverse(Quaternion q1,
                Quaternion q2)
```
    Multiplies quaternion q1 by the inverse of quaternion q2 and places the value into this quaternion. The value of both argument quaternions is preservered (this = q1 * q2^-1).
    
    Parameters:
    
    q1 - the first quaternion
    
    q2 - the second quaternion
  - mulInverse
```
void mulInverse(Quaternion 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).
    
    Parameters:
    
    q1 - the other quaternion
  - inverse
```
void inverse(Quaternion q1)
```
    Sets the value of this quaternion to quaternion inverse of quaternion q1.
    
    Parameters:
    
    q1 - the quaternion to be inverted
  - inverse
```
void inverse()
```
    Sets the value of this quaternion to the quaternion inverse of itself.
  - normalize
```
void normalize(Quaternion q1)
```
    Sets the value of this quaternion to the normalized value of quaternion q1.
    
    Parameters:
    
    q1 - the quaternion to be normalized.
  - normalize
```
void normalize()
```
    Normalizes the value of this quaternion in place.
  - setFromMatrix
```
void setFromMatrix(Matrix4d m1)
```
    Sets the value of this quaternion to the rotational component of the passed matrix.
    
    Parameters:
    
    m1 - the Matrix4f
  - setFromMatrix
```
void setFromMatrix(Matrix3d m1)
```
    Sets the value of this quaternion to the rotational component of the passed matrix.
    
    Parameters:
    
    m1 - the Matrix3f
  - set
```
void set(double x,
         double y,
         double z,
         double w)
```
    Set the quaternion coordinates.
    
    Parameters:
    
    x - x coordinate.
    
    y - y coordinate.
    
    z - z coordinate.
    
    w - w coordinate.
  - set
```
void set(Quaternion quat)
```
    Set the quaternion coordinates.
    
    Parameters:
    
    quat - the quaternion to copy.
  - setAxisAngle
```
void setAxisAngle(Vector3D<?,?> axis,
                  double angle)
```
    Sets the value of this quaternion to the equivalent rotation of the Axis-Angle arguments.
    
    Parameters:
    
    axis - is the axis of rotation.
    
    angle - is the rotation around the axis.
  - setAxisAngle
```
void setAxisAngle(double x1,
                  double y1,
                  double z1,
                  double angle)
```
    Sets the value of this quaternion to the equivalent rotation of the Axis-Angle arguments.
    
    Parameters:
    
    x1 - is the x coordinate of the rotation axis
    
    y1 - is the y coordinate of the rotation axis
    
    z1 - is the z coordinate of the rotation axis
    
    angle - is the rotation around the axis.
  - getAxis
```
@Pure
Vector3D<?,?> getAxis()
```
    Replies the rotation axis-angle represented by this quaternion.
    
    Returns:
    
    the rotation axis-angle.
  - getAngle
```
@Pure
double getAngle()
```
    Replies the rotation angle represented by this quaternion.
    
    Returns:
    
    the rotation axis
    
    See Also:
    
    setAxisAngle(Vector3D, double), setAxisAngle(double, double, double, double), getAxis()
  - getAxisAngle
```
@Pure
Quaternion.AxisAngle getAxisAngle()
```
    Replies the rotation axis represented by this quaternion.
    
    Returns:
    
    the rotation axis
    
    See Also:
    
    setAxisAngle(Vector3D, double), setAxisAngle(double, double, double, double), getAngle()
  - interpolate
```
void interpolate(Quaternion q1,
                 double alpha)
```
    Performs a great circle interpolation between this quaternion and the quaternion parameter and places the result into this quaternion.
    
    Parameters:
    
    q1 - the other quaternion
    
    alpha - the alpha interpolation parameter
  - interpolate
```
void interpolate(Quaternion q1,
                 Quaternion q2,
                 double alpha)
```
    Performs a great circle interpolation between quaternion q1 and quaternion q2 and places the result into this quaternion.
    
    Parameters:
    
    q1 - the first quaternion
    
    q2 - the second quaternion
    
    alpha - the alpha interpolation parameter
  - setEulerAngles
```
void setEulerAngles(Quaternion.EulerAngles angles)
```
    Set the quaternion with the Euler angles.
    
    Parameters:
    
    angles - the Euler angles.
    
    See Also:
    
    Euler Angles, Euler to Quaternion
  - setEulerAngles
```
void setEulerAngles(double attitude,
                    double bank,
                    double heading)
```
    Set the quaternion with the Euler angles. The default coordinate system is used from applying the Euler angles.
    
    Parameters:
    
    attitude - is the rotation around left vector.
    
    bank - is the rotation around front vector.
    
    heading - is the rotation around top vector.
    
    See Also:
    
    CoordinateSystem3D.getDefaultCoordinateSystem(), Euler Angles, Euler to Quaternion
  - setEulerAngles
```
void setEulerAngles(double attitude,
                    double bank,
                    double heading,
                    CoordinateSystem3D system)
```
    Set the quaternion with the Euler angles.
    
    Parameters:
    
    attitude - is the rotation around left vector.
    
    bank - is the rotation around front vector.
    
    heading - is the rotation around top vector.
    
    system - the coordinate system to use for applying the Euler angles.
    
    See Also:
    
    Euler Angles, Euler to Quaternion
  - getEulerAngles
```
@Pure
Quaternion.EulerAngles getEulerAngles()
```
    Replies the Euler's angles that corresponds to the quaternion. The default coordinate system is used from applying the Euler angles.
    
    Returns:
    
    the heading, attitude and bank angles.
    
    See Also:
    
    CoordinateSystem3D.getDefaultCoordinateSystem(), Euler Angles, Quaternion to Euler
  - getEulerAngles
```
@Pure
Quaternion.EulerAngles getEulerAngles(CoordinateSystem3D system)
```
    Replies the Euler's angles that corresponds to the quaternion.
    
    Parameters:
    
    system - is the coordinate system used to define the up, left and front vectors.
    
    Returns:
    
    the heading, attitude and bank angles.
    
    See Also:
    
    Euler Angles, Quaternion to Euler

Interface Quaternion

Other Rotation Representations

Axis Angles

Euler Angles

Nested Class Summary

Method Summary

Method Detail

getX

setX

getY

setY

getZ

setZ

getW

setW

epsilonEquals

conjugate

conjugate

mul

mul

mulInverse

mulInverse

inverse

inverse

normalize

normalize

setFromMatrix

setFromMatrix

set

set

setAxisAngle

setAxisAngle

getAxis

getAngle

getAxisAngle

interpolate

interpolate

setEulerAngles

setEulerAngles

setEulerAngles

getEulerAngles

getEulerAngles