Struct Quaterniond

Represents a double-precision Quaternion.

Implements

IEquatable<Quaterniond>

IFormattable

Inherited Members

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Namespace: OpenTK.Mathematics

Assembly: OpenTK.Mathematics.dll

Syntax

[Serializable]
public struct Quaterniond : IEquatable<Quaterniond>, IFormattable

Constructors

Quaterniond(Vector3d)

Initializes a new instance of the Quaterniond struct from given Euler angles in radians.

Declaration

public Quaterniond(Vector3d eulerAngles)

Parameters

Type	Name	Description
Vector3d	eulerAngles	The euler angles as a Vector3d.

Quaterniond(Vector3d, double)

Initializes a new instance of the Quaterniond struct.

Declaration

public Quaterniond(Vector3d v, double w)

Parameters

Type	Name	Description
Vector3d	v	The vector part.
double	w	The w part.

Quaterniond(double, double, double)

Initializes a new instance of the Quaterniond struct from given Euler angles in radians.

Declaration

public Quaterniond(double pitch, double yaw, double roll)

Parameters

Type	Name	Description
double	pitch	The pitch (attitude), rotation around X axis.
double	yaw	The yaw (heading), rotation around Y axis.
double	roll	The roll (bank), rotation around Z axis.

Quaterniond(double, double, double, double)

Initializes a new instance of the Quaterniond struct.

Declaration

public Quaterniond(double x, double y, double z, double w)

Parameters

Type	Name	Description
double	x	The x component.
double	y	The y component.
double	z	The z component.
double	w	The w component.

Fields

Identity

Defines the identity quaternion.

Declaration

public static readonly Quaterniond Identity

Field Value

Type	Description
Quaterniond

W

The W component of this instance.

Declaration

public double W

Field Value

Type	Description
double

Xyz

The X, Y and Z components of this instance.

Declaration

public Vector3d Xyz

Field Value

Type	Description
Vector3d

Properties

Length

Gets the length (magnitude) of the Quaterniond.

Declaration

public readonly double Length { get; }

Property Value

Type	Description
double

See Also

LengthSquared

LengthSquared

Gets the square of the Quaterniond length (magnitude).

Declaration

public readonly double LengthSquared { get; }

Property Value

Type	Description
double

X

Gets or sets the X component of this instance.

Declaration

public double X { readonly get; set; }

Property Value

Type	Description
double

Y

Gets or sets the Y component of this instance.

Declaration

public double Y { readonly get; set; }

Property Value

Type	Description
double

Z

Gets or sets the Z component of this instance.

Declaration

public double Z { readonly get; set; }

Property Value

Type	Description
double

Methods

Add(Quaterniond, Quaterniond)

Add two quaternions.

Declaration

[Pure]
public static Quaterniond Add(Quaterniond left, Quaterniond right)

Parameters

Type	Name	Description
Quaterniond	left	The first operand.
Quaterniond	right	The second operand.

Returns

Type	Description
Quaterniond	The result of the addition.

Add(in Quaterniond, in Quaterniond, out Quaterniond)

Add two quaternions.

Declaration

public static void Add(in Quaterniond left, in Quaterniond right, out Quaterniond result)

Parameters

Type	Name	Description
Quaterniond	left	The first operand.
Quaterniond	right	The second operand.
Quaterniond	result	The result of the addition.

Conjugate()

Inverts the Vector3d component of this Quaterniond.

Declaration

public void Conjugate()

Conjugate(Quaterniond)

Get the conjugate of the given Quaterniond.

Declaration

[Pure]
public static Quaterniond Conjugate(Quaterniond q)

Parameters

Type	Name	Description
Quaterniond	q	The Quaterniond.

Returns

Type	Description
Quaterniond	The conjugate of the given Quaterniond.

Conjugate(in Quaterniond, out Quaterniond)

Get the conjugate of the given Quaterniond.

Declaration

public static void Conjugate(in Quaterniond q, out Quaterniond result)

Parameters

Type	Name	Description
Quaterniond	q	The Quaterniond.
Quaterniond	result	The conjugate of the given Quaterniond.

Equals(Quaterniond)

Indicates whether the current object is equal to another object of the same type.

Declaration

public readonly bool Equals(Quaterniond other)

Parameters

Type	Name	Description
Quaterniond	other	An object to compare with this object.

Returns

Type	Description
bool	true if the current object is equal to the other parameter; otherwise, false.

Equals(object)

Indicates whether this instance and a specified object are equal.

Declaration

public override readonly bool Equals(object obj)

Parameters

Type	Name	Description
object	obj	The object to compare with the current instance.

Returns

Type	Description
bool	true if obj and this instance are the same type and represent the same value; otherwise, false.

Overrides

ValueType.Equals(object)

FromAxisAngle(Vector3d, double)

Build a Quaterniond from the given axis and angle.

Declaration

[Pure]
public static Quaterniond FromAxisAngle(Vector3d axis, double angle)

Parameters

Type	Name	Description
Vector3d	axis	The axis to rotate about.
double	angle	The rotation angle in radians.

Returns

Type	Description
Quaterniond	The quaternion.

FromEulerAngles(Vector3d)

Builds a Quaterniond from the given euler angles.

Declaration

[Pure]
public static Quaterniond FromEulerAngles(Vector3d eulerAngles)

Parameters

Type	Name	Description
Vector3d	eulerAngles	The euler angles as a vector.

Returns

Type	Description
Quaterniond	The equivalent Quaterniond.

FromEulerAngles(in Vector3d, out Quaterniond)

Builds a Quaterniond from the given euler angles.

Declaration

public static void FromEulerAngles(in Vector3d eulerAngles, out Quaterniond result)

Parameters

Type	Name	Description
Vector3d	eulerAngles	The euler angles as a vector.
Quaterniond	result	The equivalent Quaterniond.

FromEulerAngles(double, double, double)

Builds a Quaterniond from the given euler angles.

Declaration

[Pure]
public static Quaterniond FromEulerAngles(double pitch, double yaw, double roll)

Parameters

Type	Name	Description
double	pitch	The pitch (attitude), rotation around X axis.
double	yaw	The yaw (heading), rotation around Y axis.
double	roll	The roll (bank), rotation around Z axis.

Returns

Type	Description
Quaterniond	The quaternion.

FromMatrix(Matrix3d)

Builds a quaternion from the given rotation matrix.

Declaration

[Pure]
public static Quaterniond FromMatrix(Matrix3d matrix)

Parameters

Type	Name	Description
Matrix3d	matrix	A rotation matrix.

Returns

Type	Description
Quaterniond	The equivalent quaternion.

FromMatrix(in Matrix3d, out Quaterniond)

Builds a quaternion from the given rotation matrix.

Declaration

public static void FromMatrix(in Matrix3d matrix, out Quaterniond result)

Parameters

Type	Name	Description
Matrix3d	matrix	A rotation matrix.
Quaterniond	result	The equivalent quaternion.

GetHashCode()

Returns the hash code for this instance.

Declaration

public override readonly int GetHashCode()

Returns

Type	Description
int	A 32-bit signed integer that is the hash code for this instance.

Overrides

ValueType.GetHashCode()

Invert()

Inverts this Quaterniond.

Declaration

public void Invert()

Invert(Quaterniond)

Get the inverse of the given Quaterniond.

Declaration

[Pure]
public static Quaterniond Invert(Quaterniond q)

Parameters

Type	Name	Description
Quaterniond	q	The Quaterniond to invert.

Returns

Type	Description
Quaterniond	The inverse of the given Quaterniond.

Invert(in Quaterniond, out Quaterniond)

Get the inverse of the given Quaterniond.

Declaration

public static void Invert(in Quaterniond q, out Quaterniond result)

Parameters

Type	Name	Description
Quaterniond	q	The Quaterniond to invert.
Quaterniond	result	The inverse of the given Quaterniond.

Inverted()

Returns the inverse of this Quaterniond.

Declaration

public readonly Quaterniond Inverted()

Returns

Type	Description
Quaterniond	The inverted copy.

Multiply(Quaterniond, Quaterniond)

Multiplies two instances.

Declaration

[Pure]
public static Quaterniond Multiply(Quaterniond left, Quaterniond right)

Parameters

Type	Name	Description
Quaterniond	left	The first instance.
Quaterniond	right	The second instance.

Returns

Type	Description
Quaterniond	A new instance containing the result of the calculation.

Multiply(Quaterniond, double)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Quaterniond Multiply(Quaterniond quaternion, double scale)

Parameters

Type	Name	Description
Quaterniond	quaternion	The instance.
double	scale	The scalar.

Returns

Type	Description
Quaterniond	A new instance containing the result of the calculation.

Multiply(in Quaterniond, in Quaterniond, out Quaterniond)

Multiplies two instances.

Declaration

public static void Multiply(in Quaterniond left, in Quaterniond right, out Quaterniond result)

Parameters

Type	Name	Description
Quaterniond	left	The first instance.
Quaterniond	right	The second instance.
Quaterniond	result	A new instance containing the result of the calculation.

Multiply(in Quaterniond, double, out Quaterniond)

Multiplies an instance by a scalar.

Declaration

public static void Multiply(in Quaterniond quaternion, double scale, out Quaterniond result)

Parameters

Type	Name	Description
Quaterniond	quaternion	The instance.
double	scale	The scalar.
Quaterniond	result	A new instance containing the result of the calculation.

Normalize()

Scales the Quaterniond to unit length.

Declaration

public void Normalize()

Normalize(Quaterniond)

Scale the given Quaterniond to unit length.

Declaration

[Pure]
public static Quaterniond Normalize(Quaterniond q)

Parameters

Type	Name	Description
Quaterniond	q	The Quaterniond to normalize.

Returns

Type	Description
Quaterniond	The normalized copy.

Normalize(in Quaterniond, out Quaterniond)

Scale the given Quaterniond to unit length.

Declaration

public static void Normalize(in Quaterniond q, out Quaterniond result)

Parameters

Type	Name	Description
Quaterniond	q	The Quaterniond to normalize.
Quaterniond	result	The normalized Quaterniond.

Normalized()

Returns a copy of the Quaterniond scaled to unit length.

Declaration

public readonly Quaterniond Normalized()

Returns

Type	Description
Quaterniond	The normalized copy.

Slerp(Quaterniond, Quaterniond, double)

Do Spherical linear interpolation between two quaternions.

Declaration

[Pure]
public static Quaterniond Slerp(Quaterniond q1, Quaterniond q2, double blend)

Parameters

Type	Name	Description
Quaterniond	q1	The first Quaterniond.
Quaterniond	q2	The second Quaterniond.
double	blend	The blend factor.

Returns

Type	Description
Quaterniond	A smooth blend between the given quaternions.

Sub(Quaterniond, Quaterniond)

Subtracts two instances.

Declaration

[Pure]
public static Quaterniond Sub(Quaterniond left, Quaterniond right)

Parameters

Type	Name	Description
Quaterniond	left	The left instance.
Quaterniond	right	The right instance.

Returns

Type	Description
Quaterniond	The result of the operation.

Sub(in Quaterniond, in Quaterniond, out Quaterniond)

Subtracts two instances.

Declaration

public static void Sub(in Quaterniond left, in Quaterniond right, out Quaterniond result)

Parameters

Type	Name	Description
Quaterniond	left	The left instance.
Quaterniond	right	The right instance.
Quaterniond	result	The result of the operation.

ToAxisAngle()

Convert this instance to an axis-angle representation.

Declaration

public Vector4d ToAxisAngle()

Returns

Type	Description
Vector4d	A Vector4 that is the axis-angle representation of this quaternion.

ToAxisAngle(out Vector3d, out double)

Convert the current quaternion to axis angle representation.

Declaration

public void ToAxisAngle(out Vector3d axis, out double angle)

Parameters

Type	Name	Description
Vector3d	axis	The resultant axis.
double	angle	The resultant angle.

ToEulerAngles()

Convert this instance to an Euler angle representation.

Declaration

public readonly Vector3d ToEulerAngles()

Returns

Type	Description
Vector3d	The Euler angles in radians.

ToEulerAngles(in Quaterniond, out Vector3d)

Converts a quaternion to it's euler angle representation.

Declaration

public static void ToEulerAngles(in Quaterniond q, out Vector3d result)

Parameters

Type	Name	Description
Quaterniond	q	The Quaternion.
Vector3d	result	The resulting euler angles in radians.

ToEulerAngles(out Vector3d)

Convert the current quaternion to Euler angle representation.

Declaration

public readonly void ToEulerAngles(out Vector3d angles)

Parameters

Type	Name	Description
Vector3d	angles	The Euler angles in radians.

ToString()

Returns a System.String that represents the current Quaterniond.

Declaration

public override readonly string ToString()

Returns

Type	Description
string	A human-readable representation of the quaternion.

Overrides

ValueType.ToString()

ToString(IFormatProvider)

Formats the value of the current instance using the specified format.

Declaration

public readonly string ToString(IFormatProvider formatProvider)

Parameters

Type	Name	Description
IFormatProvider	formatProvider	The provider to use to format the value. -or- A null reference (Nothing in Visual Basic) to obtain the numeric format information from the current locale setting of the operating system.

Returns

Type	Description
string	The value of the current instance in the specified format.

ToString(string)

Formats the value of the current instance using the specified format.

Declaration

public readonly string ToString(string format)

Parameters

Type	Name	Description
string	format	The format to use. -or- A null reference (Nothing in Visual Basic) to use the default format defined for the type of the IFormattable implementation.

Returns

Type	Description
string	The value of the current instance in the specified format.

ToString(string, IFormatProvider)

Formats the value of the current instance using the specified format.

Declaration

public readonly string ToString(string format, IFormatProvider formatProvider)

Parameters

Type	Name	Description
string	format	The format to use. -or- A null reference (Nothing in Visual Basic) to use the default format defined for the type of the IFormattable implementation.
IFormatProvider	formatProvider	The provider to use to format the value. -or- A null reference (Nothing in Visual Basic) to obtain the numeric format information from the current locale setting of the operating system.

Returns

Type	Description
string	The value of the current instance in the specified format.

Operators

operator +(Quaterniond, Quaterniond)

Adds two instances.

Declaration

[Pure]
public static Quaterniond operator +(Quaterniond left, Quaterniond right)

Parameters

Type	Name	Description
Quaterniond	left	The first instance.
Quaterniond	right	The second instance.

Returns

Type	Description
Quaterniond	The result of the calculation.

operator ==(Quaterniond, Quaterniond)

Compares two instances for equality.

Declaration

public static bool operator ==(Quaterniond left, Quaterniond right)

Parameters

Type	Name	Description
Quaterniond	left	The first instance.
Quaterniond	right	The second instance.

Returns

Type	Description
bool	True, if left equals right; false otherwise.

operator !=(Quaterniond, Quaterniond)

Compares two instances for inequality.

Declaration

public static bool operator !=(Quaterniond left, Quaterniond right)

Parameters

Type	Name	Description
Quaterniond	left	The first instance.
Quaterniond	right	The second instance.

Returns

Type	Description
bool	True, if left does not equal right; false otherwise.

operator *(Quaterniond, Quaterniond)

Multiplies two instances.

Declaration

[Pure]
public static Quaterniond operator *(Quaterniond left, Quaterniond right)

Parameters

Type	Name	Description
Quaterniond	left	The first instance.
Quaterniond	right	The second instance.

Returns

Type	Description
Quaterniond	The result of the calculation.

operator *(Quaterniond, double)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Quaterniond operator *(Quaterniond quaternion, double scale)

Parameters

Type	Name	Description
Quaterniond	quaternion	The instance.
double	scale	The scalar.

Returns

Type	Description
Quaterniond	A new instance containing the result of the calculation.

operator *(double, Quaterniond)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Quaterniond operator *(double scale, Quaterniond quaternion)

Parameters

Type	Name	Description
double	scale	The scalar.
Quaterniond	quaternion	The instance.

Returns

Type	Description
Quaterniond	A new instance containing the result of the calculation.

operator -(Quaterniond, Quaterniond)

Subtracts two instances.

Declaration

[Pure]
public static Quaterniond operator -(Quaterniond left, Quaterniond right)

Parameters

Type	Name	Description
Quaterniond	left	The first instance.
Quaterniond	right	The second instance.

Returns

Type	Description
Quaterniond	The result of the calculation.

Implements

IEquatable<T>

IFormattable