Package org.joml

## Interface Quaternionfc

• All Known Implementing Classes:
`Quaternionf`

`public interface Quaternionfc`
Interface to a read-only view of a quaternion of single-precision floats.
Author:
Kai Burjack
• ### Method Summary

All Methods
Modifier and Type Method Description
`Quaternionf` ```add​(float x, float y, float z, float w, Quaternionf dest)```
Add the quaternion `(x, y, z, w)` to this quaternion and store the result in `dest`.
`Quaternionf` ```add​(Quaternionfc q2, Quaternionf dest)```
Add `q2` to this quaternion and store the result in `dest`.
`float` `angle()`
Return the angle in radians represented by this quaternion rotation.
`Quaternionf` `conjugate​(Quaternionf dest)`
Conjugate this quaternion and store the result in `dest`.
`Quaternionf` ```difference​(Quaternionf other, Quaternionf dest)```
Compute the difference between `this` and the `other` quaternion and store the result in `dest`.
`Quaternionf` ```div​(Quaternionfc b, Quaternionf dest)```
Divide `this` quaternion by `b` and store the result in `dest`.
`AxisAngle4f` `get​(AxisAngle4f dest)`
Set the given `AxisAngle4f` to represent the rotation of `this` quaternion.
`Matrix3d` `get​(Matrix3d dest)`
Set the given destination matrix to the rotation represented by `this`.
`Matrix3f` `get​(Matrix3f dest)`
Set the given destination matrix to the rotation represented by `this`.
`Matrix4d` `get​(Matrix4d dest)`
Set the given destination matrix to the rotation represented by `this`.
`Matrix4f` `get​(Matrix4f dest)`
Set the given destination matrix to the rotation represented by `this`.
`Matrix4x3d` `get​(Matrix4x3d dest)`
Set the given destination matrix to the rotation represented by `this`.
`Matrix4x3f` `get​(Matrix4x3f dest)`
Set the given destination matrix to the rotation represented by `this`.
`Quaterniond` `get​(Quaterniond dest)`
Set the given `Quaterniond` to the values of `this`.
`Quaternionf` `get​(Quaternionf dest)`
Set the given `Quaternionf` to the values of `this`.
`java.nio.ByteBuffer` `getAsMatrix3f​(java.nio.ByteBuffer dest)`
Store the 3x3 float matrix representation of `this` quaternion in column-major order into the given `ByteBuffer`.
`java.nio.FloatBuffer` `getAsMatrix3f​(java.nio.FloatBuffer dest)`
Store the 3x3 float matrix representation of `this` quaternion in column-major order into the given `FloatBuffer`.
`java.nio.ByteBuffer` `getAsMatrix4f​(java.nio.ByteBuffer dest)`
Store the 4x4 float matrix representation of `this` quaternion in column-major order into the given `ByteBuffer`.
`java.nio.FloatBuffer` `getAsMatrix4f​(java.nio.FloatBuffer dest)`
Store the 4x4 float matrix representation of `this` quaternion in column-major order into the given `FloatBuffer`.
`java.nio.ByteBuffer` `getAsMatrix4x3f​(java.nio.ByteBuffer dest)`
Store the 4x3 float matrix representation of `this` quaternion in column-major order into the given `ByteBuffer`.
`java.nio.FloatBuffer` `getAsMatrix4x3f​(java.nio.FloatBuffer dest)`
Store the 4x3 float matrix representation of `this` quaternion in column-major order into the given `FloatBuffer`.
`Vector3f` `getEulerAnglesXYZ​(Vector3f eulerAngles)`
Get the euler angles in radians in rotation sequence `XYZ` of this quaternion and store them in the provided parameter `eulerAngles`.
`Quaternionf` ```integrate​(float dt, float vx, float vy, float vz, Quaternionf dest)```
Integrate the rotation given by the angular velocity `(vx, vy, vz)` around the x, y and z axis, respectively, with respect to the given elapsed time delta `dt` and add the differentiate rotation to the rotation represented by this quaternion and store the result into `dest`.
`Quaternionf` `invert​(Quaternionf dest)`
Invert this quaternion and store the `normalized` result in `dest`.
`float` `lengthSquared()`
Return the square of the length of this quaternion.
`Quaternionf` ```lookAlong​(float dirX, float dirY, float dirZ, float upX, float upY, float upZ, Quaternionf dest)```
Apply a rotation to this quaternion that maps the given direction to the positive Z axis, and store the result in `dest`.
`Quaternionf` ```lookAlong​(Vector3fc dir, Vector3fc up, Quaternionf dest)```
Apply a rotation to this quaternion that maps the given direction to the positive Z axis, and store the result in `dest`.
`Quaternionf` ```mul​(float qx, float qy, float qz, float qw, Quaternionf dest)```
Multiply this quaternion by the quaternion represented via `(qx, qy, qz, qw)` and store the result in `dest`.
`Quaternionf` ```mul​(Quaternionfc q, Quaternionf dest)```
Multiply this quaternion by `q` and store the result in `dest`.
`Quaternionf` ```nlerp​(Quaternionfc q, float factor, Quaternionf dest)```
Compute a linear (non-spherical) interpolation of `this` and the given quaternion `q` and store the result in `dest`.
`Quaternionf` ```nlerpIterative​(Quaternionfc q, float alpha, float dotThreshold, Quaternionf dest)```
Compute linear (non-spherical) interpolations of `this` and the given quaternion `q` iteratively and store the result in `dest`.
`Quaternionf` `normalize​(Quaternionf dest)`
Normalize this quaternion and store the result in `dest`.
`Vector3f` `normalizedPositiveX​(Vector3f dir)`
Obtain the direction of `+X` before the rotation transformation represented by `this` normalized quaternion is applied.
`Vector3f` `normalizedPositiveY​(Vector3f dir)`
Obtain the direction of `+Y` before the rotation transformation represented by `this` normalized quaternion is applied.
`Vector3f` `normalizedPositiveZ​(Vector3f dir)`
Obtain the direction of `+Z` before the rotation transformation represented by `this` normalized quaternion is applied.
`Vector3f` `positiveX​(Vector3f dir)`
Obtain the direction of `+X` before the rotation transformation represented by `this` quaternion is applied.
`Vector3f` `positiveY​(Vector3f dir)`
Obtain the direction of `+Y` before the rotation transformation represented by `this` quaternion is applied.
`Vector3f` `positiveZ​(Vector3f dir)`
Obtain the direction of `+Z` before the rotation transformation represented by `this` quaternion is applied.
`Quaternionf` ```premul​(float qx, float qy, float qz, float qw, Quaternionf dest)```
Pre-multiply this quaternion by the quaternion represented via `(qx, qy, qz, qw)` and store the result in `dest`.
`Quaternionf` ```premul​(Quaternionfc q, Quaternionf dest)```
Pre-multiply this quaternion by `q` and store the result in `dest`.
`Quaternionf` ```rotateAxis​(float angle, float axisX, float axisY, float axisZ, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the specified axis and store the result in `dest`.
`Quaternionf` ```rotateAxis​(float angle, Vector3fc axis, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the specified axis and store the result in `dest`.
`Quaternionf` ```rotateLocalX​(float angle, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the local x axis and store the result in `dest`.
`Quaternionf` ```rotateLocalY​(float angle, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the local y axis and store the result in `dest`.
`Quaternionf` ```rotateLocalZ​(float angle, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the local z axis and store the result in `dest`.
`Quaternionf` ```rotateTo​(float fromDirX, float fromDirY, float fromDirZ, float toDirX, float toDirY, float toDirZ, Quaternionf dest)```
Apply a rotation to `this` that rotates the `fromDir` vector to point along `toDir` and store the result in `dest`.
`Quaternionf` ```rotateTo​(Vector3fc fromDir, Vector3fc toDir, Quaternionf dest)```
Apply a rotation to `this` that rotates the `fromDir` vector to point along `toDir` and store the result in `dest`.
`Quaternionf` ```rotateX​(float angle, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the x axis and store the result in `dest`.
`Quaternionf` ```rotateXYZ​(float angleX, float angleY, float angleZ, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the cartesian base unit axes, called the euler angles using rotation sequence `XYZ` and store the result in `dest`.
`Quaternionf` ```rotateY​(float angle, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the y axis and store the result in `dest`.
`Quaternionf` ```rotateYXZ​(float angleY, float angleX, float angleZ, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the cartesian base unit axes, called the euler angles, using the rotation sequence `YXZ` and store the result in `dest`.
`Quaternionf` ```rotateZ​(float angle, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the z axis and store the result in `dest`.
`Quaternionf` ```rotateZYX​(float angleZ, float angleY, float angleX, Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the cartesian base unit axes, called the euler angles, using the rotation sequence `ZYX` and store the result in `dest`.
`Quaternionf` ```scale​(float factor, Quaternionf dest)```
Apply scaling to this quaternion, which results in any vector transformed by the quaternion to change its length by the given `factor`, and store the result in `dest`.
`Quaternionf` ```slerp​(Quaternionfc target, float alpha, Quaternionf dest)```
Interpolate between `this` `unit` quaternion and the specified `target` `unit` quaternion using spherical linear interpolation using the specified interpolation factor `alpha`, and store the result in `dest`.
`Vector3f` ```transform​(float x, float y, float z, Vector3f dest)```
Transform the given vector `(x, y, z)` by this quaternion and store the result in `dest`.
`Vector4f` ```transform​(float x, float y, float z, Vector4f dest)```
Transform the given vector `(x, y, z)` by this quaternion and store the result in `dest`.
`Vector3f` `transform​(Vector3f vec)`
Transform the given vector by this quaternion.
`Vector3f` ```transform​(Vector3fc vec, Vector3f dest)```
Transform the given vector by this quaternion and store the result in `dest`.
`Vector4f` `transform​(Vector4f vec)`
Transform the given vector by this quaternion.
`Vector4f` ```transform​(Vector4fc vec, Vector4f dest)```
Transform the given vector by this quaternion and store the result in `dest`.
`Vector3f` `transformPositiveX​(Vector3f dest)`
Transform the vector `(1, 0, 0)` by this quaternion.
`Vector4f` `transformPositiveX​(Vector4f dest)`
Transform the vector `(1, 0, 0)` by this quaternion.
`Vector3f` `transformPositiveY​(Vector3f dest)`
Transform the vector `(0, 1, 0)` by this quaternion.
`Vector4f` `transformPositiveY​(Vector4f dest)`
Transform the vector `(0, 1, 0)` by this quaternion.
`Vector3f` `transformPositiveZ​(Vector3f dest)`
Transform the vector `(0, 0, 1)` by this quaternion.
`Vector4f` `transformPositiveZ​(Vector4f dest)`
Transform the vector `(0, 0, 1)` by this quaternion.
`Vector3f` `transformUnitPositiveX​(Vector3f dest)`
Transform the vector `(1, 0, 0)` by this unit quaternion.
`Vector4f` `transformUnitPositiveX​(Vector4f dest)`
Transform the vector `(1, 0, 0)` by this unit quaternion.
`Vector3f` `transformUnitPositiveY​(Vector3f dest)`
Transform the vector `(0, 1, 0)` by this unit quaternion.
`Vector4f` `transformUnitPositiveY​(Vector4f dest)`
Transform the vector `(0, 1, 0)` by this unit quaternion.
`Vector3f` `transformUnitPositiveZ​(Vector3f dest)`
Transform the vector `(0, 0, 1)` by this unit quaternion.
`Vector4f` `transformUnitPositiveZ​(Vector4f dest)`
Transform the vector `(0, 0, 1)` by this unit quaternion.
`float` `w()`
`float` `x()`
`float` `y()`
`float` `z()`
• ### Method Detail

• #### x

`float x()`
Returns:
the first component of the vector part
• #### y

`float y()`
Returns:
the second component of the vector part
• #### z

`float z()`
Returns:
the third component of the vector part
• #### w

`float w()`
Returns:
the real/scalar part of the quaternion
• #### normalize

`Quaternionf normalize​(Quaternionf dest)`
Normalize this quaternion and store the result in `dest`.
Parameters:
`dest` - will hold the result
Returns:
dest

```Quaternionf add​(float x,
float y,
float z,
float w,
Quaternionf dest)```
Add the quaternion `(x, y, z, w)` to this quaternion and store the result in `dest`.
Parameters:
`x` - the x component of the vector part
`y` - the y component of the vector part
`z` - the z component of the vector part
`w` - the real/scalar component
`dest` - will hold the result
Returns:
dest

```Quaternionf add​(Quaternionfc q2,
Quaternionf dest)```
Add `q2` to this quaternion and store the result in `dest`.
Parameters:
`q2` - the quaternion to add to this
`dest` - will hold the result
Returns:
dest
• #### angle

`float angle()`
Return the angle in radians represented by this quaternion rotation.
Returns:
the angle in radians
• #### get

`Matrix3f get​(Matrix3f dest)`
Set the given destination matrix to the rotation represented by `this`.
Parameters:
`dest` - the matrix to write the rotation into
Returns:
the passed in destination
`Matrix3f.set(Quaternionfc)`
• #### get

`Matrix3d get​(Matrix3d dest)`
Set the given destination matrix to the rotation represented by `this`.
Parameters:
`dest` - the matrix to write the rotation into
Returns:
the passed in destination
`Matrix3d.set(Quaternionfc)`
• #### get

`Matrix4f get​(Matrix4f dest)`
Set the given destination matrix to the rotation represented by `this`.
Parameters:
`dest` - the matrix to write the rotation into
Returns:
the passed in destination
`Matrix4f.set(Quaternionfc)`
• #### get

`Matrix4d get​(Matrix4d dest)`
Set the given destination matrix to the rotation represented by `this`.
Parameters:
`dest` - the matrix to write the rotation into
Returns:
the passed in destination
`Matrix4d.set(Quaternionfc)`
• #### get

`Matrix4x3f get​(Matrix4x3f dest)`
Set the given destination matrix to the rotation represented by `this`.
Parameters:
`dest` - the matrix to write the rotation into
Returns:
the passed in destination
`Matrix4x3f.set(Quaternionfc)`
• #### get

`Matrix4x3d get​(Matrix4x3d dest)`
Set the given destination matrix to the rotation represented by `this`.
Parameters:
`dest` - the matrix to write the rotation into
Returns:
the passed in destination
`Matrix4x3d.set(Quaternionfc)`
• #### get

`AxisAngle4f get​(AxisAngle4f dest)`
Set the given `AxisAngle4f` to represent the rotation of `this` quaternion.
Parameters:
`dest` - the `AxisAngle4f` to set
Returns:
the passed in destination
• #### get

`Quaternionf get​(Quaternionf dest)`
Set the given `Quaternionf` to the values of `this`.
Parameters:
`dest` - the `Quaternionf` to set
Returns:
the passed in destination
• #### getAsMatrix3f

`java.nio.ByteBuffer getAsMatrix3f​(java.nio.ByteBuffer dest)`
Store the 3x3 float matrix representation of `this` quaternion in column-major order into the given `ByteBuffer`.

This is equivalent to calling: `this.get(new Matrix3f()).get(dest)`

Parameters:
`dest` - the destination buffer
Returns:
dest
• #### getAsMatrix3f

`java.nio.FloatBuffer getAsMatrix3f​(java.nio.FloatBuffer dest)`
Store the 3x3 float matrix representation of `this` quaternion in column-major order into the given `FloatBuffer`.

This is equivalent to calling: `this.get(new Matrix3f()).get(dest)`

Parameters:
`dest` - the destination buffer
Returns:
dest
• #### getAsMatrix4f

`java.nio.ByteBuffer getAsMatrix4f​(java.nio.ByteBuffer dest)`
Store the 4x4 float matrix representation of `this` quaternion in column-major order into the given `ByteBuffer`.

This is equivalent to calling: `this.get(new Matrix4f()).get(dest)`

Parameters:
`dest` - the destination buffer
Returns:
dest
• #### getAsMatrix4f

`java.nio.FloatBuffer getAsMatrix4f​(java.nio.FloatBuffer dest)`
Store the 4x4 float matrix representation of `this` quaternion in column-major order into the given `FloatBuffer`.

This is equivalent to calling: `this.get(new Matrix4f()).get(dest)`

Parameters:
`dest` - the destination buffer
Returns:
dest
• #### getAsMatrix4x3f

`java.nio.ByteBuffer getAsMatrix4x3f​(java.nio.ByteBuffer dest)`
Store the 4x3 float matrix representation of `this` quaternion in column-major order into the given `ByteBuffer`.

This is equivalent to calling: `this.get(new Matrix4x3f()).get(dest)`

Parameters:
`dest` - the destination buffer
Returns:
dest
• #### getAsMatrix4x3f

`java.nio.FloatBuffer getAsMatrix4x3f​(java.nio.FloatBuffer dest)`
Store the 4x3 float matrix representation of `this` quaternion in column-major order into the given `FloatBuffer`.

This is equivalent to calling: `this.get(new Matrix4x3f()).get(dest)`

Parameters:
`dest` - the destination buffer
Returns:
dest
• #### mul

```Quaternionf mul​(Quaternionfc q,
Quaternionf dest)```
Multiply this quaternion by `q` and store the result in `dest`.

If `T` is `this` and `Q` is the given quaternion, then the resulting quaternion `R` is:

`R = T * Q`

So, this method uses post-multiplication like the matrix classes, resulting in a vector to be transformed by `Q` first, and then by `T`.

Parameters:
`q` - the quaternion to multiply `this` by
`dest` - will hold the result
Returns:
dest
• #### mul

```Quaternionf mul​(float qx,
float qy,
float qz,
float qw,
Quaternionf dest)```
Multiply this quaternion by the quaternion represented via `(qx, qy, qz, qw)` and store the result in `dest`.

If `T` is `this` and `Q` is the given quaternion, then the resulting quaternion `R` is:

`R = T * Q`

So, this method uses post-multiplication like the matrix classes, resulting in a vector to be transformed by `Q` first, and then by `T`.

Parameters:
`qx` - the x component of the quaternion to multiply `this` by
`qy` - the y component of the quaternion to multiply `this` by
`qz` - the z component of the quaternion to multiply `this` by
`qw` - the w component of the quaternion to multiply `this` by
`dest` - will hold the result
Returns:
dest
• #### premul

```Quaternionf premul​(Quaternionfc q,
Quaternionf dest)```
Pre-multiply this quaternion by `q` and store the result in `dest`.

If `T` is `this` and `Q` is the given quaternion, then the resulting quaternion `R` is:

`R = Q * T`

So, this method uses pre-multiplication, resulting in a vector to be transformed by `T` first, and then by `Q`.

Parameters:
`q` - the quaternion to pre-multiply `this` by
`dest` - will hold the result
Returns:
dest
• #### premul

```Quaternionf premul​(float qx,
float qy,
float qz,
float qw,
Quaternionf dest)```
Pre-multiply this quaternion by the quaternion represented via `(qx, qy, qz, qw)` and store the result in `dest`.

If `T` is `this` and `Q` is the given quaternion, then the resulting quaternion `R` is:

`R = Q * T`

So, this method uses pre-multiplication, resulting in a vector to be transformed by `T` first, and then by `Q`.

Parameters:
`qx` - the x component of the quaternion to multiply `this` by
`qy` - the y component of the quaternion to multiply `this` by
`qz` - the z component of the quaternion to multiply `this` by
`qw` - the w component of the quaternion to multiply `this` by
`dest` - will hold the result
Returns:
dest
• #### transform

`Vector3f transform​(Vector3f vec)`
Transform the given vector by this quaternion. This will apply the rotation described by this quaternion to the given vector.
Parameters:
`vec` - the vector to transform
Returns:
vec
• #### transformPositiveX

`Vector3f transformPositiveX​(Vector3f dest)`
Transform the vector `(1, 0, 0)` by this quaternion.
Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformPositiveX

`Vector4f transformPositiveX​(Vector4f dest)`
Transform the vector `(1, 0, 0)` by this quaternion.

Only the first three components of the given 4D vector are modified.

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformUnitPositiveX

`Vector3f transformUnitPositiveX​(Vector3f dest)`
Transform the vector `(1, 0, 0)` by this unit quaternion.

This method is only applicable when `this` is a unit quaternion.

Reference: https://de.mathworks.com/

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformUnitPositiveX

`Vector4f transformUnitPositiveX​(Vector4f dest)`
Transform the vector `(1, 0, 0)` by this unit quaternion.

Only the first three components of the given 4D vector are modified.

This method is only applicable when `this` is a unit quaternion.

Reference: https://de.mathworks.com/

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformPositiveY

`Vector3f transformPositiveY​(Vector3f dest)`
Transform the vector `(0, 1, 0)` by this quaternion.
Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformPositiveY

`Vector4f transformPositiveY​(Vector4f dest)`
Transform the vector `(0, 1, 0)` by this quaternion.

Only the first three components of the given 4D vector are modified.

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformUnitPositiveY

`Vector3f transformUnitPositiveY​(Vector3f dest)`
Transform the vector `(0, 1, 0)` by this unit quaternion.

This method is only applicable when `this` is a unit quaternion.

Reference: https://de.mathworks.com/

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformUnitPositiveY

`Vector4f transformUnitPositiveY​(Vector4f dest)`
Transform the vector `(0, 1, 0)` by this unit quaternion.

Only the first three components of the given 4D vector are modified.

This method is only applicable when `this` is a unit quaternion.

Reference: https://de.mathworks.com/

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformPositiveZ

`Vector3f transformPositiveZ​(Vector3f dest)`
Transform the vector `(0, 0, 1)` by this quaternion.
Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformPositiveZ

`Vector4f transformPositiveZ​(Vector4f dest)`
Transform the vector `(0, 0, 1)` by this quaternion.

Only the first three components of the given 4D vector are modified.

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformUnitPositiveZ

`Vector3f transformUnitPositiveZ​(Vector3f dest)`
Transform the vector `(0, 0, 1)` by this unit quaternion.

This method is only applicable when `this` is a unit quaternion.

Reference: https://de.mathworks.com/

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transformUnitPositiveZ

`Vector4f transformUnitPositiveZ​(Vector4f dest)`
Transform the vector `(0, 0, 1)` by this unit quaternion.

Only the first three components of the given 4D vector are modified.

This method is only applicable when `this` is a unit quaternion.

Reference: https://de.mathworks.com/

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transform

`Vector4f transform​(Vector4f vec)`
Transform the given vector by this quaternion. This will apply the rotation described by this quaternion to the given vector.

Only the first three components of the given 4D vector are being used and modified.

Parameters:
`vec` - the vector to transform
Returns:
vec
• #### transform

```Vector3f transform​(Vector3fc vec,
Vector3f dest)```
Transform the given vector by this quaternion and store the result in `dest`. This will apply the rotation described by this quaternion to the given vector.
Parameters:
`vec` - the vector to transform
`dest` - will hold the result
Returns:
dest
• #### transform

```Vector3f transform​(float x,
float y,
float z,
Vector3f dest)```
Transform the given vector `(x, y, z)` by this quaternion and store the result in `dest`. This will apply the rotation described by this quaternion to the given vector.
Parameters:
`x` - the x coordinate of the vector to transform
`y` - the y coordinate of the vector to transform
`z` - the z coordinate of the vector to transform
`dest` - will hold the result
Returns:
dest
• #### transform

```Vector4f transform​(Vector4fc vec,
Vector4f dest)```
Transform the given vector by this quaternion and store the result in `dest`. This will apply the rotation described by this quaternion to the given vector.

Only the first three components of the given 4D vector are being used and set on the destination.

Parameters:
`vec` - the vector to transform
`dest` - will hold the result
Returns:
dest
• #### transform

```Vector4f transform​(float x,
float y,
float z,
Vector4f dest)```
Transform the given vector `(x, y, z)` by this quaternion and store the result in `dest`. This will apply the rotation described by this quaternion to the given vector.
Parameters:
`x` - the x coordinate of the vector to transform
`y` - the y coordinate of the vector to transform
`z` - the z coordinate of the vector to transform
`dest` - will hold the result
Returns:
dest
• #### div

```Quaternionf div​(Quaternionfc b,
Quaternionf dest)```
Divide `this` quaternion by `b` and store the result in `dest`.

The division expressed using the inverse is performed in the following way:

`dest = this * b^-1`, where `b^-1` is the inverse of `b`.

Parameters:
`b` - the `Quaternionfc` to divide this by
`dest` - will hold the result
Returns:
dest
• #### conjugate

`Quaternionf conjugate​(Quaternionf dest)`
Conjugate this quaternion and store the result in `dest`.
Parameters:
`dest` - will hold the result
Returns:
dest
• #### rotateXYZ

```Quaternionf rotateXYZ​(float angleX,
float angleY,
float angleZ,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the cartesian base unit axes, called the euler angles using rotation sequence `XYZ` and store the result in `dest`.

This method is equivalent to calling: `rotateX(angleX, dest).rotateY(angleY).rotateZ(angleZ)`

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`angleX` - the angle in radians to rotate about the x axis
`angleY` - the angle in radians to rotate about the y axis
`angleZ` - the angle in radians to rotate about the z axis
`dest` - will hold the result
Returns:
dest
• #### rotateZYX

```Quaternionf rotateZYX​(float angleZ,
float angleY,
float angleX,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the cartesian base unit axes, called the euler angles, using the rotation sequence `ZYX` and store the result in `dest`.

This method is equivalent to calling: `rotateZ(angleZ, dest).rotateY(angleY).rotateX(angleX)`

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`angleZ` - the angle in radians to rotate about the z axis
`angleY` - the angle in radians to rotate about the y axis
`angleX` - the angle in radians to rotate about the x axis
`dest` - will hold the result
Returns:
dest
• #### rotateYXZ

```Quaternionf rotateYXZ​(float angleY,
float angleX,
float angleZ,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the cartesian base unit axes, called the euler angles, using the rotation sequence `YXZ` and store the result in `dest`.

This method is equivalent to calling: `rotateY(angleY, dest).rotateX(angleX).rotateZ(angleZ)`

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`angleY` - the angle in radians to rotate about the y axis
`angleX` - the angle in radians to rotate about the x axis
`angleZ` - the angle in radians to rotate about the z axis
`dest` - will hold the result
Returns:
dest
• #### getEulerAnglesXYZ

`Vector3f getEulerAnglesXYZ​(Vector3f eulerAngles)`
Get the euler angles in radians in rotation sequence `XYZ` of this quaternion and store them in the provided parameter `eulerAngles`.
Parameters:
`eulerAngles` - will hold the euler angles in radians
Returns:
the passed in vector
• #### lengthSquared

`float lengthSquared()`
Return the square of the length of this quaternion.
Returns:
the length
• #### slerp

```Quaternionf slerp​(Quaternionfc target,
float alpha,
Quaternionf dest)```
Interpolate between `this` `unit` quaternion and the specified `target` `unit` quaternion using spherical linear interpolation using the specified interpolation factor `alpha`, and store the result in `dest`.

This method resorts to non-spherical linear interpolation when the absolute dot product of `this` and `target` is below `1E-6f`.

Reference: http://fabiensanglard.net

Parameters:
`target` - the target of the interpolation, which should be reached with `alpha = 1.0`
`alpha` - the interpolation factor, within `[0..1]`
`dest` - will hold the result
Returns:
dest
• #### scale

```Quaternionf scale​(float factor,
Quaternionf dest)```
Apply scaling to this quaternion, which results in any vector transformed by the quaternion to change its length by the given `factor`, and store the result in `dest`.
Parameters:
`factor` - the scaling factor
`dest` - will hold the result
Returns:
dest
• #### integrate

```Quaternionf integrate​(float dt,
float vx,
float vy,
float vz,
Quaternionf dest)```
Integrate the rotation given by the angular velocity `(vx, vy, vz)` around the x, y and z axis, respectively, with respect to the given elapsed time delta `dt` and add the differentiate rotation to the rotation represented by this quaternion and store the result into `dest`.

This method pre-multiplies the rotation given by `dt` and `(vx, vy, vz)` by `this`, so the angular velocities are always relative to the local coordinate system of the rotation represented by `this` quaternion.

This method is equivalent to calling: `rotateLocal(dt * vx, dt * vy, dt * vz, dest)`

Reference: http://physicsforgames.blogspot.de/

Parameters:
`dt` - the delta time
`vx` - the angular velocity around the x axis
`vy` - the angular velocity around the y axis
`vz` - the angular velocity around the z axis
`dest` - will hold the result
Returns:
dest
• #### nlerp

```Quaternionf nlerp​(Quaternionfc q,
float factor,
Quaternionf dest)```
Compute a linear (non-spherical) interpolation of `this` and the given quaternion `q` and store the result in `dest`.

Reference: http://fabiensanglard.net

Parameters:
`q` - the other quaternion
`factor` - the interpolation factor. It is between 0.0 and 1.0
`dest` - will hold the result
Returns:
dest
• #### nlerpIterative

```Quaternionf nlerpIterative​(Quaternionfc q,
float alpha,
float dotThreshold,
Quaternionf dest)```
Compute linear (non-spherical) interpolations of `this` and the given quaternion `q` iteratively and store the result in `dest`.

This method performs a series of small-step nlerp interpolations to avoid doing a costly spherical linear interpolation, like `slerp`, by subdividing the rotation arc between `this` and `q` via non-spherical linear interpolations as long as the absolute dot product of `this` and `q` is greater than the given `dotThreshold` parameter.

Thanks to `@theagentd` at http://www.java-gaming.org/ for providing the code.

Parameters:
`q` - the other quaternion
`alpha` - the interpolation factor, between 0.0 and 1.0
`dotThreshold` - the threshold for the dot product of `this` and `q` above which this method performs another iteration of a small-step linear interpolation
`dest` - will hold the result
Returns:
dest
• #### lookAlong

```Quaternionf lookAlong​(Vector3fc dir,
Vector3fc up,
Quaternionf dest)```
Apply a rotation to this quaternion that maps the given direction to the positive Z axis, and store the result in `dest`.

Because there are multiple possibilities for such a rotation, this method will choose the one that ensures the given up direction to remain parallel to the plane spanned by the `up` and `dir` vectors.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`dir` - the direction to map to the positive Z axis
`up` - the vector which will be mapped to a vector parallel to the plane spanned by the given `dir` and `up`
`dest` - will hold the result
Returns:
dest
`lookAlong(float, float, float, float, float, float, Quaternionf)`
• #### lookAlong

```Quaternionf lookAlong​(float dirX,
float dirY,
float dirZ,
float upX,
float upY,
float upZ,
Quaternionf dest)```
Apply a rotation to this quaternion that maps the given direction to the positive Z axis, and store the result in `dest`.

Because there are multiple possibilities for such a rotation, this method will choose the one that ensures the given up direction to remain parallel to the plane spanned by the `up` and `dir` vectors.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`dirX` - the x-coordinate of the direction to look along
`dirY` - the y-coordinate of the direction to look along
`dirZ` - the z-coordinate of the direction to look along
`upX` - the x-coordinate of the up vector
`upY` - the y-coordinate of the up vector
`upZ` - the z-coordinate of the up vector
`dest` - will hold the result
Returns:
dest
• #### rotateTo

```Quaternionf rotateTo​(float fromDirX,
float fromDirY,
float fromDirZ,
float toDirX,
float toDirY,
float toDirZ,
Quaternionf dest)```
Apply a rotation to `this` that rotates the `fromDir` vector to point along `toDir` and store the result in `dest`.

Since there can be multiple possible rotations, this method chooses the one with the shortest arc.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Reference: stackoverflow.com

Parameters:
`fromDirX` - the x-coordinate of the direction to rotate into the destination direction
`fromDirY` - the y-coordinate of the direction to rotate into the destination direction
`fromDirZ` - the z-coordinate of the direction to rotate into the destination direction
`toDirX` - the x-coordinate of the direction to rotate to
`toDirY` - the y-coordinate of the direction to rotate to
`toDirZ` - the z-coordinate of the direction to rotate to
`dest` - will hold the result
Returns:
dest
• #### rotateTo

```Quaternionf rotateTo​(Vector3fc fromDir,
Vector3fc toDir,
Quaternionf dest)```
Apply a rotation to `this` that rotates the `fromDir` vector to point along `toDir` and store the result in `dest`.

Because there can be multiple possible rotations, this method chooses the one with the shortest arc.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`fromDir` - the starting direction
`toDir` - the destination direction
`dest` - will hold the result
Returns:
dest
`rotateTo(float, float, float, float, float, float, Quaternionf)`
• #### rotateX

```Quaternionf rotateX​(float angle,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the x axis and store the result in `dest`.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`angle` - the angle in radians to rotate about the x axis
`dest` - will hold the result
Returns:
dest
• #### rotateY

```Quaternionf rotateY​(float angle,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the y axis and store the result in `dest`.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`angle` - the angle in radians to rotate about the y axis
`dest` - will hold the result
Returns:
dest
• #### rotateZ

```Quaternionf rotateZ​(float angle,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the z axis and store the result in `dest`.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`angle` - the angle in radians to rotate about the z axis
`dest` - will hold the result
Returns:
dest
• #### rotateLocalX

```Quaternionf rotateLocalX​(float angle,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the local x axis and store the result in `dest`.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `R * Q`. So when transforming a vector `v` with the new quaternion by using `R * Q * v`, the rotation represented by `this` will be applied first!

Parameters:
`angle` - the angle in radians to rotate about the local x axis
`dest` - will hold the result
Returns:
dest
• #### rotateLocalY

```Quaternionf rotateLocalY​(float angle,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the local y axis and store the result in `dest`.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `R * Q`. So when transforming a vector `v` with the new quaternion by using `R * Q * v`, the rotation represented by `this` will be applied first!

Parameters:
`angle` - the angle in radians to rotate about the local y axis
`dest` - will hold the result
Returns:
dest
• #### rotateLocalZ

```Quaternionf rotateLocalZ​(float angle,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the local z axis and store the result in `dest`.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `R * Q`. So when transforming a vector `v` with the new quaternion by using `R * Q * v`, the rotation represented by `this` will be applied first!

Parameters:
`angle` - the angle in radians to rotate about the local z axis
`dest` - will hold the result
Returns:
dest
• #### rotateAxis

```Quaternionf rotateAxis​(float angle,
float axisX,
float axisY,
float axisZ,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the specified axis and store the result in `dest`.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`angle` - the angle in radians to rotate about the specified axis
`axisX` - the x coordinate of the rotation axis
`axisY` - the y coordinate of the rotation axis
`axisZ` - the z coordinate of the rotation axis
`dest` - will hold the result
Returns:
dest
• #### rotateAxis

```Quaternionf rotateAxis​(float angle,
Vector3fc axis,
Quaternionf dest)```
Apply a rotation to `this` quaternion rotating the given radians about the specified axis and store the result in `dest`.

If `Q` is `this` quaternion and `R` the quaternion representing the specified rotation, then the new quaternion will be `Q * R`. So when transforming a vector `v` with the new quaternion by using `Q * R * v`, the rotation added by this method will be applied first!

Parameters:
`angle` - the angle in radians to rotate about the specified axis
`axis` - the rotation axis
`dest` - will hold the result
Returns:
dest
`rotateAxis(float, float, float, float, Quaternionf)`
• #### difference

```Quaternionf difference​(Quaternionf other,
Quaternionf dest)```
Compute the difference between `this` and the `other` quaternion and store the result in `dest`.

The difference is the rotation that has to be applied to get from `this` rotation to `other`. If `T` is `this`, `Q` is `other` and `D` is the computed difference, then the following equation holds:

`T * D = Q`

It is defined as: `D = T^-1 * Q`, where `T^-1` denotes the `inverse` of `T`.

Parameters:
`other` - the other quaternion
`dest` - will hold the result
Returns:
dest
• #### positiveX

`Vector3f positiveX​(Vector3f dir)`
Obtain the direction of `+X` before the rotation transformation represented by `this` quaternion is applied.

This method is equivalent to the following code:

``` Quaternionf inv = new Quaternionf(this).invert();
inv.transform(dir.set(1, 0, 0));
```
Parameters:
`dir` - will hold the direction of `+X`
Returns:
dir
• #### normalizedPositiveX

`Vector3f normalizedPositiveX​(Vector3f dir)`
Obtain the direction of `+X` before the rotation transformation represented by `this` normalized quaternion is applied. The quaternion must be `normalized` for this method to work.

This method is equivalent to the following code:

``` Quaternionf inv = new Quaternionf(this).conjugate();
inv.transform(dir.set(1, 0, 0));
```
Parameters:
`dir` - will hold the direction of `+X`
Returns:
dir
• #### positiveY

`Vector3f positiveY​(Vector3f dir)`
Obtain the direction of `+Y` before the rotation transformation represented by `this` quaternion is applied.

This method is equivalent to the following code:

``` Quaternionf inv = new Quaternionf(this).invert();
inv.transform(dir.set(0, 1, 0));
```
Parameters:
`dir` - will hold the direction of `+Y`
Returns:
dir
• #### normalizedPositiveY

`Vector3f normalizedPositiveY​(Vector3f dir)`
Obtain the direction of `+Y` before the rotation transformation represented by `this` normalized quaternion is applied. The quaternion must be `normalized` for this method to work.

This method is equivalent to the following code:

``` Quaternionf inv = new Quaternionf(this).conjugate();
inv.transform(dir.set(0, 1, 0));
```
Parameters:
`dir` - will hold the direction of `+Y`
Returns:
dir
• #### positiveZ

`Vector3f positiveZ​(Vector3f dir)`
Obtain the direction of `+Z` before the rotation transformation represented by `this` quaternion is applied.

This method is equivalent to the following code:

``` Quaternionf inv = new Quaternionf(this).invert();
inv.transform(dir.set(0, 0, 1));
```
Parameters:
`dir` - will hold the direction of `+Z`
Returns:
dir
• #### normalizedPositiveZ

`Vector3f normalizedPositiveZ​(Vector3f dir)`
Obtain the direction of `+Z` before the rotation transformation represented by `this` normalized quaternion is applied. The quaternion must be `normalized` for this method to work.

This method is equivalent to the following code:

``` Quaternionf inv = new Quaternionf(this).conjugate();
inv.transform(dir.set(0, 0, 1));
```
Parameters:
`dir` - will hold the direction of `+Z`
Returns:
dir