Package civitas.celestis.math.complex

Class Quaternions

java.lang.Object
civitas.celestis.math.complex.Quaternions
public final class Quaternions extends Object
Contains utility methods related to quaternions.

  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    angle(Quaternion q)
    Given a rotation quaternion q, this returns the angle of the rotation, in the context of axis/angle notation.
    static Vector3
    axis(Quaternion q)
    Given a rotation quaternion q, this returns the axis of the rotation.
    static Double4
    axisAngle(Quaternion q)
    Given a rotation quaternion q, this returns an axis/angle pair denoting the rotation of the quaternion.
    static Double3
    eulerAngles(Quaternion q)
    Given a rotation quaternion q, this returns a tuple of doubles containing the pitch, yaw, and roll angles of the quaternion in pitch-yaw-roll order.
    static Quaternion
    from(double pitch, double yaw, double roll)
    Creates a new rotation quaternion from Euler angle representation.
    static Quaternion
    from(Matrix m)
    Creates a new quaternion from a 3x3 rotation matrix.
    static Quaternion
    from(Vector3 axis, double angle)
    Creates a new rotation quaternion from an axis/angle notation.
    static Quaternion
    from(Double3 pyr)
    Creates a new rotation quaternion from Euler angle representation.
    static Quaternion
    from(Double4 axisAngle)
    Creates a new rotation quaternion from an axis/angle notation.
    static Quaternion
    lerp(Quaternion s, Quaternion e, double t)
    Performs linear interpolation (LERP) between the starting value s and the ending value e.
    static Matrix
    matrix(Quaternion q)
    Given a rotation quaternion q, this converts the rotation into a 3x3 rotation matrix.
    static double
    pitch(Quaternion q)
    Given a rotation quaternion q, this returns the pitch of the rotation.
    static Quaternion
    random()
    Returns a random rotation quaternion.
    static double
    roll(Quaternion q)
    Given a rotation quaternion q, this returns the roll of this rotation.
    static Quaternion
    slerp(Quaternion start, Quaternion end, double t)
    Performs spherical linear interpolation (SLERP) between two quaternions.
    static double
    yaw(Quaternion q)
    Given a rotation quaternion q, this returns the yaw of the rotation.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • random

      @Nonnull public static Quaternion random()
      Returns a random rotation quaternion.
      Returns:
      A random rotation quaternion

    • lerp

      @Nonnull public static Quaternion lerp(@Nonnull Quaternion s, @Nonnull Quaternion e, double t)
      Performs linear interpolation (LERP) between the starting value s and the ending value e.
      Parameters:
      s - The starting value
      e - The ending value
      t - The interpolation parameter ([0, 1])
      Returns:
      The interpolated value between the starting and ending values s and e

    • slerp

      @Nonnull public static Quaternion slerp(@Nonnull Quaternion start, @Nonnull Quaternion end, double t)
      Performs spherical linear interpolation (SLERP) between two quaternions. This assumes that the input quaternions are already normalized.
      Parameters:
      start - The starting quaternion
      end - The end quaternion
      t - The interpolation parameter t (0-1)
      Returns:
      The interpolated quaternion

    • from

      @Nonnull public static Quaternion from(@Nonnull Double3 pyr)
      Creates a new rotation quaternion from Euler angle representation. This method uses the right-handed coordinate system.
      Parameters:
      pyr - A tuple of doubles containing the Euler angles in pitch-yaw-roll order
      Returns:
      The constructed quaternion

    • from

      @Nonnull public static Quaternion from(double pitch, double yaw, double roll)
      Creates a new rotation quaternion from Euler angle representation. This method uses the right-handed coordinate system.
      Parameters:
      pitch - The pitch of the rotation in radians (rotation along X axis)
      yaw - The yaw of the rotation in radians (rotation along Y axis)
      roll - The roll of the rotation in radians (rotation along Z axis)
      Returns:
      The constructed quaternion

    • eulerAngles

      @Nonnull public static Double3 eulerAngles(@Nonnull Quaternion q)
      Given a rotation quaternion q, this returns a tuple of doubles containing the pitch, yaw, and roll angles of the quaternion in pitch-yaw-roll order.
      Parameters:
      q - The quaternion of which to get the Euler angles of
      Returns:
      The Euler angles of the quaternion, denoted in radians

    • pitch

      public static double pitch(@Nonnull Quaternion q)
      Given a rotation quaternion q, this returns the pitch of the rotation. Pitch is defined as rotation along the X axis, and follows a right-handed coordinate system.
      Parameters:
      q - The quaternion of which to get the pitch of
      Returns:
      The pitch of the quaternion in radians

    • yaw

      public static double yaw(@Nonnull Quaternion q)
      Given a rotation quaternion q, this returns the yaw of the rotation. Yaw is defined as rotation along the Y axis, and follows a right-handed coordinate system.
      Parameters:
      q - The quaternion of which to get the yaw of
      Returns:
      The yaw of the quaternion in radians

    • roll

      public static double roll(@Nonnull Quaternion q)
      Given a rotation quaternion q, this returns the roll of this rotation. Roll is defined as rotation along the Z axis, and follows a right-handed coordinate system.
      Parameters:
      q - The quaternion of which to get the roll of
      Returns:
      The roll of the quaternion in radians

    • from

      @Nonnull public static Quaternion from(@Nonnull Double4 axisAngle)
      Creates a new rotation quaternion from an axis/angle notation. This method uses the right-handed coordinate system.
      Parameters:
      axisAngle - The axis/angle representation of the rotation
      Returns:
      The constructed quaternion

    • from

      @Nonnull public static Quaternion from(@Nonnull Vector3 axis, double angle)
      Creates a new rotation quaternion from an axis/angle notation. This method uses the right-handed coordinate system.
      Parameters:
      axis - The axis of rotation as a unit vector
      angle - The angle of rotation in radians
      Returns:
      The constructed quaternion

    • axisAngle

      @Nonnull public static Double4 axisAngle(@Nonnull Quaternion q)
      Given a rotation quaternion q, this returns an axis/angle pair denoting the rotation of the quaternion. Axis/angle notation follows the right-handed coordinate system. The W component represents the angle of rotation in radians, and the XYZ components represent the axis of rotation.
      Parameters:
      q - The quaternion of which to convert to axis/angle notation
      Returns:
      The axis/angle representation of the quaternion

    • angle

      public static double angle(@Nonnull Quaternion q)
      Given a rotation quaternion q, this returns the angle of the rotation, in the context of axis/angle notation. Axis/angle notation follows the right-handed coordinate system.
      Parameters:
      q - The quaternion of which to get the angle of
      Returns:
      The angle of rotation of the quaternion in radians

    • axis

      @Nonnull public static Vector3 axis(@Nonnull Quaternion q)
      Given a rotation quaternion q, this returns the axis of the rotation. If the quaternion represents no rotation (the Euclidean norm is nearly zero), this will return a fallback value Vector3.POSITIVE_Y.
      Parameters:
      q - The quaternion of which to get the axis of
      Returns:
      The axis of rotation of the quaternion as a unit vector

    • from

      @Nonnull public static Quaternion from(@Nonnull Matrix m) throws IllegalArgumentException
      Creates a new quaternion from a 3x3 rotation matrix.
      Parameters:
      m - The rotation matrix which represents the rotation
      Returns:
      The constructed quaternion
      Throws:
      IllegalArgumentException - When the matrix's dimensions is not 3x3

    • matrix

      @Nonnull public static Matrix matrix(@Nonnull Quaternion q)
      Given a rotation quaternion q, this converts the rotation into a 3x3 rotation matrix.
      Parameters:
      q - The quaternion of which to convert into a rotation matrix
      Returns:
      The matrix representation of the provided quaternion q