Package org.joml

Class Quaterniond

java.lang.Object
org.joml.Quaterniond
All Implemented Interfaces:
Externalizable, Serializable, Cloneable, Quaterniondc

public class Quaterniond extends Object implements Externalizable, Cloneable, Quaterniondc
Quaternion of 4 double-precision floats which can represent rotation and uniform scaling.
Author:
Richard Greenlees, Kai Burjack
See Also:
Serialized Form
  • Field Details

    • x

      public double x
      The first component of the vector part.
    • y

      public double y
      The second component of the vector part.
    • z

      public double z
      The third component of the vector part.
    • w

      public double w
      The real/scalar part of the quaternion.
  • Constructor Details

    • Quaterniond

      public Quaterniond()
      Create a new Quaterniond and initialize it with (x=0, y=0, z=0, w=1), where (x, y, z) is the vector part of the quaternion and w is the real/scalar part.
    • Quaterniond

      public Quaterniond(double x, double y, double z, double w)
      Create a new Quaterniond and initialize its components to the given values.
      Parameters:
      x - the first component of the imaginary part
      y - the second component of the imaginary part
      z - the third component of the imaginary part
      w - the real part
    • Quaterniond

      public Quaterniond(Quaterniondc source)
      Create a new Quaterniond and initialize its components to the same values as the given Quaterniondc.
      Parameters:
      source - the Quaterniondc to take the component values from
    • Quaterniond

      public Quaterniond(Quaternionfc source)
      Create a new Quaterniond and initialize its components to the same values as the given Quaternionfc.
      Parameters:
      source - the Quaternionfc to take the component values from
    • Quaterniond

      public Quaterniond(AxisAngle4f axisAngle)
      Create a new Quaterniond and initialize it to represent the same rotation as the given AxisAngle4f.
      Parameters:
      axisAngle - the axis-angle to initialize this quaternion with
    • Quaterniond

      public Quaterniond(AxisAngle4d axisAngle)
      Create a new Quaterniond and initialize it to represent the same rotation as the given AxisAngle4d.
      Parameters:
      axisAngle - the axis-angle to initialize this quaternion with
  • Method Details

    • x

      public double x()
      Specified by:
      x in interface Quaterniondc
      Returns:
      the first component of the vector part
    • y

      public double y()
      Specified by:
      y in interface Quaterniondc
      Returns:
      the second component of the vector part
    • z

      public double z()
      Specified by:
      z in interface Quaterniondc
      Returns:
      the third component of the vector part
    • w

      public double w()
      Specified by:
      w in interface Quaterniondc
      Returns:
      the real/scalar part of the quaternion
    • normalize

      public Quaterniond normalize()
      Normalize this quaternion.
      Returns:
      this
    • normalize

      public Quaterniond normalize(Quaterniond dest)
      Description copied from interface: Quaterniondc
      Normalize this quaternion and store the result in dest.
      Specified by:
      normalize in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • add

      public Quaterniond add(double x, double y, double z, double w)
      Add the quaternion (x, y, z, w) to this quaternion.
      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
      Returns:
      this
    • add

      public Quaterniond add(double x, double y, double z, double w, Quaterniond dest)
      Description copied from interface: Quaterniondc
      Add the quaternion (x, y, z, w) to this quaternion and store the result in dest.
      Specified by:
      add in interface Quaterniondc
      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
    • add

      public Quaterniond add(Quaterniondc q2)
      Add q2 to this quaternion.
      Parameters:
      q2 - the quaternion to add to this
      Returns:
      this
    • add

      public Quaterniond add(Quaterniondc q2, Quaterniond dest)
      Description copied from interface: Quaterniondc
      Add q2 to this quaternion and store the result in dest.
      Specified by:
      add in interface Quaterniondc
      Parameters:
      q2 - the quaternion to add to this
      dest - will hold the result
      Returns:
      dest
    • dot

      public double dot(Quaterniondc otherQuat)
      Description copied from interface: Quaterniondc
      Return the dot product of this Quaterniond and otherQuat.
      Specified by:
      dot in interface Quaterniondc
      Parameters:
      otherQuat - the other quaternion
      Returns:
      the dot product
    • angle

      public double angle()
      Description copied from interface: Quaterniondc
      Return the angle in radians represented by this normalized quaternion rotation.

      This quaternion must be normalized.

      Specified by:
      angle in interface Quaterniondc
      Returns:
      the angle in radians
    • get

      public Matrix3d get(Matrix3d dest)
      Description copied from interface: Quaterniondc
      Set the given destination matrix to the rotation represented by this.
      Specified by:
      get in interface Quaterniondc
      Parameters:
      dest - the matrix to write the rotation into
      Returns:
      the passed in destination
      See Also:
      Matrix3d.set(Quaterniondc)
    • get

      public Matrix3f get(Matrix3f dest)
      Description copied from interface: Quaterniondc
      Set the given destination matrix to the rotation represented by this.
      Specified by:
      get in interface Quaterniondc
      Parameters:
      dest - the matrix to write the rotation into
      Returns:
      the passed in destination
      See Also:
      Matrix3f.set(Quaterniondc)
    • get

      public Matrix4d get(Matrix4d dest)
      Description copied from interface: Quaterniondc
      Set the given destination matrix to the rotation represented by this.
      Specified by:
      get in interface Quaterniondc
      Parameters:
      dest - the matrix to write the rotation into
      Returns:
      the passed in destination
      See Also:
      Matrix4d.set(Quaterniondc)
    • get

      public Matrix4f get(Matrix4f dest)
      Description copied from interface: Quaterniondc
      Set the given destination matrix to the rotation represented by this.
      Specified by:
      get in interface Quaterniondc
      Parameters:
      dest - the matrix to write the rotation into
      Returns:
      the passed in destination
      See Also:
      Matrix4f.set(Quaterniondc)
    • get

      public AxisAngle4f get(AxisAngle4f dest)
      Description copied from interface: Quaterniondc
      Set the given AxisAngle4f to represent the rotation of this quaternion.
      Specified by:
      get in interface Quaterniondc
      Parameters:
      dest - the AxisAngle4f to set
      Returns:
      the passed in destination
    • get

      public AxisAngle4d get(AxisAngle4d dest)
      Description copied from interface: Quaterniondc
      Set the given AxisAngle4d to represent the rotation of this quaternion.
      Specified by:
      get in interface Quaterniondc
      Parameters:
      dest - the AxisAngle4d to set
      Returns:
      the passed in destination
    • get

      public Quaterniond get(Quaterniond dest)
      Set the given Quaterniond to the values of this.
      Specified by:
      get in interface Quaterniondc
      Parameters:
      dest - the Quaterniond to set
      Returns:
      the passed in destination
      See Also:
      set(Quaterniondc)
    • get

      public Quaternionf get(Quaternionf dest)
      Set the given Quaternionf to the values of this.
      Specified by:
      get in interface Quaterniondc
      Parameters:
      dest - the Quaternionf to set
      Returns:
      the passed in destination
      See Also:
      set(Quaterniondc)
    • set

      public Quaterniond set(double x, double y, double z, double w)
      Set this quaternion to the new values.
      Parameters:
      x - the new value of x
      y - the new value of y
      z - the new value of z
      w - the new value of w
      Returns:
      this
    • set

      public Quaterniond set(Quaterniondc q)
      Set this quaternion to be a copy of q.
      Parameters:
      q - the Quaterniondc to copy
      Returns:
      this
    • set

      public Quaterniond set(Quaternionfc q)
      Set this quaternion to be a copy of q.
      Parameters:
      q - the Quaternionfc to copy
      Returns:
      this
    • set

      public Quaterniond set(AxisAngle4f axisAngle)
      Set this Quaterniond to be equivalent to the given AxisAngle4f.
      Parameters:
      axisAngle - the AxisAngle4f
      Returns:
      this
    • set

      public Quaterniond set(AxisAngle4d axisAngle)
      Set this Quaterniond to be equivalent to the given AxisAngle4d.
      Parameters:
      axisAngle - the AxisAngle4d
      Returns:
      this
    • setAngleAxis

      public Quaterniond setAngleAxis(double angle, double x, double y, double z)
      Set this quaternion to a rotation equivalent to the supplied axis and angle (in radians).

      This method assumes that the given rotation axis (x, y, z) is already normalized

      Parameters:
      angle - the angle in radians
      x - the x-component of the normalized rotation axis
      y - the y-component of the normalized rotation axis
      z - the z-component of the normalized rotation axis
      Returns:
      this
    • setAngleAxis

      public Quaterniond setAngleAxis(double angle, Vector3dc axis)
      Set this quaternion to be a representation of the supplied axis and angle (in radians).
      Parameters:
      angle - the angle in radians
      axis - the rotation axis
      Returns:
      this
    • setFromUnnormalized

      public Quaterniond setFromUnnormalized(Matrix4fc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromUnnormalized

      public Quaterniond setFromUnnormalized(Matrix4x3fc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromUnnormalized

      public Quaterniond setFromUnnormalized(Matrix4x3dc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromNormalized

      public Quaterniond setFromNormalized(Matrix4fc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromNormalized

      public Quaterniond setFromNormalized(Matrix4x3fc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromNormalized

      public Quaterniond setFromNormalized(Matrix4x3dc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromUnnormalized

      public Quaterniond setFromUnnormalized(Matrix4dc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromNormalized

      public Quaterniond setFromNormalized(Matrix4dc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromUnnormalized

      public Quaterniond setFromUnnormalized(Matrix3fc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromNormalized

      public Quaterniond setFromNormalized(Matrix3fc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromUnnormalized

      public Quaterniond setFromUnnormalized(Matrix3dc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.

      This method assumes that the first three columns of the upper left 3x3 submatrix are no unit vectors.

      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • setFromNormalized

      public Quaterniond setFromNormalized(Matrix3dc mat)
      Set this quaternion to be a representation of the rotational component of the given matrix.
      Parameters:
      mat - the matrix whose rotational component is used to set this quaternion
      Returns:
      this
    • fromAxisAngleRad

      public Quaterniond fromAxisAngleRad(Vector3dc axis, double angle)
      Set this quaternion to be a representation of the supplied axis and angle (in radians).
      Parameters:
      axis - the rotation axis
      angle - the angle in radians
      Returns:
      this
    • fromAxisAngleRad

      public Quaterniond fromAxisAngleRad(double axisX, double axisY, double axisZ, double angle)
      Set this quaternion to be a representation of the supplied axis and angle (in radians).
      Parameters:
      axisX - the x component of the rotation axis
      axisY - the y component of the rotation axis
      axisZ - the z component of the rotation axis
      angle - the angle in radians
      Returns:
      this
    • fromAxisAngleDeg

      public Quaterniond fromAxisAngleDeg(Vector3dc axis, double angle)
      Set this quaternion to be a representation of the supplied axis and angle (in degrees).
      Parameters:
      axis - the rotation axis
      angle - the angle in degrees
      Returns:
      this
    • fromAxisAngleDeg

      public Quaterniond fromAxisAngleDeg(double axisX, double axisY, double axisZ, double angle)
      Set this quaternion to be a representation of the supplied axis and angle (in degrees).
      Parameters:
      axisX - the x component of the rotation axis
      axisY - the y component of the rotation axis
      axisZ - the z component of the rotation axis
      angle - the angle in radians
      Returns:
      this
    • mul

      public Quaterniond mul(Quaterniondc q)
      Multiply this quaternion by q.

      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
      Returns:
      this
    • mul

      public Quaterniond mul(Quaterniondc q, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      mul in interface Quaterniondc
      Parameters:
      q - the quaternion to multiply this by
      dest - will hold the result
      Returns:
      dest
    • mul

      public Quaterniond mul(double qx, double qy, double qz, double qw)
      Multiply this quaternion by the quaternion represented via (qx, qy, qz, qw).

      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
      Returns:
      this
    • mul

      public Quaterniond mul(double qx, double qy, double qz, double qw, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      mul in interface Quaterniondc
      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

      public Quaterniond premul(Quaterniondc q)
      Pre-multiply this quaternion by q.

      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
      Returns:
      this
    • premul

      public Quaterniond premul(Quaterniondc q, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      premul in interface Quaterniondc
      Parameters:
      q - the quaternion to pre-multiply this by
      dest - will hold the result
      Returns:
      dest
    • premul

      public Quaterniond premul(double qx, double qy, double qz, double qw)
      Pre-multiply this quaternion by the quaternion represented via (qx, qy, qz, qw).

      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
      Returns:
      this
    • premul

      public Quaterniond premul(double qx, double qy, double qz, double qw, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      premul in interface Quaterniondc
      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

      public Vector3d transform(Vector3d vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by this quaternion.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transform in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformInverse

      public Vector3d transformInverse(Vector3d vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this quaternion.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transformInverse in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformUnit

      public Vector3d transformUnit(Vector3d vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by this unit quaternion.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformInverseUnit

      public Vector3d transformInverseUnit(Vector3d vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this unit quaternion.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformPositiveX

      public Vector3d transformPositiveX(Vector3d dest)
      Description copied from interface: Quaterniondc
      Transform the vector (1, 0, 0) by this quaternion.
      Specified by:
      transformPositiveX in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveX

      public Vector4d transformPositiveX(Vector4d dest)
      Description copied from interface: Quaterniondc
      Transform the vector (1, 0, 0) by this quaternion.

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

      Specified by:
      transformPositiveX in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveX

      public Vector3d transformUnitPositiveX(Vector3d dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveX in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveX

      public Vector4d transformUnitPositiveX(Vector4d dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveX in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveY

      public Vector3d transformPositiveY(Vector3d dest)
      Description copied from interface: Quaterniondc
      Transform the vector (0, 1, 0) by this quaternion.
      Specified by:
      transformPositiveY in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveY

      public Vector4d transformPositiveY(Vector4d dest)
      Description copied from interface: Quaterniondc
      Transform the vector (0, 1, 0) by this quaternion.

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

      Specified by:
      transformPositiveY in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveY

      public Vector4d transformUnitPositiveY(Vector4d dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveY in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveY

      public Vector3d transformUnitPositiveY(Vector3d dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveY in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveZ

      public Vector3d transformPositiveZ(Vector3d dest)
      Description copied from interface: Quaterniondc
      Transform the vector (0, 0, 1) by this quaternion.
      Specified by:
      transformPositiveZ in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveZ

      public Vector4d transformPositiveZ(Vector4d dest)
      Description copied from interface: Quaterniondc
      Transform the vector (0, 0, 1) by this quaternion.

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

      Specified by:
      transformPositiveZ in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveZ

      public Vector4d transformUnitPositiveZ(Vector4d dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveZ in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveZ

      public Vector3d transformUnitPositiveZ(Vector3d dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveZ in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transform

      public Vector4d transform(Vector4d vec)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformInverse

      public Vector4d transformInverse(Vector4d vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of 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.

      Specified by:
      transformInverse in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transform

      public Vector3d transform(Vector3dc vec, Vector3d dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformInverse

      public Vector3d transformInverse(Vector3dc vec, Vector3d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transformInverse in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transform

      public Vector3d transform(double x, double y, double z, Vector3d dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      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
    • transformInverse

      public Vector3d transformInverse(double x, double y, double z, Vector3d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by the inverse of this quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transformInverse in interface Quaterniondc
      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

      public Vector4d transform(Vector4dc vec, Vector4d dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformInverse

      public Vector4d transformInverse(Vector4dc vec, Vector4d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of 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.

      Specified by:
      transformInverse in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transform

      public Vector4d transform(double x, double y, double z, Vector4d dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      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
    • transformInverse

      public Vector4d transformInverse(double x, double y, double z, Vector4d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by the inverse of this quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transformInverse in interface Quaterniondc
      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

      public Vector3f transform(Vector3f vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by this quaternion.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transform in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformInverse

      public Vector3f transformInverse(Vector3f vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this quaternion.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transformInverse in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformUnit

      public Vector4d transformUnit(Vector4d vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by this unit 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.

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

      Specified by:
      transformUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformInverseUnit

      public Vector4d transformInverseUnit(Vector4d vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this unit 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.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformUnit

      public Vector3d transformUnit(Vector3dc vec, Vector3d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformInverseUnit

      public Vector3d transformInverseUnit(Vector3dc vec, Vector3d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformUnit

      public Vector3d transformUnit(double x, double y, double z, Vector3d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformUnit in interface Quaterniondc
      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
    • transformInverseUnit

      public Vector3d transformInverseUnit(double x, double y, double z, Vector3d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by the inverse of this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      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
    • transformUnit

      public Vector4d transformUnit(Vector4dc vec, Vector4d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by this unit 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.

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

      Specified by:
      transformUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformInverseUnit

      public Vector4d transformInverseUnit(Vector4dc vec, Vector4d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this unit 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.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformUnit

      public Vector4d transformUnit(double x, double y, double z, Vector4d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformUnit in interface Quaterniondc
      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
    • transformInverseUnit

      public Vector4d transformInverseUnit(double x, double y, double z, Vector4d dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by the inverse of this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      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
    • transformUnit

      public Vector3f transformUnit(Vector3f vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by this unit quaternion.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformInverseUnit

      public Vector3f transformInverseUnit(Vector3f vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this unit quaternion.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformPositiveX

      public Vector3f transformPositiveX(Vector3f dest)
      Description copied from interface: Quaterniondc
      Transform the vector (1, 0, 0) by this quaternion.
      Specified by:
      transformPositiveX in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveX

      public Vector4f transformPositiveX(Vector4f dest)
      Description copied from interface: Quaterniondc
      Transform the vector (1, 0, 0) by this quaternion.

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

      Specified by:
      transformPositiveX in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveX

      public Vector3f transformUnitPositiveX(Vector3f dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveX in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveX

      public Vector4f transformUnitPositiveX(Vector4f dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveX in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveY

      public Vector3f transformPositiveY(Vector3f dest)
      Description copied from interface: Quaterniondc
      Transform the vector (0, 1, 0) by this quaternion.
      Specified by:
      transformPositiveY in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveY

      public Vector4f transformPositiveY(Vector4f dest)
      Description copied from interface: Quaterniondc
      Transform the vector (0, 1, 0) by this quaternion.

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

      Specified by:
      transformPositiveY in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveY

      public Vector4f transformUnitPositiveY(Vector4f dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveY in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveY

      public Vector3f transformUnitPositiveY(Vector3f dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveY in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveZ

      public Vector3f transformPositiveZ(Vector3f dest)
      Description copied from interface: Quaterniondc
      Transform the vector (0, 0, 1) by this quaternion.
      Specified by:
      transformPositiveZ in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformPositiveZ

      public Vector4f transformPositiveZ(Vector4f dest)
      Description copied from interface: Quaterniondc
      Transform the vector (0, 0, 1) by this quaternion.

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

      Specified by:
      transformPositiveZ in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveZ

      public Vector4f transformUnitPositiveZ(Vector4f dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveZ in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transformUnitPositiveZ

      public Vector3f transformUnitPositiveZ(Vector3f dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      transformUnitPositiveZ in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • transform

      public Vector4f transform(Vector4f vec)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformInverse

      public Vector4f transformInverse(Vector4f vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of 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.

      Specified by:
      transformInverse in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transform

      public Vector3f transform(Vector3fc vec, Vector3f dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformInverse

      public Vector3f transformInverse(Vector3fc vec, Vector3f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transformInverse in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transform

      public Vector3f transform(double x, double y, double z, Vector3f dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      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
    • transformInverse

      public Vector3f transformInverse(double x, double y, double z, Vector3f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by the inverse of this quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transformInverse in interface Quaterniondc
      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

      public Vector4f transform(Vector4fc vec, Vector4f dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformInverse

      public Vector4f transformInverse(Vector4fc vec, Vector4f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of 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.

      Specified by:
      transformInverse in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transform

      public Vector4f transform(double x, double y, double z, Vector4f dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      transform in interface Quaterniondc
      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
    • transformInverse

      public Vector4f transformInverse(double x, double y, double z, Vector4f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by the inverse of this quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

      Specified by:
      transformInverse in interface Quaterniondc
      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
    • transformUnit

      public Vector4f transformUnit(Vector4f vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by this unit 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.

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

      Specified by:
      transformUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformInverseUnit

      public Vector4f transformInverseUnit(Vector4f vec)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this unit 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.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      Returns:
      vec
    • transformUnit

      public Vector3f transformUnit(Vector3fc vec, Vector3f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformInverseUnit

      public Vector3f transformInverseUnit(Vector3fc vec, Vector3f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformUnit

      public Vector3f transformUnit(double x, double y, double z, Vector3f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformUnit in interface Quaterniondc
      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
    • transformInverseUnit

      public Vector3f transformInverseUnit(double x, double y, double z, Vector3f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by the inverse of this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      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
    • transformUnit

      public Vector4f transformUnit(Vector4fc vec, Vector4f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by this unit 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.

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

      Specified by:
      transformUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformInverseUnit

      public Vector4f transformInverseUnit(Vector4fc vec, Vector4f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector by the inverse of this unit 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.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      Parameters:
      vec - the vector to transform
      dest - will hold the result
      Returns:
      dest
    • transformUnit

      public Vector4f transformUnit(double x, double y, double z, Vector4f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformUnit in interface Quaterniondc
      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
    • transformInverseUnit

      public Vector4f transformInverseUnit(double x, double y, double z, Vector4f dest)
      Description copied from interface: Quaterniondc
      Transform the given vector (x, y, z) by the inverse of this unit quaternion and store the result in dest.

      This will apply the rotation described by this quaternion to the given vector.

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

      Specified by:
      transformInverseUnit in interface Quaterniondc
      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
    • invert

      public Quaterniond invert(Quaterniond dest)
      Description copied from interface: Quaterniondc
      Invert this quaternion and store the normalized result in dest.

      If this quaternion is already normalized, then Quaterniondc.conjugate(Quaterniond) should be used instead.

      Specified by:
      invert in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
      See Also:
      Quaterniondc.conjugate(Quaterniond)
    • invert

      public Quaterniond invert()
      Invert this quaternion and normalize it.

      If this quaternion is already normalized, then conjugate() should be used instead.

      Returns:
      this
      See Also:
      conjugate()
    • div

      public Quaterniond div(Quaterniondc b, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      div in interface Quaterniondc
      Parameters:
      b - the Quaterniondc to divide this by
      dest - will hold the result
      Returns:
      dest
    • div

      public Quaterniond div(Quaterniondc b)
      Divide this quaternion by b.

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

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

      Parameters:
      b - the Quaterniondc to divide this by
      Returns:
      this
    • conjugate

      public Quaterniond conjugate()
      Conjugate this quaternion.
      Returns:
      this
    • conjugate

      public Quaterniond conjugate(Quaterniond dest)
      Description copied from interface: Quaterniondc
      Conjugate this quaternion and store the result in dest.
      Specified by:
      conjugate in interface Quaterniondc
      Parameters:
      dest - will hold the result
      Returns:
      dest
    • identity

      public Quaterniond identity()
      Set this quaternion to the identity.
      Returns:
      this
    • lengthSquared

      public double lengthSquared()
      Description copied from interface: Quaterniondc
      Return the square of the length of this quaternion.
      Specified by:
      lengthSquared in interface Quaterniondc
      Returns:
      the length
    • rotationXYZ

      public Quaterniond rotationXYZ(double angleX, double angleY, double angleZ)
      Set this quaternion from the supplied euler angles (in radians) with rotation order XYZ.

      This method is equivalent to calling: rotationX(angleX).rotateY(angleY).rotateZ(angleZ)

      Reference: this stackexchange answer

      Parameters:
      angleX - the angle in radians to rotate about x
      angleY - the angle in radians to rotate about y
      angleZ - the angle in radians to rotate about z
      Returns:
      this
    • rotationZYX

      public Quaterniond rotationZYX(double angleZ, double angleY, double angleX)
      Set this quaternion from the supplied euler angles (in radians) with rotation order ZYX.

      This method is equivalent to calling: rotationZ(angleZ).rotateY(angleY).rotateX(angleX)

      Reference: this stackexchange answer

      Parameters:
      angleX - the angle in radians to rotate about x
      angleY - the angle in radians to rotate about y
      angleZ - the angle in radians to rotate about z
      Returns:
      this
    • rotationYXZ

      public Quaterniond rotationYXZ(double angleY, double angleX, double angleZ)
      Set this quaternion from the supplied euler angles (in radians) with rotation order YXZ.

      This method is equivalent to calling: rotationY(angleY).rotateX(angleX).rotateZ(angleZ)

      Reference: https://en.wikipedia.org

      Parameters:
      angleY - the angle in radians to rotate about y
      angleX - the angle in radians to rotate about x
      angleZ - the angle in radians to rotate about z
      Returns:
      this
    • slerp

      public Quaterniond slerp(Quaterniondc target, double alpha)
      Interpolate between this unit quaternion and the specified target unit quaternion using spherical linear interpolation using the specified interpolation factor alpha.

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

      Parameters:
      target - the target of the interpolation, which should be reached with alpha = 1.0
      alpha - the interpolation factor, within [0..1]
      Returns:
      this
    • slerp

      public Quaterniond slerp(Quaterniondc target, double alpha, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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 between this and target is below 1E-6.

      Reference: http://fabiensanglard.net

      Specified by:
      slerp in interface Quaterniondc
      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
    • slerp

      public static Quaterniondc slerp(Quaterniond[] qs, double[] weights, Quaterniond dest)
      Interpolate between all of the quaternions given in qs via spherical linear interpolation using the specified interpolation factors weights, and store the result in dest.

      This method will interpolate between each two successive quaternions via slerp(Quaterniondc, double) using their relative interpolation weights.

      This method resorts to non-spherical linear interpolation when the absolute dot product of any two interpolated quaternions is below 1E-6f.

      Reference: http://gamedev.stackexchange.com/

      Parameters:
      qs - the quaternions to interpolate over
      weights - the weights of each individual quaternion in qs
      dest - will hold the result
      Returns:
      dest
    • scale

      public Quaterniond scale(double factor)
      Apply scaling to this quaternion, which results in any vector transformed by this quaternion to change its length by the given factor.
      Parameters:
      factor - the scaling factor
      Returns:
      this
    • scale

      public Quaterniond scale(double factor, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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.
      Specified by:
      scale in interface Quaterniondc
      Parameters:
      factor - the scaling factor
      dest - will hold the result
      Returns:
      dest
    • scaling

      public Quaterniond scaling(double factor)
      Set this quaternion to represent scaling, which results in a transformed vector to change its length by the given factor.
      Parameters:
      factor - the scaling factor
      Returns:
      this
    • integrate

      public Quaterniond integrate(double dt, double vx, double vy, double vz)
      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.

      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)

      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
      Returns:
      this
    • integrate

      public Quaterniond integrate(double dt, double vx, double vy, double vz, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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/

      Specified by:
      integrate in interface Quaterniondc
      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

      public Quaterniond nlerp(Quaterniondc q, double factor)
      Compute a linear (non-spherical) interpolation of this and the given quaternion q and store the result in this.
      Parameters:
      q - the other quaternion
      factor - the interpolation factor. It is between 0.0 and 1.0
      Returns:
      this
    • nlerp

      public Quaterniond nlerp(Quaterniondc q, double factor, Quaterniond dest)
      Description copied from interface: Quaterniondc
      Compute a linear (non-spherical) interpolation of this and the given quaternion q and store the result in dest.

      Reference: http://fabiensanglard.net

      Specified by:
      nlerp in interface Quaterniondc
      Parameters:
      q - the other quaternion
      factor - the interpolation factor. It is between 0.0 and 1.0
      dest - will hold the result
      Returns:
      dest
    • nlerp

      public static Quaterniondc nlerp(Quaterniond[] qs, double[] weights, Quaterniond dest)
      Interpolate between all of the quaternions given in qs via non-spherical linear interpolation using the specified interpolation factors weights, and store the result in dest.

      This method will interpolate between each two successive quaternions via nlerp(Quaterniondc, double) using their relative interpolation weights.

      Reference: http://gamedev.stackexchange.com/

      Parameters:
      qs - the quaternions to interpolate over
      weights - the weights of each individual quaternion in qs
      dest - will hold the result
      Returns:
      dest
    • nlerpIterative

      public Quaterniond nlerpIterative(Quaterniondc q, double alpha, double dotThreshold, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      nlerpIterative in interface Quaterniondc
      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
    • nlerpIterative

      public Quaterniond nlerpIterative(Quaterniondc q, double alpha, double dotThreshold)
      Compute linear (non-spherical) interpolations of this and the given quaternion q iteratively and store the result in this.

      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
      Returns:
      this
    • nlerpIterative

      public static Quaterniond nlerpIterative(Quaterniondc[] qs, double[] weights, double dotThreshold, Quaterniond dest)
      Interpolate between all of the quaternions given in qs via iterative non-spherical linear interpolation using the specified interpolation factors weights, and store the result in dest.

      This method will interpolate between each two successive quaternions via nlerpIterative(Quaterniondc, double, double) using their relative interpolation weights.

      Reference: http://gamedev.stackexchange.com/

      Parameters:
      qs - the quaternions to interpolate over
      weights - the weights of each individual quaternion in qs
      dotThreshold - the threshold for the dot product of each two interpolated quaternions above which nlerpIterative(Quaterniondc, double, double) performs another iteration of a small-step linear interpolation
      dest - will hold the result
      Returns:
      dest
    • lookAlong

      public Quaterniond lookAlong(Vector3dc dir, Vector3dc up)
      Apply a rotation to this quaternion that maps the given direction to the positive Z axis.

      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!

      Reference: http://answers.unity3d.com

      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
      Returns:
      this
      See Also:
      lookAlong(double, double, double, double, double, double, Quaterniond)
    • lookAlong

      public Quaterniond lookAlong(Vector3dc dir, Vector3dc up, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Reference: http://answers.unity3d.com

      Specified by:
      lookAlong in interface Quaterniondc
      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
      See Also:
      Quaterniondc.lookAlong(double, double, double, double, double, double, Quaterniond)
    • lookAlong

      public Quaterniond lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ)
      Apply a rotation to this quaternion that maps the given direction to the positive Z axis.

      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!

      Reference: http://answers.unity3d.com

      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
      Returns:
      this
      See Also:
      lookAlong(double, double, double, double, double, double, Quaterniond)
    • lookAlong

      public Quaterniond lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Reference: http://answers.unity3d.com

      Specified by:
      lookAlong in interface Quaterniondc
      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
    • toString

      public String toString()
      Return a string representation of this quaternion.

      This method creates a new DecimalFormat on every invocation with the format string "0.000E0;-".

      Overrides:
      toString in class Object
      Returns:
      the string representation
    • toString

      public String toString(NumberFormat formatter)
      Return a string representation of this quaternion by formatting the components with the given NumberFormat.
      Parameters:
      formatter - the NumberFormat used to format the quaternion components with
      Returns:
      the string representation
    • writeExternal

      public void writeExternal(ObjectOutput out) throws IOException
      Specified by:
      writeExternal in interface Externalizable
      Throws:
      IOException
    • readExternal

      public void readExternal(ObjectInput in) throws IOException, ClassNotFoundException
      Specified by:
      readExternal in interface Externalizable
      Throws:
      IOException
      ClassNotFoundException
    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object
    • equals

      public boolean equals(Object obj)
      Overrides:
      equals in class Object
    • difference

      public Quaterniond difference(Quaterniondc other)
      Compute the difference between this and the other quaternion and store the result in this.

      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
      Returns:
      this
    • difference

      public Quaterniond difference(Quaterniondc other, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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.

      Specified by:
      difference in interface Quaterniondc
      Parameters:
      other - the other quaternion
      dest - will hold the result
      Returns:
      dest
    • rotationTo

      public Quaterniond rotationTo(double fromDirX, double fromDirY, double fromDirZ, double toDirX, double toDirY, double toDirZ)
      Set this quaternion to a rotation that rotates the fromDir vector to point along toDir.

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

      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
      Returns:
      this
    • rotationTo

      public Quaterniond rotationTo(Vector3dc fromDir, Vector3dc toDir)
      Set this quaternion to a rotation that rotates the fromDir vector to point along toDir.

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

      Parameters:
      fromDir - the starting direction
      toDir - the destination direction
      Returns:
      this
      See Also:
      rotationTo(double, double, double, double, double, double)
    • rotateTo

      public Quaterniond rotateTo(double fromDirX, double fromDirY, double fromDirZ, double toDirX, double toDirY, double toDirZ, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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

      Specified by:
      rotateTo in interface Quaterniondc
      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
    • rotationAxis

      public Quaterniond rotationAxis(AxisAngle4f axisAngle)
      Set this Quaterniond to a rotation of the given angle in radians about the supplied axis, all of which are specified via the AxisAngle4f.
      Parameters:
      axisAngle - the AxisAngle4f giving the rotation angle in radians and the axis to rotate about
      Returns:
      this
      See Also:
      rotationAxis(double, double, double, double)
    • rotationAxis

      public Quaterniond rotationAxis(double angle, double axisX, double axisY, double axisZ)
      Set this quaternion to a rotation of the given angle in radians about the supplied axis.
      Parameters:
      angle - the rotation angle in radians
      axisX - the x-coordinate of the rotation axis
      axisY - the y-coordinate of the rotation axis
      axisZ - the z-coordinate of the rotation axis
      Returns:
      this
    • rotationX

      public Quaterniond rotationX(double angle)
      Set this quaternion to represent a rotation of the given radians about the x axis.
      Parameters:
      angle - the angle in radians to rotate about the x axis
      Returns:
      this
    • rotationY

      public Quaterniond rotationY(double angle)
      Set this quaternion to represent a rotation of the given radians about the y axis.
      Parameters:
      angle - the angle in radians to rotate about the y axis
      Returns:
      this
    • rotationZ

      public Quaterniond rotationZ(double angle)
      Set this quaternion to represent a rotation of the given radians about the z axis.
      Parameters:
      angle - the angle in radians to rotate about the z axis
      Returns:
      this
    • rotateTo

      public Quaterniond rotateTo(double fromDirX, double fromDirY, double fromDirZ, double toDirX, double toDirY, double toDirZ)
      Apply a rotation to this that rotates the fromDir vector to point along toDir.

      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!

      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
      Returns:
      this
      See Also:
      rotateTo(double, double, double, double, double, double, Quaterniond)
    • rotateTo

      public Quaterniond rotateTo(Vector3dc fromDir, Vector3dc toDir, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateTo in interface Quaterniondc
      Parameters:
      fromDir - the starting direction
      toDir - the destination direction
      dest - will hold the result
      Returns:
      dest
      See Also:
      Quaterniondc.rotateTo(double, double, double, double, double, double, Quaterniond)
    • rotateTo

      public Quaterniond rotateTo(Vector3dc fromDir, Vector3dc toDir)
      Apply a rotation to this that rotates the fromDir vector to point along toDir.

      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
      Returns:
      this
      See Also:
      rotateTo(double, double, double, double, double, double, Quaterniond)
    • rotateX

      public Quaterniond rotateX(double angle)
      Apply a rotation to this quaternion rotating the given radians about the x axis.

      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
      Returns:
      this
    • rotateX

      public Quaterniond rotateX(double angle, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateX in interface Quaterniondc
      Parameters:
      angle - the angle in radians to rotate about the x axis
      dest - will hold the result
      Returns:
      dest
    • rotateY

      public Quaterniond rotateY(double angle)
      Apply a rotation to this quaternion rotating the given radians about the y axis.

      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
      Returns:
      this
    • rotateY

      public Quaterniond rotateY(double angle, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateY in interface Quaterniondc
      Parameters:
      angle - the angle in radians to rotate about the y axis
      dest - will hold the result
      Returns:
      dest
    • rotateZ

      public Quaterniond rotateZ(double angle)
      Apply a rotation to this quaternion rotating the given radians about the z axis.

      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
      Returns:
      this
    • rotateZ

      public Quaterniond rotateZ(double angle, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateZ in interface Quaterniondc
      Parameters:
      angle - the angle in radians to rotate about the z axis
      dest - will hold the result
      Returns:
      dest
    • rotateLocalX

      public Quaterniond rotateLocalX(double angle)
      Apply a rotation to this quaternion rotating the given radians about the local x axis.

      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
      Returns:
      this
    • rotateLocalX

      public Quaterniond rotateLocalX(double angle, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateLocalX in interface Quaterniondc
      Parameters:
      angle - the angle in radians to rotate about the local x axis
      dest - will hold the result
      Returns:
      dest
    • rotateLocalY

      public Quaterniond rotateLocalY(double angle)
      Apply a rotation to this quaternion rotating the given radians about the local y axis.

      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
      Returns:
      this
    • rotateLocalY

      public Quaterniond rotateLocalY(double angle, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateLocalY in interface Quaterniondc
      Parameters:
      angle - the angle in radians to rotate about the local y axis
      dest - will hold the result
      Returns:
      dest
    • rotateLocalZ

      public Quaterniond rotateLocalZ(double angle)
      Apply a rotation to this quaternion rotating the given radians about the local z axis.

      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
      Returns:
      this
    • rotateLocalZ

      public Quaterniond rotateLocalZ(double angle, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateLocalZ in interface Quaterniondc
      Parameters:
      angle - the angle in radians to rotate about the local z axis
      dest - will hold the result
      Returns:
      dest
    • rotateXYZ

      public Quaterniond rotateXYZ(double angleX, double angleY, double angleZ)
      Apply a rotation to this quaternion rotating the given radians about the cartesian base unit axes, called the euler angles using rotation sequence XYZ.

      This method is equivalent to calling: rotateX(angleX).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
      Returns:
      this
    • rotateXYZ

      public Quaterniond rotateXYZ(double angleX, double angleY, double angleZ, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateXYZ in interface Quaterniondc
      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

      public Quaterniond rotateZYX(double angleZ, double angleY, double angleX)
      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.

      This method is equivalent to calling: rotateZ(angleZ).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
      Returns:
      this
    • rotateZYX

      public Quaterniond rotateZYX(double angleZ, double angleY, double angleX, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateZYX in interface Quaterniondc
      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

      public Quaterniond rotateYXZ(double angleY, double angleX, double angleZ)
      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.

      This method is equivalent to calling: rotateY(angleY).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
      Returns:
      this
    • rotateYXZ

      public Quaterniond rotateYXZ(double angleY, double angleX, double angleZ, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateYXZ in interface Quaterniondc
      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

      public Vector3d getEulerAnglesXYZ(Vector3d eulerAngles)
      Description copied from interface: Quaterniondc
      Get the euler angles in radians in rotation sequence XYZ of this quaternion and store them in the provided parameter eulerAngles.
      Specified by:
      getEulerAnglesXYZ in interface Quaterniondc
      Parameters:
      eulerAngles - will hold the euler angles in radians
      Returns:
      the passed in vector
    • rotateAxis

      public Quaterniond rotateAxis(double angle, double axisX, double axisY, double axisZ, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateAxis in interface Quaterniondc
      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

      public Quaterniond rotateAxis(double angle, Vector3dc axis, Quaterniond dest)
      Description copied from interface: Quaterniondc
      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!

      Specified by:
      rotateAxis in interface Quaterniondc
      Parameters:
      angle - the angle in radians to rotate about the specified axis
      axis - the rotation axis
      dest - will hold the result
      Returns:
      dest
      See Also:
      Quaterniondc.rotateAxis(double, double, double, double, Quaterniond)
    • rotateAxis

      public Quaterniond rotateAxis(double angle, Vector3dc axis)
      Apply a rotation to this quaternion rotating the given radians about the specified axis.

      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
      Returns:
      this
      See Also:
      rotateAxis(double, double, double, double, Quaterniond)
    • rotateAxis

      public Quaterniond rotateAxis(double angle, double axisX, double axisY, double axisZ)
      Apply a rotation to this quaternion rotating the given radians about the specified axis.

      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
      Returns:
      this
      See Also:
      rotateAxis(double, double, double, double, Quaterniond)
    • positiveX

      public Vector3d positiveX(Vector3d dir)
      Description copied from interface: Quaterniondc
      Obtain the direction of +X before the rotation transformation represented by this quaternion is applied.

      This method is equivalent to the following code:

       Quaterniond inv = new Quaterniond(this).invert();
       inv.transform(dir.set(1, 0, 0));
       
      Specified by:
      positiveX in interface Quaterniondc
      Parameters:
      dir - will hold the direction of +X
      Returns:
      dir
    • normalizedPositiveX

      public Vector3d normalizedPositiveX(Vector3d dir)
      Description copied from interface: Quaterniondc
      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:

       Quaterniond inv = new Quaterniond(this).conjugate();
       inv.transform(dir.set(1, 0, 0));
       
      Specified by:
      normalizedPositiveX in interface Quaterniondc
      Parameters:
      dir - will hold the direction of +X
      Returns:
      dir
    • positiveY

      public Vector3d positiveY(Vector3d dir)
      Description copied from interface: Quaterniondc
      Obtain the direction of +Y before the rotation transformation represented by this quaternion is applied.

      This method is equivalent to the following code:

       Quaterniond inv = new Quaterniond(this).invert();
       inv.transform(dir.set(0, 1, 0));
       
      Specified by:
      positiveY in interface Quaterniondc
      Parameters:
      dir - will hold the direction of +Y
      Returns:
      dir
    • normalizedPositiveY

      public Vector3d normalizedPositiveY(Vector3d dir)
      Description copied from interface: Quaterniondc
      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:

       Quaterniond inv = new Quaterniond(this).conjugate();
       inv.transform(dir.set(0, 1, 0));
       
      Specified by:
      normalizedPositiveY in interface Quaterniondc
      Parameters:
      dir - will hold the direction of +Y
      Returns:
      dir
    • positiveZ

      public Vector3d positiveZ(Vector3d dir)
      Description copied from interface: Quaterniondc
      Obtain the direction of +Z before the rotation transformation represented by this quaternion is applied.

      This method is equivalent to the following code:

       Quaterniond inv = new Quaterniond(this).invert();
       inv.transform(dir.set(0, 0, 1));
       
      Specified by:
      positiveZ in interface Quaterniondc
      Parameters:
      dir - will hold the direction of +Z
      Returns:
      dir
    • normalizedPositiveZ

      public Vector3d normalizedPositiveZ(Vector3d dir)
      Description copied from interface: Quaterniondc
      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:

       Quaterniond inv = new Quaterniond(this).conjugate();
       inv.transform(dir.set(0, 0, 1));
       
      Specified by:
      normalizedPositiveZ in interface Quaterniondc
      Parameters:
      dir - will hold the direction of +Z
      Returns:
      dir
    • conjugateBy

      public Quaterniond conjugateBy(Quaterniondc q)
      Conjugate this by the given quaternion q by computing q * this * q^-1.
      Parameters:
      q - the Quaterniondc to conjugate this by
      Returns:
      this
    • conjugateBy

      public Quaterniond conjugateBy(Quaterniondc q, Quaterniond dest)
      Conjugate this by the given quaternion q by computing q * this * q^-1 and store the result into dest.
      Specified by:
      conjugateBy in interface Quaterniondc
      Parameters:
      q - the Quaterniondc to conjugate this by
      dest - will hold the result
      Returns:
      dest
    • isFinite

      public boolean isFinite()
      Description copied from interface: Quaterniondc
      Determine whether all components are finite floating-point values, that is, they are not NaN and not infinity.
      Specified by:
      isFinite in interface Quaterniondc
      Returns:
      true if all components are finite floating-point values; false otherwise
    • equals

      public boolean equals(Quaterniondc q, double delta)
      Description copied from interface: Quaterniondc
      Compare the quaternion components of this quaternion with the given quaternion using the given delta and return whether all of them are equal within a maximum difference of delta.

      Please note that this method is not used by any data structure such as ArrayList HashSet or HashMap and their operations, such as ArrayList.contains(Object) or HashSet.remove(Object), since those data structures only use the Object.equals(Object) and Object.hashCode() methods.

      Specified by:
      equals in interface Quaterniondc
      Parameters:
      q - the other quaternion
      delta - the allowed maximum difference
      Returns:
      true whether all of the quaternion components are equal; false otherwise
    • equals

      public boolean equals(double x, double y, double z, double w)
      Specified by:
      equals in interface Quaterniondc
      Parameters:
      x - the x component to compare to
      y - the y component to compare to
      z - the z component to compare to
      w - the w component to compare to
      Returns:
      true if all the quaternion components are equal
    • clone

      public Object clone() throws CloneNotSupportedException
      Overrides:
      clone in class Object
      Throws:
      CloneNotSupportedException