Quaternion Struct

    Namespace: Stride.Core.Mathematics
    Assembly: Stride.Core.Mathematics.dll

    Represents a four dimensional mathematical quaternion.

    [DataContract("quaternion")]
[DataStyle(DataStyle.Compact)]
public struct Quaternion : IEquatable<Quaternion>, IFormattable
    Name Description
    Constructors
    Quaternion(Vector2, Single, Single)

    Initializes a new instance of the Quaternion struct.
    Quaternion(Vector3, Single)

    Initializes a new instance of the Quaternion struct.
    Quaternion(Vector4)

    Initializes a new instance of the Quaternion struct.
    Quaternion(Single)

    Initializes a new instance of the Quaternion struct.
    Quaternion(Single, Single, Single, Single)

    Initializes a new instance of the Quaternion struct.
    Quaternion(Single[])

    Initializes a new instance of the Quaternion struct.
    Fields
    Identity

    The identity Quaternion (0, 0, 0, 1).
    One

    A Quaternion with all of its components set to one.
    SizeInBytes

    The size of the Quaternion type, in bytes.
    W

    The W component of the quaternion.
    X

    The X component of the quaternion.
    Y

    The Y component of the quaternion.
    Z

    The Z component of the quaternion.
    Zero

    A Quaternion with all of its components set to zero.
    Properties
    Angle

    Gets the angle of the quaternion.
    Axis

    Gets the axis components of the quaternion.
    IsIdentity

    Gets a value indicating whether this instance is equivalent to the identity quaternion.
    IsNormalized

    Gets a value indicting whether this instance is normalized.
    Item[Int32]

    Gets or sets the component at the specified index.
    YawPitchRoll

    Gets yaw/pitch/roll equivalent of the quaternion
    Methods
    Add(Quaternion, Quaternion)

    Adds two quaternions.
    Add(ref Quaternion, ref Quaternion, out Quaternion)

    Adds two quaternions.
    Barycentric(Quaternion, Quaternion, Quaternion, Single, Single)

    Returns a Quaternion containing the 4D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 2D triangle.
    Barycentric(ref Quaternion, ref Quaternion, ref Quaternion, Single, Single, out Quaternion)

    Returns a Quaternion containing the 4D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 2D triangle.
    BetweenDirections(Vector3, Vector3)

    Computes a quaternion corresponding to the rotation transforming the vector source to the vector target.
    BetweenDirections(ref Vector3, ref Vector3, out Quaternion)

    Computes a quaternion corresponding to the rotation transforming the vector source to the vector target.
    Conjugate()

    Conjugates the quaternion.
    Conjugate(Quaternion)

    Conjugates a quaternion.
    Conjugate(ref Quaternion, out Quaternion)

    Conjugates a quaternion.
    Dot(Quaternion, Quaternion)

    Calculates the dot product of two quaternions.
    Dot(ref Quaternion, ref Quaternion, out Single)

    Calculates the dot product of two quaternions.
    Equals(Quaternion)

    Determines whether the specified Quaternion is equal to this instance.
    Equals(Object)

    Determines whether the specified System.Object is equal to this instance.
    Exponential(Quaternion)

    Exponentiates a quaternion.
    Exponential(ref Quaternion, out Quaternion)

    Exponentiates a quaternion.
    GetHashCode()

    Returns a hash code for this instance.
    Invert()

    Conjugates and renormalizes the quaternion.
    Invert(Quaternion)

    Conjugates and renormalizes the quaternion.
    Invert(ref Quaternion, out Quaternion)

    Conjugates and renormalizes the quaternion.
    Length()

    Calculates the length of the quaternion.
    LengthSquared()

    Calculates the squared length of the quaternion.
    Lerp(Quaternion, Quaternion, Single)

    Performs a linear interpolation between two quaternion.
    Lerp(ref Quaternion, ref Quaternion, Single, out Quaternion)

    Performs a linear interpolation between two quaternions.
    Logarithm(Quaternion)

    Calculates the natural logarithm of the specified quaternion.
    Logarithm(ref Quaternion, out Quaternion)

    Calculates the natural logarithm of the specified quaternion.
    Multiply(Quaternion, Quaternion)

    Modulates a quaternion by another.
    Multiply(Quaternion, Single)

    Scales a quaternion by the given value.
    Multiply(ref Quaternion, ref Quaternion, out Quaternion)

    Modulates a quaternion by another.
    Multiply(ref Quaternion, Single, out Quaternion)

    Scales a quaternion by the given value.
    Negate(Quaternion)

    Reverses the direction of a given quaternion.
    Negate(ref Quaternion, out Quaternion)

    Reverses the direction of a given quaternion.
    Normalize()

    Converts the quaternion into a unit quaternion.
    Normalize(Quaternion)

    Converts the quaternion into a unit quaternion.
    Normalize(ref Quaternion, out Quaternion)

    Converts the quaternion into a unit quaternion.
    Rotate(ref Vector3)

    Rotates a Vector3 by the specified quaternion rotation.
    RotationAxis(Vector3, Single)

    Creates a quaternion given a rotation and an axis.
    RotationAxis(ref Vector3, Single, out Quaternion)

    Creates a quaternion given a rotation and an axis.
    RotationMatrix(Matrix)

    Creates a quaternion given a rotation matrix.
    RotationMatrix(ref Matrix, out Quaternion)

    Creates a quaternion given a rotation matrix.
    RotationX(Single)

    Creates a quaternion that rotates around the x-axis.
    RotationX(Single, out Quaternion)

    Creates a quaternion that rotates around the x-axis.
    RotationY(Single)

    Creates a quaternion that rotates around the y-axis.
    RotationY(Single, out Quaternion)

    Creates a quaternion that rotates around the y-axis.
    RotationYawPitchRoll(ref Quaternion, out Single, out Single, out Single)

    Calculate the yaw/pitch/roll rotation equivalent to the provided quaternion.
    RotationYawPitchRoll(Single, Single, Single)

    Creates a quaternion given a yaw, pitch, and roll value.
    RotationYawPitchRoll(Single, Single, Single, out Quaternion)

    Creates a quaternion given a yaw, pitch, and roll value (angles in radians).
    RotationZ(Single)

    Creates a quaternion that rotates around the z-axis.
    RotationZ(Single, out Quaternion)

    Creates a quaternion that rotates around the z-axis.
    Slerp(Quaternion, Quaternion, Single)

    Interpolates between two quaternions, using spherical linear interpolation.
    Slerp(ref Quaternion, ref Quaternion, Single, out Quaternion)

    Interpolates between two quaternions, using spherical linear interpolation.
    Squad(Quaternion, Quaternion, Quaternion, Quaternion, Single)

    Interpolates between quaternions, using spherical quadrangle interpolation.
    Squad(ref Quaternion, ref Quaternion, ref Quaternion, ref Quaternion, Single, out Quaternion)

    Interpolates between quaternions, using spherical quadrangle interpolation.
    SquadSetup(Quaternion, Quaternion, Quaternion, Quaternion)

    Sets up control points for spherical quadrangle interpolation.
    Subtract(Quaternion, Quaternion)

    Subtracts two quaternions.
    Subtract(ref Quaternion, ref Quaternion, out Quaternion)

    Subtracts two quaternions.
    ToArray()

    Creates an array containing the elements of the quaternion.
    ToString()

    Returns a System.String that represents this instance.
    ToString(IFormatProvider)

    Returns a System.String that represents this instance.
    ToString(String)

    Returns a System.String that represents this instance.
    ToString(String, IFormatProvider)

    Returns a System.String that represents this instance.
    Operators
    Addition(Quaternion, Quaternion)

    Adds two quaternions.
    Equality(Quaternion, Quaternion)

    Tests for equality between two objects.
    Inequality(Quaternion, Quaternion)

    Tests for inequality between two objects.
    Multiply(Quaternion, Quaternion)

    Multiplies a quaternion by another.
    Multiply(Quaternion, Single)

    Scales a quaternion by the given value.
    Multiply(Single, Quaternion)

    Scales a quaternion by the given value.
    Subtraction(Quaternion, Quaternion)

    Subtracts two quaternions.
    UnaryNegation(Quaternion)

    Reverses the direction of a given quaternion.
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    Constructors

    Quaternion(Vector2, Single, Single)

    Initializes a new instance of the Quaternion struct.

    public Quaternion(Vector2 value, float z, float w)
    Parameters
    Type Name Description
    Vector2 value

    A vector containing the values with which to initialize the X and Y components.
    System.Single z

    Initial value for the Z component of the quaternion.
    System.Single w

    Initial value for the W component of the quaternion.

    Quaternion(Vector3, Single)

    Initializes a new instance of the Quaternion struct.

    public Quaternion(Vector3 value, float w)
    Parameters
    Type Name Description
    Vector3 value

    A vector containing the values with which to initialize the X, Y, and Z components.
    System.Single w

    Initial value for the W component of the quaternion.

    Quaternion(Vector4)

    Initializes a new instance of the Quaternion struct.

    public Quaternion(Vector4 value)
    Parameters
    Type Name Description
    Vector4 value

    A vector containing the values with which to initialize the components.

    Quaternion(Single)

    Initializes a new instance of the Quaternion struct.

    public Quaternion(float value)
    Parameters
    Type Name Description
    System.Single value

    The value that will be assigned to all components.

    Quaternion(Single, Single, Single, Single)

    Initializes a new instance of the Quaternion struct.

    public Quaternion(float x, float y, float z, float w)
    Parameters
    Type Name Description
    System.Single x

    Initial value for the X component of the quaternion.
    System.Single y

    Initial value for the Y component of the quaternion.
    System.Single z

    Initial value for the Z component of the quaternion.
    System.Single w

    Initial value for the W component of the quaternion.

    Quaternion(Single[])

    Initializes a new instance of the Quaternion struct.

    public Quaternion(float[] values)
    Parameters
    Type Name Description
    System.Single[] values

    The values to assign to the X, Y, Z, and W components of the quaternion. This must be an array with four elements.
    Exceptions
    Type Condition
    System.ArgumentNullException

    Thrown when values is null.
    System.ArgumentOutOfRangeException

    Thrown when values contains more or less than four elements.
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    Fields

    Identity

    The identity Quaternion (0, 0, 0, 1).

    public static readonly Quaternion Identity
    Field Value
    Type Description
    Quaternion

    One

    A Quaternion with all of its components set to one.

    public static readonly Quaternion One
    Field Value
    Type Description
    Quaternion

    SizeInBytes

    The size of the Quaternion type, in bytes.

    public static readonly int SizeInBytes
    Field Value
    Type Description
    System.Int32

    W

    The W component of the quaternion.

    public float W
    Field Value
    Type Description
    System.Single

    X

    The X component of the quaternion.

    public float X
    Field Value
    Type Description
    System.Single

    Y

    The Y component of the quaternion.

    public float Y
    Field Value
    Type Description
    System.Single

    Z

    The Z component of the quaternion.

    public float Z
    Field Value
    Type Description
    System.Single

    Zero

    A Quaternion with all of its components set to zero.

    public static readonly Quaternion Zero
    Field Value
    Type Description
    Quaternion
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    Properties

    Angle

    Gets the angle of the quaternion.

    public readonly float Angle { get; }
    Property Value
    Type Description
    System.Single

    The quaternion's angle.

    Axis

    Gets the axis components of the quaternion.

    public readonly Vector3 Axis { get; }
    Property Value
    Type Description
    Vector3

    The axis components of the quaternion.

    IsIdentity

    Gets a value indicating whether this instance is equivalent to the identity quaternion.

    public readonly bool IsIdentity { get; }
    Property Value
    Type Description
    System.Boolean

    true if this instance is an identity quaternion; otherwise, false.

    IsNormalized

    Gets a value indicting whether this instance is normalized.

    public readonly bool IsNormalized { get; }
    Property Value
    Type Description
    System.Boolean

    Item[Int32]

    Gets or sets the component at the specified index.

    public float this[int index] { get; set; }
    Parameters
    Type Name Description
    System.Int32 index

    The index of the component to access. Use 0 for the X component, 1 for the Y component, 2 for the Z component, and 3 for the W component.
    Property Value
    Type Description
    System.Single

    The value of the X, Y, Z, or W component, depending on the index.
    Exceptions
    Type Condition
    System.ArgumentOutOfRangeException

    Thrown when the index is out of the range [0, 3].

    YawPitchRoll

    Gets yaw/pitch/roll equivalent of the quaternion

    public readonly Vector3 YawPitchRoll { get; }
    Property Value
    Type Description
    Vector3
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    Methods

    Add(Quaternion, Quaternion)

    Adds two quaternions.

    public static Quaternion Add(Quaternion left, Quaternion right)
    Parameters
    Type Name Description
    Quaternion left

    The first quaternion to add.
    Quaternion right

    The second quaternion to add.
    Returns
    Type Description
    Quaternion

    The sum of the two quaternions.

    Add(ref Quaternion, ref Quaternion, out Quaternion)

    Adds two quaternions.

    public static void Add(ref Quaternion left, ref Quaternion right, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion left

    The first quaternion to add.
    Quaternion right

    The second quaternion to add.
    Quaternion result

    When the method completes, contains the sum of the two quaternions.

    Barycentric(Quaternion, Quaternion, Quaternion, Single, Single)

    Returns a Quaternion containing the 4D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 2D triangle.

    public static Quaternion Barycentric(Quaternion value1, Quaternion value2, Quaternion value3, float amount1, float amount2)
    Parameters
    Type Name Description
    Quaternion value1

    A Quaternion containing the 4D Cartesian coordinates of vertex 1 of the triangle.
    Quaternion value2

    A Quaternion containing the 4D Cartesian coordinates of vertex 2 of the triangle.
    Quaternion value3

    A Quaternion containing the 4D Cartesian coordinates of vertex 3 of the triangle.
    System.Single amount1

    Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in value2).
    System.Single amount2

    Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in value3).
    Returns
    Type Description
    Quaternion

    A new Quaternion containing the 4D Cartesian coordinates of the specified point.

    Barycentric(ref Quaternion, ref Quaternion, ref Quaternion, Single, Single, out Quaternion)

    Returns a Quaternion containing the 4D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 2D triangle.

    public static void Barycentric(ref Quaternion value1, ref Quaternion value2, ref Quaternion value3, float amount1, float amount2, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion value1

    A Quaternion containing the 4D Cartesian coordinates of vertex 1 of the triangle.
    Quaternion value2

    A Quaternion containing the 4D Cartesian coordinates of vertex 2 of the triangle.
    Quaternion value3

    A Quaternion containing the 4D Cartesian coordinates of vertex 3 of the triangle.
    System.Single amount1

    Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in value2).
    System.Single amount2

    Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in value3).
    Quaternion result

    When the method completes, contains a new Quaternion containing the 4D Cartesian coordinates of the specified point.

    BetweenDirections(Vector3, Vector3)

    Computes a quaternion corresponding to the rotation transforming the vector source to the vector target.

    public static Quaternion BetweenDirections(Vector3 source, Vector3 target)
    Parameters
    Type Name Description
    Vector3 source

    The source vector of the transformation.
    Vector3 target

    The target vector of the transformation.
    Returns
    Type Description
    Quaternion

    The resulting quaternion corresponding to the transformation of the source vector to the target vector.

    BetweenDirections(ref Vector3, ref Vector3, out Quaternion)

    Computes a quaternion corresponding to the rotation transforming the vector source to the vector target.

    public static void BetweenDirections(ref Vector3 source, ref Vector3 target, out Quaternion result)
    Parameters
    Type Name Description
    Vector3 source

    The source vector of the transformation.
    Vector3 target

    The target vector of the transformation.
    Quaternion result

    The resulting quaternion corresponding to the transformation of the source vector to the target vector.

    Conjugate()

    Conjugates the quaternion.

    public void Conjugate()

    Conjugate(Quaternion)

    Conjugates a quaternion.

    public static Quaternion Conjugate(Quaternion value)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to conjugate.
    Returns
    Type Description
    Quaternion

    The conjugated quaternion.

    Conjugate(ref Quaternion, out Quaternion)

    Conjugates a quaternion.

    public static void Conjugate(ref Quaternion value, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to conjugate.
    Quaternion result

    When the method completes, contains the conjugated quaternion.

    Dot(Quaternion, Quaternion)

    Calculates the dot product of two quaternions.

    public static float Dot(Quaternion left, Quaternion right)
    Parameters
    Type Name Description
    Quaternion left

    First source quaternion.
    Quaternion right

    Second source quaternion.
    Returns
    Type Description
    System.Single

    The dot product of the two quaternions.

    Dot(ref Quaternion, ref Quaternion, out Single)

    Calculates the dot product of two quaternions.

    public static void Dot(ref Quaternion left, ref Quaternion right, out float result)
    Parameters
    Type Name Description
    Quaternion left

    First source quaternion.
    Quaternion right

    Second source quaternion.
    System.Single result

    When the method completes, contains the dot product of the two quaternions.

    Equals(Quaternion)

    Determines whether the specified Quaternion is equal to this instance.

    public bool Equals(Quaternion other)
    Parameters
    Type Name Description
    Quaternion other

    The Quaternion to compare with this instance.
    Returns
    Type Description
    System.Boolean

    true if the specified Quaternion is equal to this instance; otherwise, false.

    Equals(Object)

    Determines whether the specified System.Object is equal to this instance.

    public override bool Equals(object value)
    Parameters
    Type Name Description
    System.Object value

    The System.Object to compare with this instance.
    Returns
    Type Description
    System.Boolean

    true if the specified System.Object is equal to this instance; otherwise, false.
    Overrides
    System.ValueType.Equals(System.Object)

    Exponential(Quaternion)

    Exponentiates a quaternion.

    public static Quaternion Exponential(Quaternion value)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to exponentiate.
    Returns
    Type Description
    Quaternion

    The exponentiated quaternion.

    Exponential(ref Quaternion, out Quaternion)

    Exponentiates a quaternion.

    public static void Exponential(ref Quaternion value, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to exponentiate.
    Quaternion result

    When the method completes, contains the exponentiated quaternion.

    GetHashCode()

    Returns a hash code for this instance.

    public override int GetHashCode()
    Returns
    Type Description
    System.Int32

    A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.

    Overrides
    System.ValueType.GetHashCode()

    Invert()

    Conjugates and renormalizes the quaternion.

    public void Invert()

    Invert(Quaternion)

    Conjugates and renormalizes the quaternion.

    public static Quaternion Invert(Quaternion value)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to conjugate and renormalize.
    Returns
    Type Description
    Quaternion

    The conjugated and renormalized quaternion.

    Invert(ref Quaternion, out Quaternion)

    Conjugates and renormalizes the quaternion.

    public static void Invert(ref Quaternion value, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to conjugate and renormalize.
    Quaternion result

    When the method completes, contains the conjugated and renormalized quaternion.

    Length()

    Calculates the length of the quaternion.

    public float Length()
    Returns
    Type Description
    System.Single

    The length of the quaternion.
    Remarks

    LengthSquared() may be preferred when only the relative length is needed and speed is of the essence.

    LengthSquared()

    Calculates the squared length of the quaternion.

    public float LengthSquared()
    Returns
    Type Description
    System.Single

    The squared length of the quaternion.
    Remarks

    This method may be preferred to Length() when only a relative length is needed and speed is of the essence.

    Lerp(Quaternion, Quaternion, Single)

    Performs a linear interpolation between two quaternion.

    public static Quaternion Lerp(Quaternion start, Quaternion end, float amount)
    Parameters
    Type Name Description
    Quaternion start

    Start quaternion.
    Quaternion end

    End quaternion.
    System.Single amount

    Value between 0 and 1 indicating the weight of end.
    Returns
    Type Description
    Quaternion

    The linear interpolation of the two quaternions.
    Remarks

    This method performs the linear interpolation based on the following formula.

    start + (end - start) * amount

    Passing amount a value of 0 will cause start to be returned; a value of 1 will cause end to be returned.

    Lerp(ref Quaternion, ref Quaternion, Single, out Quaternion)

    Performs a linear interpolation between two quaternions.

    public static void Lerp(ref Quaternion start, ref Quaternion end, float amount, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion start

    Start quaternion.
    Quaternion end

    End quaternion.
    System.Single amount

    Value between 0 and 1 indicating the weight of end.
    Quaternion result

    When the method completes, contains the linear interpolation of the two quaternions.
    Remarks

    This method performs the linear interpolation based on the following formula.

    start + (end - start) * amount

    Passing amount a value of 0 will cause start to be returned; a value of 1 will cause end to be returned.

    Logarithm(Quaternion)

    Calculates the natural logarithm of the specified quaternion.

    public static Quaternion Logarithm(Quaternion value)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion whose logarithm will be calculated.
    Returns
    Type Description
    Quaternion

    The natural logarithm of the quaternion.

    Logarithm(ref Quaternion, out Quaternion)

    Calculates the natural logarithm of the specified quaternion.

    public static void Logarithm(ref Quaternion value, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion whose logarithm will be calculated.
    Quaternion result

    When the method completes, contains the natural logarithm of the quaternion.

    Multiply(Quaternion, Quaternion)

    Modulates a quaternion by another.

    public static Quaternion Multiply(Quaternion left, Quaternion right)
    Parameters
    Type Name Description
    Quaternion left

    The first quaternion to modulate.
    Quaternion right

    The second quaternion to modulate.
    Returns
    Type Description
    Quaternion

    The modulated quaternion.

    Multiply(Quaternion, Single)

    Scales a quaternion by the given value.

    public static Quaternion Multiply(Quaternion value, float scale)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to scale.
    System.Single scale

    The amount by which to scale the quaternion.
    Returns
    Type Description
    Quaternion

    The scaled quaternion.

    Multiply(ref Quaternion, ref Quaternion, out Quaternion)

    Modulates a quaternion by another.

    public static void Multiply(ref Quaternion left, ref Quaternion right, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion left

    The first quaternion to modulate.
    Quaternion right

    The second quaternion to modulate.
    Quaternion result

    When the moethod completes, contains the modulated quaternion.

    Multiply(ref Quaternion, Single, out Quaternion)

    Scales a quaternion by the given value.

    public static void Multiply(ref Quaternion value, float scale, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to scale.
    System.Single scale

    The amount by which to scale the quaternion.
    Quaternion result

    When the method completes, contains the scaled quaternion.

    Negate(Quaternion)

    Reverses the direction of a given quaternion.

    public static Quaternion Negate(Quaternion value)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to negate.
    Returns
    Type Description
    Quaternion

    A quaternion facing in the opposite direction.

    Negate(ref Quaternion, out Quaternion)

    Reverses the direction of a given quaternion.

    public static void Negate(ref Quaternion value, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to negate.
    Quaternion result

    When the method completes, contains a quaternion facing in the opposite direction.

    Normalize()

    Converts the quaternion into a unit quaternion.

    public void Normalize()

    Normalize(Quaternion)

    Converts the quaternion into a unit quaternion.

    public static Quaternion Normalize(Quaternion value)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to normalize.
    Returns
    Type Description
    Quaternion

    The normalized quaternion.

    Normalize(ref Quaternion, out Quaternion)

    Converts the quaternion into a unit quaternion.

    public static void Normalize(ref Quaternion value, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to normalize.
    Quaternion result

    When the method completes, contains the normalized quaternion.

    Rotate(ref Vector3)

    Rotates a Vector3 by the specified quaternion rotation.

    public void Rotate(ref Vector3 vector)
    Parameters
    Type Name Description
    Vector3 vector

    The vector to rotate.

    RotationAxis(Vector3, Single)

    Creates a quaternion given a rotation and an axis.

    public static Quaternion RotationAxis(Vector3 axis, float angle)
    Parameters
    Type Name Description
    Vector3 axis

    The axis of rotation.
    System.Single angle

    The angle of rotation.
    Returns
    Type Description
    Quaternion

    The newly created quaternion.

    RotationAxis(ref Vector3, Single, out Quaternion)

    Creates a quaternion given a rotation and an axis.

    public static void RotationAxis(ref Vector3 axis, float angle, out Quaternion result)
    Parameters
    Type Name Description
    Vector3 axis

    The axis of rotation.
    System.Single angle

    The angle of rotation.
    Quaternion result

    When the method completes, contains the newly created quaternion.

    RotationMatrix(Matrix)

    Creates a quaternion given a rotation matrix.

    public static Quaternion RotationMatrix(Matrix matrix)
    Parameters
    Type Name Description
    Matrix matrix

    The rotation matrix.
    Returns
    Type Description
    Quaternion

    The newly created quaternion.

    RotationMatrix(ref Matrix, out Quaternion)

    Creates a quaternion given a rotation matrix.

    public static void RotationMatrix(ref Matrix matrix, out Quaternion result)
    Parameters
    Type Name Description
    Matrix matrix

    The rotation matrix.
    Quaternion result

    When the method completes, contains the newly created quaternion.

    RotationX(Single)

    Creates a quaternion that rotates around the x-axis.

    public static Quaternion RotationX(float angle)
    Parameters
    Type Name Description
    System.Single angle

    Angle of rotation in radians.
    Returns
    Type Description
    Quaternion

    The created rotation quaternion.

    RotationX(Single, out Quaternion)

    Creates a quaternion that rotates around the x-axis.

    public static void RotationX(float angle, out Quaternion result)
    Parameters
    Type Name Description
    System.Single angle

    Angle of rotation in radians.
    Quaternion result

    When the method completes, contains the newly created quaternion.

    RotationY(Single)

    Creates a quaternion that rotates around the y-axis.

    public static Quaternion RotationY(float angle)
    Parameters
    Type Name Description
    System.Single angle

    Angle of rotation in radians.
    Returns
    Type Description
    Quaternion

    The created rotation quaternion.

    RotationY(Single, out Quaternion)

    Creates a quaternion that rotates around the y-axis.

    public static void RotationY(float angle, out Quaternion result)
    Parameters
    Type Name Description
    System.Single angle

    Angle of rotation in radians.
    Quaternion result

    When the method completes, contains the newly created quaternion.

    RotationYawPitchRoll(ref Quaternion, out Single, out Single, out Single)

    Calculate the yaw/pitch/roll rotation equivalent to the provided quaternion.

    public static void RotationYawPitchRoll(ref Quaternion rotation, out float yaw, out float pitch, out float roll)
    Parameters
    Type Name Description
    Quaternion rotation

    The input quaternion
    System.Single yaw

    The yaw component
    System.Single pitch

    The pitch component
    System.Single roll

    The roll component

    RotationYawPitchRoll(Single, Single, Single)

    Creates a quaternion given a yaw, pitch, and roll value.

    public static Quaternion RotationYawPitchRoll(float yaw, float pitch, float roll)
    Parameters
    Type Name Description
    System.Single yaw

    The yaw of rotation.
    System.Single pitch

    The pitch of rotation.
    System.Single roll

    The roll of rotation.
    Returns
    Type Description
    Quaternion

    The newly created quaternion.

    RotationYawPitchRoll(Single, Single, Single, out Quaternion)

    Creates a quaternion given a yaw, pitch, and roll value (angles in radians).

    public static void RotationYawPitchRoll(float yaw, float pitch, float roll, out Quaternion result)
    Parameters
    Type Name Description
    System.Single yaw

    The yaw of rotation in radians.
    System.Single pitch

    The pitch of rotation in radians.
    System.Single roll

    The roll of rotation in radians.
    Quaternion result

    When the method completes, contains the newly created quaternion.

    RotationZ(Single)

    Creates a quaternion that rotates around the z-axis.

    public static Quaternion RotationZ(float angle)
    Parameters
    Type Name Description
    System.Single angle

    Angle of rotation in radians.
    Returns
    Type Description
    Quaternion

    The created rotation quaternion.

    RotationZ(Single, out Quaternion)

    Creates a quaternion that rotates around the z-axis.

    public static void RotationZ(float angle, out Quaternion result)
    Parameters
    Type Name Description
    System.Single angle

    Angle of rotation in radians.
    Quaternion result

    When the method completes, contains the newly created quaternion.

    Slerp(Quaternion, Quaternion, Single)

    Interpolates between two quaternions, using spherical linear interpolation.

    public static Quaternion Slerp(Quaternion start, Quaternion end, float amount)
    Parameters
    Type Name Description
    Quaternion start

    Start quaternion.
    Quaternion end

    End quaternion.
    System.Single amount

    Value between 0 and 1 indicating the weight of end.
    Returns
    Type Description
    Quaternion

    The spherical linear interpolation of the two quaternions.

    Slerp(ref Quaternion, ref Quaternion, Single, out Quaternion)

    Interpolates between two quaternions, using spherical linear interpolation.

    public static void Slerp(ref Quaternion start, ref Quaternion end, float amount, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion start

    Start quaternion.
    Quaternion end

    End quaternion.
    System.Single amount

    Value between 0 and 1 indicating the weight of end.
    Quaternion result

    When the method completes, contains the spherical linear interpolation of the two quaternions.

    Squad(Quaternion, Quaternion, Quaternion, Quaternion, Single)

    Interpolates between quaternions, using spherical quadrangle interpolation.

    public static Quaternion Squad(Quaternion value1, Quaternion value2, Quaternion value3, Quaternion value4, float amount)
    Parameters
    Type Name Description
    Quaternion value1

    First source quaternion.
    Quaternion value2

    Second source quaternion.
    Quaternion value3

    Thrid source quaternion.
    Quaternion value4

    Fourth source quaternion.
    System.Single amount

    Value between 0 and 1 indicating the weight of interpolation.
    Returns
    Type Description
    Quaternion

    The spherical quadrangle interpolation of the quaternions.

    Squad(ref Quaternion, ref Quaternion, ref Quaternion, ref Quaternion, Single, out Quaternion)

    Interpolates between quaternions, using spherical quadrangle interpolation.

    public static void Squad(ref Quaternion value1, ref Quaternion value2, ref Quaternion value3, ref Quaternion value4, float amount, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion value1

    First source quaternion.
    Quaternion value2

    Second source quaternion.
    Quaternion value3

    Thrid source quaternion.
    Quaternion value4

    Fourth source quaternion.
    System.Single amount

    Value between 0 and 1 indicating the weight of interpolation.
    Quaternion result

    When the method completes, contains the spherical quadrangle interpolation of the quaternions.

    SquadSetup(Quaternion, Quaternion, Quaternion, Quaternion)

    Sets up control points for spherical quadrangle interpolation.

    public static Quaternion[] SquadSetup(Quaternion value1, Quaternion value2, Quaternion value3, Quaternion value4)
    Parameters
    Type Name Description
    Quaternion value1

    First source quaternion.
    Quaternion value2

    Second source quaternion.
    Quaternion value3

    Third source quaternion.
    Quaternion value4

    Fourth source quaternion.
    Returns
    Type Description
    Quaternion[]

    An array of three quaternions that represent control points for spherical quadrangle interpolation.

    Subtract(Quaternion, Quaternion)

    Subtracts two quaternions.

    public static Quaternion Subtract(Quaternion left, Quaternion right)
    Parameters
    Type Name Description
    Quaternion left

    The first quaternion to subtract.
    Quaternion right

    The second quaternion to subtract.
    Returns
    Type Description
    Quaternion

    The difference of the two quaternions.

    Subtract(ref Quaternion, ref Quaternion, out Quaternion)

    Subtracts two quaternions.

    public static void Subtract(ref Quaternion left, ref Quaternion right, out Quaternion result)
    Parameters
    Type Name Description
    Quaternion left

    The first quaternion to subtract.
    Quaternion right

    The second quaternion to subtract.
    Quaternion result

    When the method completes, contains the difference of the two quaternions.

    ToArray()

    Creates an array containing the elements of the quaternion.

    public float[] ToArray()
    Returns
    Type Description
    System.Single[]

    A four-element array containing the components of the quaternion.

    ToString()

    Returns a System.String that represents this instance.

    public override string ToString()
    Returns
    Type Description
    System.String

    A System.String that represents this instance.
    Overrides
    System.ValueType.ToString()

    ToString(IFormatProvider)

    Returns a System.String that represents this instance.

    public string ToString(IFormatProvider formatProvider)
    Parameters
    Type Name Description
    System.IFormatProvider formatProvider

    The format provider.
    Returns
    Type Description
    System.String

    A System.String that represents this instance.

    ToString(String)

    Returns a System.String that represents this instance.

    public string ToString(string format)
    Parameters
    Type Name Description
    System.String format

    The format.
    Returns
    Type Description
    System.String

    A System.String that represents this instance.

    ToString(String, IFormatProvider)

    Returns a System.String that represents this instance.

    public string ToString(string format, IFormatProvider formatProvider)
    Parameters
    Type Name Description
    System.String format

    The format.
    System.IFormatProvider formatProvider

    The format provider.
    Returns
    Type Description
    System.String

    A System.String that represents this instance.
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    Operators

    Addition(Quaternion, Quaternion)

    Adds two quaternions.

    public static Quaternion operator +(Quaternion left, Quaternion right)
    Parameters
    Type Name Description
    Quaternion left

    The first quaternion to add.
    Quaternion right

    The second quaternion to add.
    Returns
    Type Description
    Quaternion

    The sum of the two quaternions.

    Equality(Quaternion, Quaternion)

    Tests for equality between two objects.

    public static bool operator ==(Quaternion left, Quaternion right)
    Parameters
    Type Name Description
    Quaternion left

    The first value to compare.
    Quaternion right

    The second value to compare.
    Returns
    Type Description
    System.Boolean

    true if left has the same value as right; otherwise, false.

    Inequality(Quaternion, Quaternion)

    Tests for inequality between two objects.

    public static bool operator !=(Quaternion left, Quaternion right)
    Parameters
    Type Name Description
    Quaternion left

    The first value to compare.
    Quaternion right

    The second value to compare.
    Returns
    Type Description
    System.Boolean

    true if left has a different value than right; otherwise, false.

    Multiply(Quaternion, Quaternion)

    Multiplies a quaternion by another.

    public static Quaternion operator *(Quaternion left, Quaternion right)
    Parameters
    Type Name Description
    Quaternion left

    The first quaternion to multiply.
    Quaternion right

    The second quaternion to multiply.
    Returns
    Type Description
    Quaternion

    The multiplied quaternion.

    Multiply(Quaternion, Single)

    Scales a quaternion by the given value.

    public static Quaternion operator *(Quaternion value, float scale)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to scale.
    System.Single scale

    The amount by which to scale the quaternion.
    Returns
    Type Description
    Quaternion

    The scaled quaternion.

    Multiply(Single, Quaternion)

    Scales a quaternion by the given value.

    public static Quaternion operator *(float scale, Quaternion value)
    Parameters
    Type Name Description
    System.Single scale

    The amount by which to scale the quaternion.
    Quaternion value

    The quaternion to scale.
    Returns
    Type Description
    Quaternion

    The scaled quaternion.

    Subtraction(Quaternion, Quaternion)

    Subtracts two quaternions.

    public static Quaternion operator -(Quaternion left, Quaternion right)
    Parameters
    Type Name Description
    Quaternion left

    The first quaternion to subtract.
    Quaternion right

    The second quaternion to subtract.
    Returns
    Type Description
    Quaternion

    The difference of the two quaternions.

    UnaryNegation(Quaternion)

    Reverses the direction of a given quaternion.

    public static Quaternion operator -(Quaternion value)
    Parameters
    Type Name Description
    Quaternion value

    The quaternion to negate.
    Returns
    Type Description
    Quaternion

    A quaternion facing in the opposite direction.

    Extension Methods